task_name,problem_type,instruction,instance,solution,obj,instance_variant,solution_variant,context_index,input_format,input_index_base
QSPP,QSPP,"I work as the dispatcher planning a single run from pickup to delivery, thinking of the city as a set of intersections and one-way streets. The job is to pick one continuous route that starts at the pickup spot and ends at the drop-off, following only the allowed one-way streets. Every street taken has a normal charge and also its own little extra fee just for being used, and whenever two streets both end up on the route there can be additional combination charges — those combo fees can even depend on direction, and if both directions between a pair matter they both get added. The best route is simply the one that makes the total bill (all the street charges plus each street’s extra fee and all the pairwise combo fees for every pair of streets included) as small as possible. The final plan should be shown as a straight list of place names from pickup to delivery, with each step actually being a legal one-way move and nothing skipped or listed twice. The concrete map and numbers are shown below.

{
  ""intersection_count"": 9,
  ""directed_street_count"": 12,
  ""intersections"": [
    1,
    2,
    3,
    4,
    5,
    6,
    7,
    8,
    9
  ],
  ""pickup_location"": 1,
  ""delivery_location"": 9,
  ""edges"": [
    {
      ""segment_start_intersection"": 1,
      ""segment_end_intersection"": 2,
      ""segment_id"": 0
    },
    {
      ""segment_start_intersection"": 1,
      ""segment_end_intersection"": 4,
      ""segment_id"": 1
    },
    {
      ""segment_start_intersection"": 2,
      ""segment_end_intersection"": 3,
      ""segment_id"": 2
    },
    {
      ""segment_start_intersection"": 2,
      ""segment_end_intersection"": 5,
      ""segment_id"": 3
    },
    {
      ""segment_start_intersection"": 3,
      ""segment_end_intersection"": 6,
      ""segment_id"": 4
    },
    {
      ""segment_start_intersection"": 4,
      ""segment_end_intersection"": 5,
      ""segment_id"": 5
    },
    {
      ""segment_start_intersection"": 4,
      ""segment_end_intersection"": 7,
      ""segment_id"": 6
    },
    {
      ""segment_start_intersection"": 5,
      ""segment_end_intersection"": 6,
      ""segment_id"": 7
    },
    {
      ""segment_start_intersection"": 5,
      ""segment_end_intersection"": 8,
      ""segment_id"": 8
    },
    {
      ""segment_start_intersection"": 6,
      ""segment_end_intersection"": 9,
      ""segment_id"": 9
    },
    {
      ""segment_start_intersection"": 7,
      ""segment_end_intersection"": 8,
      ""segment_id"": 10
    },
    {
      ""segment_start_intersection"": 8,
      ""segment_end_intersection"": 9,
      ""segment_id"": 11
    }
  ],
  ""linear_costs"": [
    {
      ""segment_id"": 0,
      ""segment_base_charge"": 1.0
    },
    {
      ""segment_id"": 1,
      ""segment_base_charge"": 5.0
    },
    {
      ""segment_id"": 2,
      ""segment_base_charge"": 6.0
    },
    {
      ""segment_id"": 3,
      ""segment_base_charge"": 9.0
    },
    {
      ""segment_id"": 4,
      ""segment_base_charge"": 8.0
    },
    {
      ""segment_id"": 5,
      ""segment_base_charge"": 10.0
    },
    {
      ""segment_id"": 6,
      ""segment_base_charge"": 1.0
    },
    {
      ""segment_id"": 7,
      ""segment_base_charge"": 8.0
    },
    {
      ""segment_id"": 8,
      ""segment_base_charge"": 5.0
    },
    {
      ""segment_id"": 9,
      ""segment_base_charge"": 4.0
    },
    {
      ""segment_id"": 10,
      ""segment_base_charge"": 9.0
    },
    {
      ""segment_id"": 11,
      ""segment_base_charge"": 3.0
    }
  ]
}

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (segment_i_id, segment_j_id). If two segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| segment_i_id\segment_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 2.0 | 7.0 | 9.0 | 7.0 | 9.0 | 9.0 | 10.0 | 5.0 | 7.0 | 4.0 | 10.0 | 7.0 |
| 1 | 7.0 | 9.0 | 10.0 | 7.0 | 5.0 | 10.0 | 1.0 | 9.0 | 2.0 | 1.0 | 3.0 | 7.0 |
| 2 | 9.0 | 10.0 | 8.0 | 6.0 | 2.0 | 9.0 | 5.0 | 9.0 | 1.0 | 8.0 | 8.0 | 9.0 |
| 3 | 7.0 | 7.0 | 6.0 | 9.0 | 9.0 | 7.0 | 10.0 | 6.0 | 7.0 | 7.0 | 10.0 | 4.0 |
| 4 | 9.0 | 5.0 | 2.0 | 9.0 | 9.0 | 4.0 | 6.0 | 8.0 | 2.0 | 4.0 | 9.0 | 10.0 |
| 5 | 9.0 | 10.0 | 9.0 | 7.0 | 4.0 | 4.0 | 3.0 | 10.0 | 2.0 | 6.0 | 7.0 | 8.0 |
| 6 | 10.0 | 1.0 | 5.0 | 10.0 | 6.0 | 3.0 | 5.0 | 1.0 | 4.0 | 5.0 | 3.0 | 1.0 |
| 7 | 5.0 | 9.0 | 9.0 | 6.0 | 8.0 | 10.0 | 1.0 | 9.0 | 3.0 | 6.0 | 8.0 | 1.0 |
| 8 | 7.0 | 2.0 | 1.0 | 7.0 | 2.0 | 2.0 | 4.0 | 3.0 | 9.0 | 5.0 | 5.0 | 9.0 |
| 9 | 4.0 | 1.0 | 8.0 | 7.0 | 4.0 | 6.0 | 5.0 | 6.0 | 5.0 | 8.0 | 10.0 | 5.0 |
| 10 | 10.0 | 3.0 | 8.0 | 10.0 | 9.0 | 7.0 | 3.0 | 8.0 | 5.0 | 10.0 | 1.0 | 3.0 |
| 11 | 7.0 | 7.0 | 9.0 | 4.0 | 10.0 | 8.0 | 1.0 | 1.0 | 9.0 | 5.0 | 3.0 | 2.0 |

And when you send the final route back, please stick it in a tiny JSON box so it's easy to read and parse. Something like this is exactly the shape I expect:

{
  ""solution"": []
}

Think of that ""solution"" array as where you'll list the sequence of place names (node identifiers) from pickup to drop-off, in order — each step is a real one-way move on the map. This JSON is just a sketch of the shape I need, not the actual answer itself.

Quick reminder: use the node identifiers exactly as they appear in the instance input — don't rename them or invent new labels. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'name': 'Rostami_Grid1_k3_seedNone', 'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8], 'edges': [{'from': 0, 'to': 1, 'var_index': 0}, {'from': 0, 'to': 3, 'var_index': 1}, {'from': 1, 'to': 2, 'var_index': 2}, {'from': 1, 'to': 4, 'var_index': 3}, {'from': 2, 'to': 5, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 3, 'to': 6, 'var_index': 6}, {'from': 4, 'to': 5, 'var_index': 7}, {'from': 4, 'to': 7, 'var_index': 8}, {'from': 5, 'to': 8, 'var_index': 9}, {'from': 6, 'to': 7, 'var_index': 10}, {'from': 7, 'to': 8, 'var_index': 11}], 'objective': {'constant': 0.0, 'linear': [1.0, 5.0, 6.0, 9.0, 8.0, 10.0, 1.0, 8.0, 5.0, 4.0, 9.0, 3.0], 'quadratic': [[2.0, 7.0, 9.0, 7.0, 9.0, 9.0, 10.0, 5.0, 7.0, 4.0, 10.0, 7.0], [7.0, 9.0, 10.0, 7.0, 5.0, 10.0, 1.0, 9.0, 2.0, 1.0, 3.0, 7.0], [9.0, 10.0, 8.0, 6.0, 2.0, 9.0, 5.0, 9.0, 1.0, 8.0, 8.0, 9.0], [7.0, 7.0, 6.0, 9.0, 9.0, 7.0, 10.0, 6.0, 7.0, 7.0, 10.0, 4.0], [9.0, 5.0, 2.0, 9.0, 9.0, 4.0, 6.0, 8.0, 2.0, 4.0, 9.0, 10.0], [9.0, 10.0, 9.0, 7.0, 4.0, 4.0, 3.0, 10.0, 2.0, 6.0, 7.0, 8.0], [10.0, 1.0, 5.0, 10.0, 6.0, 3.0, 5.0, 1.0, 4.0, 5.0, 3.0, 1.0], [5.0, 9.0, 9.0, 6.0, 8.0, 10.0, 1.0, 9.0, 3.0, 6.0, 8.0, 1.0], [7.0, 2.0, 1.0, 7.0, 2.0, 2.0, 4.0, 3.0, 9.0, 5.0, 5.0, 9.0], [4.0, 1.0, 8.0, 7.0, 4.0, 6.0, 5.0, 6.0, 5.0, 8.0, 10.0, 5.0], [10.0, 3.0, 8.0, 10.0, 9.0, 7.0, 3.0, 8.0, 5.0, 10.0, 1.0, 3.0], [7.0, 7.0, 9.0, 4.0, 10.0, 8.0, 1.0, 1.0, 9.0, 5.0, 3.0, 2.0]]}, 'source': 0, 'target': 8}","[0, 3, 6, 7, 8]",71.0,"{'problem_type': 'QSPP', 'num_nodes': 9, 'num_edges': 12, 'nodes': [1, 2, 3, 4, 5, 6, 7, 8, 9], 'source': 1, 'target': 9, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 1.0}, {'var_index': 1, 'linear_cost': 5.0}, {'var_index': 2, 'linear_cost': 6.0}, {'var_index': 3, 'linear_cost': 9.0}, {'var_index': 4, 'linear_cost': 8.0}, {'var_index': 5, 'linear_cost': 10.0}, {'var_index': 6, 'linear_cost': 1.0}, {'var_index': 7, 'linear_cost': 8.0}, {'var_index': 8, 'linear_cost': 5.0}, {'var_index': 9, 'linear_cost': 4.0}, {'var_index': 10, 'linear_cost': 9.0}, {'var_index': 11, 'linear_cost': 3.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 7, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 7, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 7, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 8, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 8, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 8, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 8, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 8, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 9, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 9, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 9, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 9, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 9, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 9, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 9, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 9, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 10, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 10, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 10, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 10, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 10, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 10, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 10, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 11, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 11, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 11, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 11, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 11, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 11, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 11, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 11, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 11, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 11, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 11, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 11, 'var_j': 11, 'quadratic_cost': 2.0}]}, 'edges': [{'from': 1, 'to': 2, 'var_index': 0}, {'from': 1, 'to': 4, 'var_index': 1}, {'from': 2, 'to': 3, 'var_index': 2}, {'from': 2, 'to': 5, 'var_index': 3}, {'from': 3, 'to': 6, 'var_index': 4}, {'from': 4, 'to': 5, 'var_index': 5}, {'from': 4, 'to': 7, 'var_index': 6}, {'from': 5, 'to': 6, 'var_index': 7}, {'from': 5, 'to': 8, 'var_index': 8}, {'from': 6, 'to': 9, 'var_index': 9}, {'from': 7, 'to': 8, 'var_index': 10}, {'from': 8, 'to': 9, 'var_index': 11}], 'node_id_map': {0: 1, 1: 2, 2: 3, 3: 4, 4: 5, 5: 6, 6: 7, 7: 8, 8: 9}}","[1, 4, 7, 8, 9]",1,json,1
QSPP,QSPP,"On a busy morning the trail crew wanted one clean, one-directional route from the trailhead to the overlook that sticks to the marked directional paths. Each trail segment takes a certain amount of effort, some segments also carry a little extra surcharge just for taking them, and some pairs of segments create extra penalties when both are used — with the size (and sometimes the direction) of that penalty depending on which segment comes first. So the task is to pick the single continuous list of places that, when summing all the segment efforts, individual surcharges, and pair penalties, comes out with the lowest total. The map and the exact effort and penalty figures are shown below, and the final path should be the ordered sequence of locations from the trailhead to the overlook with every step legally following a one-way trail.

# num_locations=8
# num_trail_segments=17
# location_ids=A, B, C, D, E, F, G, H
# trailhead_location=G
# overlook_location=H

segment_start_location,segment_end_location,segment_id
G,A,0
G,B,1
G,C,2
G,D,3
G,E,4
G,F,5
A,H,6
B,H,7
C,H,8
D,H,9
E,H,10
F,H,11
A,B,12
B,C,13
C,D,14
D,E,15
E,F,16

segment_id,base_effort
0,3.0
1,5.0
2,7.0
3,10.0
4,9.0
5,10.0
6,10.0
7,8.0
8,3.0
9,1.0
10,6.0
11,3.0
12,9.0
13,9.0
14,1.0
15,8.0
16,8.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (segment_i_id, segment_j_id). If two segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| segment_i_id\segment_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 2.0 | 1.0 | 6.0 | 6.0 | 9.0 | 3.0 | 5.0 | 2.0 | 4.0 | 8.0 | 2.0 | 1.0 | 9.0 | 5.0 | 2.0 | 9.0 | 9.0 |
| 1 | 1.0 | 6.0 | 9.0 | 10.0 | 1.0 | 7.0 | 10.0 | 2.0 | 8.0 | 10.0 | 4.0 | 8.0 | 8.0 | 9.0 | 2.0 | 4.0 | 2.0 |
| 2 | 6.0 | 9.0 | 1.0 | 4.0 | 8.0 | 6.0 | 3.0 | 1.0 | 6.0 | 4.0 | 6.0 | 5.0 | 4.0 | 3.0 | 9.0 | 8.0 | 1.0 |
| 3 | 6.0 | 10.0 | 4.0 | 9.0 | 1.0 | 1.0 | 3.0 | 1.0 | 7.0 | 8.0 | 7.0 | 2.0 | 5.0 | 8.0 | 6.0 | 3.0 | 6.0 |
| 4 | 9.0 | 1.0 | 8.0 | 1.0 | 9.0 | 9.0 | 5.0 | 6.0 | 8.0 | 9.0 | 8.0 | 4.0 | 8.0 | 9.0 | 4.0 | 9.0 | 1.0 |
| 5 | 3.0 | 7.0 | 6.0 | 1.0 | 9.0 | 7.0 | 4.0 | 8.0 | 9.0 | 4.0 | 10.0 | 8.0 | 3.0 | 3.0 | 9.0 | 5.0 | 7.0 |
| 6 | 5.0 | 10.0 | 3.0 | 3.0 | 5.0 | 4.0 | 5.0 | 5.0 | 3.0 | 8.0 | 4.0 | 1.0 | 7.0 | 6.0 | 10.0 | 1.0 | 6.0 |
| 7 | 2.0 | 2.0 | 1.0 | 1.0 | 6.0 | 8.0 | 5.0 | 10.0 | 5.0 | 1.0 | 6.0 | 2.0 | 7.0 | 6.0 | 2.0 | 1.0 | 8.0 |
| 8 | 4.0 | 8.0 | 6.0 | 7.0 | 8.0 | 9.0 | 3.0 | 5.0 | 2.0 | 9.0 | 7.0 | 7.0 | 9.0 | 9.0 | 4.0 | 7.0 | 9.0 |
| 9 | 8.0 | 10.0 | 4.0 | 8.0 | 9.0 | 4.0 | 8.0 | 1.0 | 9.0 | 7.0 | 5.0 | 8.0 | 10.0 | 8.0 | 9.0 | 7.0 | 7.0 |
| 10 | 2.0 | 4.0 | 6.0 | 7.0 | 8.0 | 10.0 | 4.0 | 6.0 | 7.0 | 5.0 | 7.0 | 6.0 | 2.0 | 10.0 | 4.0 | 5.0 | 2.0 |
| 11 | 1.0 | 8.0 | 5.0 | 2.0 | 4.0 | 8.0 | 1.0 | 2.0 | 7.0 | 8.0 | 6.0 | 9.0 | 7.0 | 6.0 | 8.0 | 6.0 | 2.0 |
| 12 | 9.0 | 8.0 | 4.0 | 5.0 | 8.0 | 3.0 | 7.0 | 7.0 | 9.0 | 10.0 | 2.0 | 7.0 | 10.0 | 4.0 | 3.0 | 7.0 | 2.0 |
| 13 | 5.0 | 9.0 | 3.0 | 8.0 | 9.0 | 3.0 | 6.0 | 6.0 | 9.0 | 8.0 | 10.0 | 6.0 | 4.0 | 9.0 | 9.0 | 6.0 | 2.0 |
| 14 | 2.0 | 2.0 | 9.0 | 6.0 | 4.0 | 9.0 | 10.0 | 2.0 | 4.0 | 9.0 | 4.0 | 8.0 | 3.0 | 9.0 | 6.0 | 7.0 | 7.0 |
| 15 | 9.0 | 4.0 | 8.0 | 3.0 | 9.0 | 5.0 | 1.0 | 1.0 | 7.0 | 7.0 | 5.0 | 6.0 | 7.0 | 6.0 | 7.0 | 7.0 | 1.0 |
| 16 | 9.0 | 2.0 | 1.0 | 6.0 | 1.0 | 7.0 | 6.0 | 8.0 | 9.0 | 7.0 | 2.0 | 2.0 | 2.0 | 2.0 | 7.0 | 1.0 | 7.0 |

Also, when you give the final route, please put it in a tiny JSON sketch like this so it's easy to parse:

{
  ""solution"": []
}

Here ""solution"" is where you list the ordered sequence of place names from the trailhead to the overlook — just the node identifiers, in order (no extra numbers or cost labels). Think of this as the simple form to fill out with the route; it's only showing the shape, not the actual answer.

Please use the exact identifiers shown in the map/input and don’t rename or invent labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7], 'edges': [{'from': 6, 'to': 0, 'var_index': 0}, {'from': 6, 'to': 1, 'var_index': 1}, {'from': 6, 'to': 2, 'var_index': 2}, {'from': 6, 'to': 3, 'var_index': 3}, {'from': 6, 'to': 4, 'var_index': 4}, {'from': 6, 'to': 5, 'var_index': 5}, {'from': 0, 'to': 7, 'var_index': 6}, {'from': 1, 'to': 7, 'var_index': 7}, {'from': 2, 'to': 7, 'var_index': 8}, {'from': 3, 'to': 7, 'var_index': 9}, {'from': 4, 'to': 7, 'var_index': 10}, {'from': 5, 'to': 7, 'var_index': 11}, {'from': 0, 'to': 1, 'var_index': 12}, {'from': 1, 'to': 2, 'var_index': 13}, {'from': 2, 'to': 3, 'var_index': 14}, {'from': 3, 'to': 4, 'var_index': 15}, {'from': 4, 'to': 5, 'var_index': 16}], 'objective': {'constant': 0.0, 'linear': [3.0, 5.0, 7.0, 10.0, 9.0, 10.0, 10.0, 8.0, 3.0, 1.0, 6.0, 3.0, 9.0, 9.0, 1.0, 8.0, 8.0], 'quadratic': [[2.0, 1.0, 6.0, 6.0, 9.0, 3.0, 5.0, 2.0, 4.0, 8.0, 2.0, 1.0, 9.0, 5.0, 2.0, 9.0, 9.0], [1.0, 6.0, 9.0, 10.0, 1.0, 7.0, 10.0, 2.0, 8.0, 10.0, 4.0, 8.0, 8.0, 9.0, 2.0, 4.0, 2.0], [6.0, 9.0, 1.0, 4.0, 8.0, 6.0, 3.0, 1.0, 6.0, 4.0, 6.0, 5.0, 4.0, 3.0, 9.0, 8.0, 1.0], [6.0, 10.0, 4.0, 9.0, 1.0, 1.0, 3.0, 1.0, 7.0, 8.0, 7.0, 2.0, 5.0, 8.0, 6.0, 3.0, 6.0], [9.0, 1.0, 8.0, 1.0, 9.0, 9.0, 5.0, 6.0, 8.0, 9.0, 8.0, 4.0, 8.0, 9.0, 4.0, 9.0, 1.0], [3.0, 7.0, 6.0, 1.0, 9.0, 7.0, 4.0, 8.0, 9.0, 4.0, 10.0, 8.0, 3.0, 3.0, 9.0, 5.0, 7.0], [5.0, 10.0, 3.0, 3.0, 5.0, 4.0, 5.0, 5.0, 3.0, 8.0, 4.0, 1.0, 7.0, 6.0, 10.0, 1.0, 6.0], [2.0, 2.0, 1.0, 1.0, 6.0, 8.0, 5.0, 10.0, 5.0, 1.0, 6.0, 2.0, 7.0, 6.0, 2.0, 1.0, 8.0], [4.0, 8.0, 6.0, 7.0, 8.0, 9.0, 3.0, 5.0, 2.0, 9.0, 7.0, 7.0, 9.0, 9.0, 4.0, 7.0, 9.0], [8.0, 10.0, 4.0, 8.0, 9.0, 4.0, 8.0, 1.0, 9.0, 7.0, 5.0, 8.0, 10.0, 8.0, 9.0, 7.0, 7.0], [2.0, 4.0, 6.0, 7.0, 8.0, 10.0, 4.0, 6.0, 7.0, 5.0, 7.0, 6.0, 2.0, 10.0, 4.0, 5.0, 2.0], [1.0, 8.0, 5.0, 2.0, 4.0, 8.0, 1.0, 2.0, 7.0, 8.0, 6.0, 9.0, 7.0, 6.0, 8.0, 6.0, 2.0], [9.0, 8.0, 4.0, 5.0, 8.0, 3.0, 7.0, 7.0, 9.0, 10.0, 2.0, 7.0, 10.0, 4.0, 3.0, 7.0, 2.0], [5.0, 9.0, 3.0, 8.0, 9.0, 3.0, 6.0, 6.0, 9.0, 8.0, 10.0, 6.0, 4.0, 9.0, 9.0, 6.0, 2.0], [2.0, 2.0, 9.0, 6.0, 4.0, 9.0, 10.0, 2.0, 4.0, 9.0, 4.0, 8.0, 3.0, 9.0, 6.0, 7.0, 7.0], [9.0, 4.0, 8.0, 3.0, 9.0, 5.0, 1.0, 1.0, 7.0, 7.0, 5.0, 6.0, 7.0, 6.0, 7.0, 7.0, 1.0], [9.0, 2.0, 1.0, 6.0, 1.0, 7.0, 6.0, 8.0, 9.0, 7.0, 2.0, 2.0, 2.0, 2.0, 7.0, 1.0, 7.0]]}, 'source': 6, 'target': 7}","[6, 2, 7]",25.0,"{'problem_type': 'QSPP', 'num_nodes': 8, 'num_edges': 17, 'nodes': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H'], 'source': 'G', 'target': 'H', 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 3.0}, {'var_index': 1, 'linear_cost': 5.0}, {'var_index': 2, 'linear_cost': 7.0}, {'var_index': 3, 'linear_cost': 10.0}, {'var_index': 4, 'linear_cost': 9.0}, {'var_index': 5, 'linear_cost': 10.0}, {'var_index': 6, 'linear_cost': 10.0}, {'var_index': 7, 'linear_cost': 8.0}, {'var_index': 8, 'linear_cost': 3.0}, {'var_index': 9, 'linear_cost': 1.0}, {'var_index': 10, 'linear_cost': 6.0}, {'var_index': 11, 'linear_cost': 3.0}, {'var_index': 12, 'linear_cost': 9.0}, {'var_index': 13, 'linear_cost': 9.0}, {'var_index': 14, 'linear_cost': 1.0}, {'var_index': 15, 'linear_cost': 8.0}, {'var_index': 16, 'linear_cost': 8.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 13, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 14, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 15, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 14, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 15, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 12, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 15, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 16, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 15, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 16, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 14, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 15, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 16, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 15, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 16, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 14, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 15, 'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 16, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 14, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 15, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 16, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 8, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 8, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 14, 'quadratic_cost': 4.0}, {'var_i': 8, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 9, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 9, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 9, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 9, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 9, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 9, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 9, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 9, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 12, 'quadratic_cost': 10.0}, {'var_i': 9, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 9, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 9, 'var_j': 16, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 10, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 10, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 10, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 10, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 10, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 12, 'quadratic_cost': 2.0}, {'var_i': 10, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 10, 'var_j': 14, 'quadratic_cost': 4.0}, {'var_i': 10, 'var_j': 15, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 11, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 11, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 11, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 11, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 11, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 11, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 11, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 11, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 11, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 11, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 11, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 11, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 11, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 14, 'quadratic_cost': 8.0}, {'var_i': 11, 'var_j': 15, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 12, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 12, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 12, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 12, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 12, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 12, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 12, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 12, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 12, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 12, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 12, 'quadratic_cost': 10.0}, {'var_i': 12, 'var_j': 13, 'quadratic_cost': 4.0}, {'var_i': 12, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 12, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 13, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 13, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 13, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 13, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 13, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 13, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 13, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 13, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 13, 'var_j': 12, 'quadratic_cost': 4.0}, {'var_i': 13, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 13, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 13, 'var_j': 15, 'quadratic_cost': 6.0}, {'var_i': 13, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 14, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 14, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 14, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 14, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 14, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 14, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 14, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 14, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 14, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 14, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 14, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 14, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 14, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 14, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 14, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 14, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 14, 'var_j': 16, 'quadratic_cost': 7.0}, {'var_i': 15, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 15, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 15, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 15, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 15, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 15, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 15, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 15, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 15, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 15, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 15, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 15, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 15, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 15, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 15, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 15, 'var_j': 16, 'quadratic_cost': 1.0}, {'var_i': 16, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 16, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 16, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 16, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 16, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 16, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 16, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 16, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 16, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 16, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 16, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 16, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 16, 'var_j': 12, 'quadratic_cost': 2.0}, {'var_i': 16, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 16, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 16, 'var_j': 15, 'quadratic_cost': 1.0}, {'var_i': 16, 'var_j': 16, 'quadratic_cost': 7.0}]}, 'edges': [{'from': 'G', 'to': 'A', 'var_index': 0}, {'from': 'G', 'to': 'B', 'var_index': 1}, {'from': 'G', 'to': 'C', 'var_index': 2}, {'from': 'G', 'to': 'D', 'var_index': 3}, {'from': 'G', 'to': 'E', 'var_index': 4}, {'from': 'G', 'to': 'F', 'var_index': 5}, {'from': 'A', 'to': 'H', 'var_index': 6}, {'from': 'B', 'to': 'H', 'var_index': 7}, {'from': 'C', 'to': 'H', 'var_index': 8}, {'from': 'D', 'to': 'H', 'var_index': 9}, {'from': 'E', 'to': 'H', 'var_index': 10}, {'from': 'F', 'to': 'H', 'var_index': 11}, {'from': 'A', 'to': 'B', 'var_index': 12}, {'from': 'B', 'to': 'C', 'var_index': 13}, {'from': 'C', 'to': 'D', 'var_index': 14}, {'from': 'D', 'to': 'E', 'var_index': 15}, {'from': 'E', 'to': 'F', 'var_index': 16}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E', 5: 'F', 6: 'G', 7: 'H'}}","['G', 'C', 'H']",2,csv,names
QSPP,QSPP,"I’m looking at a router map and have to pick one single route from the start node to the end node that actually follows the arrows between routers. The “score” of a route is what happens when all the link delays are added up, plus any extra interference hits that appear whenever certain pairs of links are used together (and some links even carry a little extra hit just for being used). The better route is simply the one with the lowest total of those link delays and pairwise interference amounts. The route must be one continuous path from the source to the destination, each hop must be a real directed link, and the answer will be shown below with the concrete details.

{
  ""total_routers"": 10,
  ""total_links"": 14,
  ""router_ids"": [
    0,
    1,
    2,
    3,
    4,
    5,
    6,
    7,
    8,
    9
  ],
  ""start_router"": 8,
  ""end_router"": 9,
  ""edges"": [
    {
      ""link_from_router"": 8,
      ""link_to_router"": 0,
      ""link_id"": 0
    },
    {
      ""link_from_router"": 8,
      ""link_to_router"": 4,
      ""link_id"": 1
    },
    {
      ""link_from_router"": 3,
      ""link_to_router"": 9,
      ""link_id"": 2
    },
    {
      ""link_from_router"": 7,
      ""link_to_router"": 9,
      ""link_id"": 3
    },
    {
      ""link_from_router"": 0,
      ""link_to_router"": 1,
      ""link_id"": 4
    },
    {
      ""link_from_router"": 0,
      ""link_to_router"": 4,
      ""link_id"": 5
    },
    {
      ""link_from_router"": 1,
      ""link_to_router"": 2,
      ""link_id"": 6
    },
    {
      ""link_from_router"": 1,
      ""link_to_router"": 5,
      ""link_id"": 7
    },
    {
      ""link_from_router"": 2,
      ""link_to_router"": 3,
      ""link_id"": 8
    },
    {
      ""link_from_router"": 2,
      ""link_to_router"": 6,
      ""link_id"": 9
    },
    {
      ""link_from_router"": 3,
      ""link_to_router"": 7,
      ""link_id"": 10
    },
    {
      ""link_from_router"": 4,
      ""link_to_router"": 5,
      ""link_id"": 11
    },
    {
      ""link_from_router"": 5,
      ""link_to_router"": 6,
      ""link_id"": 12
    },
    {
      ""link_from_router"": 6,
      ""link_to_router"": 7,
      ""link_id"": 13
    }
  ],
  ""linear_costs"": [
    {
      ""link_id"": 0,
      ""per_link_latency"": 3.0
    },
    {
      ""link_id"": 1,
      ""per_link_latency"": 10.0
    },
    {
      ""link_id"": 2,
      ""per_link_latency"": 8.0
    },
    {
      ""link_id"": 3,
      ""per_link_latency"": 6.0
    },
    {
      ""link_id"": 4,
      ""per_link_latency"": 4.0
    },
    {
      ""link_id"": 5,
      ""per_link_latency"": 2.0
    },
    {
      ""link_id"": 6,
      ""per_link_latency"": 8.0
    },
    {
      ""link_id"": 7,
      ""per_link_latency"": 4.0
    },
    {
      ""link_id"": 8,
      ""per_link_latency"": 8.0
    },
    {
      ""link_id"": 9,
      ""per_link_latency"": 8.0
    },
    {
      ""link_id"": 10,
      ""per_link_latency"": 9.0
    },
    {
      ""link_id"": 11,
      ""per_link_latency"": 6.0
    },
    {
      ""link_id"": 12,
      ""per_link_latency"": 8.0
    },
    {
      ""link_id"": 13,
      ""per_link_latency"": 9.0
    }
  ]
}

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (link_i_id, link_j_id). If two links with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| link_i_id\link_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 4.0 | 6.0 | 8.0 | 7.0 | 1.0 | 5.0 | 4.0 | 10.0 | 10.0 | 6.0 | 8.0 | 5.0 | 1.0 | 4.0 |
| 1 | 6.0 | 4.0 | 4.0 | 10.0 | 9.0 | 7.0 | 1.0 | 9.0 | 8.0 | 10.0 | 10.0 | 2.0 | 8.0 | 7.0 |
| 2 | 8.0 | 4.0 | 5.0 | 3.0 | 1.0 | 3.0 | 2.0 | 1.0 | 10.0 | 5.0 | 3.0 | 9.0 | 10.0 | 1.0 |
| 3 | 7.0 | 10.0 | 3.0 | 1.0 | 1.0 | 7.0 | 9.0 | 8.0 | 5.0 | 2.0 | 6.0 | 9.0 | 10.0 | 3.0 |
| 4 | 1.0 | 9.0 | 1.0 | 1.0 | 7.0 | 6.0 | 3.0 | 1.0 | 7.0 | 3.0 | 9.0 | 4.0 | 8.0 | 10.0 |
| 5 | 5.0 | 7.0 | 3.0 | 7.0 | 6.0 | 10.0 | 2.0 | 1.0 | 3.0 | 2.0 | 8.0 | 4.0 | 2.0 | 1.0 |
| 6 | 4.0 | 1.0 | 2.0 | 9.0 | 3.0 | 2.0 | 3.0 | 3.0 | 7.0 | 5.0 | 5.0 | 2.0 | 1.0 | 5.0 |
| 7 | 10.0 | 9.0 | 1.0 | 8.0 | 1.0 | 1.0 | 3.0 | 2.0 | 3.0 | 10.0 | 9.0 | 8.0 | 2.0 | 1.0 |
| 8 | 10.0 | 8.0 | 10.0 | 5.0 | 7.0 | 3.0 | 7.0 | 3.0 | 5.0 | 4.0 | 10.0 | 6.0 | 9.0 | 10.0 |
| 9 | 6.0 | 10.0 | 5.0 | 2.0 | 3.0 | 2.0 | 5.0 | 10.0 | 4.0 | 6.0 | 5.0 | 9.0 | 3.0 | 7.0 |
| 10 | 8.0 | 10.0 | 3.0 | 6.0 | 9.0 | 8.0 | 5.0 | 9.0 | 10.0 | 5.0 | 5.0 | 4.0 | 1.0 | 5.0 |
| 11 | 5.0 | 2.0 | 9.0 | 9.0 | 4.0 | 4.0 | 2.0 | 8.0 | 6.0 | 9.0 | 4.0 | 6.0 | 9.0 | 1.0 |
| 12 | 1.0 | 8.0 | 10.0 | 10.0 | 8.0 | 2.0 | 1.0 | 2.0 | 9.0 | 3.0 | 1.0 | 9.0 | 6.0 | 10.0 |
| 13 | 4.0 | 7.0 | 1.0 | 3.0 | 10.0 | 1.0 | 5.0 | 1.0 | 10.0 | 7.0 | 5.0 | 1.0 | 10.0 | 2.0 |

I'll put the route in a simple JSON layout so it's easy to copy/paste and see the shape I expect.

{
  ""solution"": []
}

Here ""solution"" is meant to be a list (in order) of the node identifiers that form the single directed path from the start to the end. Think of it like filling in a short form: just the sequence of router names or numbers, first the start, last the destination, and every step must be a real arrow in the map. This JSON is just a sketch of the shape I want, not the final answer itself.

Please use the exact identifiers from the instance input — do not rename or invent labels. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 'edges': [{'from': 8, 'to': 0, 'var_index': 0}, {'from': 8, 'to': 4, 'var_index': 1}, {'from': 3, 'to': 9, 'var_index': 2}, {'from': 7, 'to': 9, 'var_index': 3}, {'from': 0, 'to': 1, 'var_index': 4}, {'from': 0, 'to': 4, 'var_index': 5}, {'from': 1, 'to': 2, 'var_index': 6}, {'from': 1, 'to': 5, 'var_index': 7}, {'from': 2, 'to': 3, 'var_index': 8}, {'from': 2, 'to': 6, 'var_index': 9}, {'from': 3, 'to': 7, 'var_index': 10}, {'from': 4, 'to': 5, 'var_index': 11}, {'from': 5, 'to': 6, 'var_index': 12}, {'from': 6, 'to': 7, 'var_index': 13}], 'objective': {'constant': 0.0, 'linear': [3.0, 10.0, 8.0, 6.0, 4.0, 2.0, 8.0, 4.0, 8.0, 8.0, 9.0, 6.0, 8.0, 9.0], 'quadratic': [[4.0, 6.0, 8.0, 7.0, 1.0, 5.0, 4.0, 10.0, 10.0, 6.0, 8.0, 5.0, 1.0, 4.0], [6.0, 4.0, 4.0, 10.0, 9.0, 7.0, 1.0, 9.0, 8.0, 10.0, 10.0, 2.0, 8.0, 7.0], [8.0, 4.0, 5.0, 3.0, 1.0, 3.0, 2.0, 1.0, 10.0, 5.0, 3.0, 9.0, 10.0, 1.0], [7.0, 10.0, 3.0, 1.0, 1.0, 7.0, 9.0, 8.0, 5.0, 2.0, 6.0, 9.0, 10.0, 3.0], [1.0, 9.0, 1.0, 1.0, 7.0, 6.0, 3.0, 1.0, 7.0, 3.0, 9.0, 4.0, 8.0, 10.0], [5.0, 7.0, 3.0, 7.0, 6.0, 10.0, 2.0, 1.0, 3.0, 2.0, 8.0, 4.0, 2.0, 1.0], [4.0, 1.0, 2.0, 9.0, 3.0, 2.0, 3.0, 3.0, 7.0, 5.0, 5.0, 2.0, 1.0, 5.0], [10.0, 9.0, 1.0, 8.0, 1.0, 1.0, 3.0, 2.0, 3.0, 10.0, 9.0, 8.0, 2.0, 1.0], [10.0, 8.0, 10.0, 5.0, 7.0, 3.0, 7.0, 3.0, 5.0, 4.0, 10.0, 6.0, 9.0, 10.0], [6.0, 10.0, 5.0, 2.0, 3.0, 2.0, 5.0, 10.0, 4.0, 6.0, 5.0, 9.0, 3.0, 7.0], [8.0, 10.0, 3.0, 6.0, 9.0, 8.0, 5.0, 9.0, 10.0, 5.0, 5.0, 4.0, 1.0, 5.0], [5.0, 2.0, 9.0, 9.0, 4.0, 4.0, 2.0, 8.0, 6.0, 9.0, 4.0, 6.0, 9.0, 1.0], [1.0, 8.0, 10.0, 10.0, 8.0, 2.0, 1.0, 2.0, 9.0, 3.0, 1.0, 9.0, 6.0, 10.0], [4.0, 7.0, 1.0, 3.0, 10.0, 1.0, 5.0, 1.0, 10.0, 7.0, 5.0, 1.0, 10.0, 2.0]]}, 'source': 8, 'target': 9}","[8, 0, 1, 2, 3, 9]",161.0,"{'problem_type': 'QSPP', 'num_nodes': 10, 'num_edges': 14, 'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 'source': 8, 'target': 9, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 3.0}, {'var_index': 1, 'linear_cost': 10.0}, {'var_index': 2, 'linear_cost': 8.0}, {'var_index': 3, 'linear_cost': 6.0}, {'var_index': 4, 'linear_cost': 4.0}, {'var_index': 5, 'linear_cost': 2.0}, {'var_index': 6, 'linear_cost': 8.0}, {'var_index': 7, 'linear_cost': 4.0}, {'var_index': 8, 'linear_cost': 8.0}, {'var_index': 9, 'linear_cost': 8.0}, {'var_index': 10, 'linear_cost': 9.0}, {'var_index': 11, 'linear_cost': 6.0}, {'var_index': 12, 'linear_cost': 8.0}, {'var_index': 13, 'linear_cost': 9.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 5, 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{'var_i': 13, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 13, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 13, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 13, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 13, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 13, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 13, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 13, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 13, 'var_j': 12, 'quadratic_cost': 10.0}, {'var_i': 13, 'var_j': 13, 'quadratic_cost': 2.0}]}, 'edges': [{'from': 8, 'to': 0, 'var_index': 0}, {'from': 8, 'to': 4, 'var_index': 1}, {'from': 3, 'to': 9, 'var_index': 2}, {'from': 7, 'to': 9, 'var_index': 3}, {'from': 0, 'to': 1, 'var_index': 4}, {'from': 0, 'to': 4, 'var_index': 5}, {'from': 1, 'to': 2, 'var_index': 6}, {'from': 1, 'to': 5, 'var_index': 7}, {'from': 2, 'to': 3, 'var_index': 8}, {'from': 2, 'to': 6, 'var_index': 9}, {'from': 3, 'to': 7, 'var_index': 10}, {'from': 4, 'to': 5, 'var_index': 11}, {'from': 5, 'to': 6, 'var_index': 12}, {'from': 6, 'to': 7, 'var_index': 13}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7, 8: 8, 9: 9}}","[8, 0, 1, 2, 3, 9]",3,json,0
QSPP,QSPP,"We manage a stretch of conveyors between the loading station and the packing station and need to decide on exactly one route that follows the arrows on the belts. Every conveyor segment burns energy and may have a one-off surcharge for using it, and sometimes two particular segments together trigger another small fee. The winner is simply the one route whose total bill — the sum of each segment’s cost plus any extra charges for pairs of segments used together — is smallest. The route must be a single, connected sequence from the loading spot to packing, with each connection actually existing and no duplicates; the specific map and costs appear below.

# total_locations=7
# total_conveyor_segments=6
# location_ids=0, 1, 2, 3, 4, 5, 6
# loading_station=5
# packing_station=6

segment_tail_location,segment_head_location,segment_id
5,0,0
4,6,1
0,1,2
1,2,3
2,3,4
3,4,5

segment_id,energy_and_usage_surcharge
0,4.0
1,9.0
2,1.0
3,6.0
4,7.0
5,9.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (segment_i_id, segment_j_id). If two segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| segment_i_id\segment_j_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 10.0 | 7.0 | 3.0 | 7.0 | 4.0 | 10.0 |
| 1 | 7.0 | 4.0 | 6.0 | 9.0 | 5.0 | 8.0 |
| 2 | 3.0 | 6.0 | 10.0 | 1.0 | 10.0 | 8.0 |
| 3 | 7.0 | 9.0 | 1.0 | 4.0 | 2.0 | 8.0 |
| 4 | 4.0 | 5.0 | 10.0 | 2.0 | 5.0 | 10.0 |
| 5 | 10.0 | 8.0 | 8.0 | 8.0 | 10.0 | 8.0 |

Also, when you send the chosen route back, please put it in a tiny JSON shape so it's easy to read and machine-friendly. Something like this:

{
  ""solution"": []
}

Here, ""solution"" is just a list of node identifiers in order from the loading spot to the packing spot — first item is the source, last item is the target. Think of it like filling out a one-line route on a form; this block just shows the expected shape, not the actual route itself.

Please use the node identifiers exactly as they appear in the instance input — no renaming, no made-up labels — and don't include any edge IDs or cost numbers, only node names. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6], 'edges': [{'from': 5, 'to': 0, 'var_index': 0}, {'from': 4, 'to': 6, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}], 'objective': {'constant': 0.0, 'linear': [4.0, 9.0, 1.0, 6.0, 7.0, 9.0], 'quadratic': [[10.0, 7.0, 3.0, 7.0, 4.0, 10.0], [7.0, 4.0, 6.0, 9.0, 5.0, 8.0], [3.0, 6.0, 10.0, 1.0, 10.0, 8.0], [7.0, 9.0, 1.0, 4.0, 2.0, 8.0], [4.0, 5.0, 10.0, 2.0, 5.0, 10.0], [10.0, 8.0, 8.0, 8.0, 10.0, 8.0]]}, 'source': 5, 'target': 6}","[5, 0, 1, 2, 3, 4, 6]",273.0,"{'problem_type': 'QSPP', 'num_nodes': 7, 'num_edges': 6, 'nodes': [0, 1, 2, 3, 4, 5, 6], 'source': 5, 'target': 6, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 4.0}, {'var_index': 1, 'linear_cost': 9.0}, {'var_index': 2, 'linear_cost': 1.0}, {'var_index': 3, 'linear_cost': 6.0}, {'var_index': 4, 'linear_cost': 7.0}, {'var_index': 5, 'linear_cost': 9.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 8.0}]}, 'edges': [{'from': 5, 'to': 0, 'var_index': 0}, {'from': 4, 'to': 6, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6}}","[5, 0, 1, 2, 3, 4, 6]",4,csv,0
QSPP,QSPP,"Many people on the planning team are comparing possible single-channel routes from the reservoir inlet to the treatment outfall, all of which must follow the arrows on the canal map. Every candidate has to be a single, uninterrupted path—no skipping pieces, no splitting, no revisiting the same segment. Each canal segment brings its own pumping/erosion cost plus a usage surcharge, and some pairs of consecutive segments bring extra charges when used together (those extra charges can vary with the order of the two segments). The route we want is simply the one that results in the lowest total bill after summing every segment’s charges and any extra pairwise fees. The map and cost details are shown below.

The map contains 5 junctions and 4 directed segments; the valid junctions are 0, 1, 2, 3, 4, and every candidate route must start at 3 and end at 4.

| segment_start_node | segment_end_node | segment_id |
|---|---|---|
| 3 | 0 | 0 |
| 2 | 4 | 1 |
| 0 | 1 | 2 |
| 1 | 2 | 3 |

| segment_id | segment_usage_fee |
|---|---|
| 0 | 3.0 |
| 1 | 4.0 |
| 2 | 1.0 |
| 3 | 8.0 |

*Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (first_segment_id, second_segment_id). If two segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).*

**quadratic_costs**

| first_segment_id\second_segment_id | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| 0 | 6.0 | 9.0 | 3.0 | 6.0 |
| 1 | 9.0 | 1.0 | 5.0 | 4.0 |
| 2 | 3.0 | 5.0 | 1.0 | 8.0 |
| 3 | 6.0 | 4.0 | 8.0 | 9.0 |

The planning team will sum each selected segment's charges and any applicable ordered-pair fees to identify the single uninterrupted route with the lowest total bill.

When you send the chosen route back, please tuck it into a tiny JSON sketch so it's easy to parse. Nothing fancy — just the one key below holding the ordered list of nodes from source to target:

{
  ""solution"": []
}

Think of ""solution"" as the form field where you drop the path: that array should contain the node identifiers in order (start at the reservoir inlet, end at the treatment outfall), and nothing else — node IDs only, no edge IDs, no costs. This JSON is just a template showing the shape I expect, not the actual path itself.

Please use the node identifiers exactly as they appear in the instance input — do not rename them or invent new labels. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'nodes': [0, 1, 2, 3, 4], 'edges': [{'from': 3, 'to': 0, 'var_index': 0}, {'from': 2, 'to': 4, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}], 'objective': {'constant': 0.0, 'linear': [3.0, 4.0, 1.0, 8.0], 'quadratic': [[6.0, 9.0, 3.0, 6.0], [9.0, 1.0, 5.0, 4.0], [3.0, 5.0, 1.0, 8.0], [6.0, 4.0, 8.0, 9.0]]}, 'source': 3, 'target': 4}","[3, 0, 1, 2, 4]",103.0,"{'problem_type': 'QSPP', 'num_nodes': 5, 'num_edges': 4, 'nodes': [0, 1, 2, 3, 4], 'source': 3, 'target': 4, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 3.0}, {'var_index': 1, 'linear_cost': 4.0}, {'var_index': 2, 'linear_cost': 1.0}, {'var_index': 3, 'linear_cost': 8.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 9.0}]}, 'edges': [{'from': 3, 'to': 0, 'var_index': 0}, {'from': 2, 'to': 4, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4}}","[3, 0, 1, 2, 4]",5,markdown_table,0
QSPP,QSPP,"I’m imagining a transit planner staring at a city map, trying to pick one single route for a bus to go from the depot to the terminal. The choice has to be a continuous, allowed one-way path that follows the direction of each road, starts at the depot and ends at the terminal — nothing magical, no teleporting or skipping segments, and the plan will be written down as a list of locations. Each road taken carries a basic fuel/toll charge and sometimes an extra tag that applies when that road is used; on top of that, certain pairs of road segments bump up the bill if both are on the trip. The trick is to pick the route that makes the total bill smallest by adding every road’s basic charge, any per-road use charges, and every extra charge for pairs of segments that appear together. The concrete map and numbers are shown below.

# total_intersections=7
# total_road_segments=6
# location_ids=1, 2, 3, 4, 5, 6, 7
# depot_location=6
# terminal_location=7

road_start_location,road_end_location,road_segment_id
6,1,0
5,7,1
1,2,2
2,3,3
3,4,4
4,5,5

road_segment_id,base_fuel_toll_cost
0,8.0
1,1.0
2,3.0
3,7.0
4,6.0
5,2.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (segment_i_id, segment_j_id). If two road_segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| segment_i_id\segment_j_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 3.0 | 9.0 | 1.0 | 3.0 | 10.0 | 7.0 |
| 1 | 9.0 | 8.0 | 8.0 | 8.0 | 6.0 | 7.0 |
| 2 | 1.0 | 8.0 | 8.0 | 7.0 | 4.0 | 6.0 |
| 3 | 3.0 | 8.0 | 7.0 | 4.0 | 9.0 | 5.0 |
| 4 | 10.0 | 6.0 | 4.0 | 9.0 | 1.0 | 1.0 |
| 5 | 7.0 | 7.0 | 6.0 | 5.0 | 1.0 | 6.0 |

You can just hand the final route back in a tiny JSON snippet — keeps things neat. Below is the shape I expect:

{
  ""solution"": []
}

This little object is just a form: put the chosen path into the solution array as a sequence of NODE identifiers (start with the source/depot and end with the target/terminal). Use only node names, in order, and make sure each consecutive pair follows a directed edge on the map. The JSON above is only a sketch of the expected shape, not the actual route.

Please use the exact identifiers given in the instance input — don’t rename nodes or invent new labels, and don’t include any edge identifiers. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6], 'edges': [{'from': 5, 'to': 0, 'var_index': 0}, {'from': 4, 'to': 6, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}], 'objective': {'constant': 0.0, 'linear': [8.0, 1.0, 3.0, 7.0, 6.0, 2.0], 'quadratic': [[3.0, 9.0, 1.0, 3.0, 10.0, 7.0], [9.0, 8.0, 8.0, 8.0, 6.0, 7.0], [1.0, 8.0, 8.0, 7.0, 4.0, 6.0], [3.0, 8.0, 7.0, 4.0, 9.0, 5.0], [10.0, 6.0, 4.0, 9.0, 1.0, 1.0], [7.0, 7.0, 6.0, 5.0, 1.0, 6.0]]}, 'source': 5, 'target': 6}","[5, 0, 1, 2, 3, 4, 6]",239.0,"{'problem_type': 'QSPP', 'num_nodes': 7, 'num_edges': 6, 'nodes': [1, 2, 3, 4, 5, 6, 7], 'source': 6, 'target': 7, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 8.0}, {'var_index': 1, 'linear_cost': 1.0}, {'var_index': 2, 'linear_cost': 3.0}, {'var_index': 3, 'linear_cost': 7.0}, {'var_index': 4, 'linear_cost': 6.0}, {'var_index': 5, 'linear_cost': 2.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 6.0}]}, 'edges': [{'from': 6, 'to': 1, 'var_index': 0}, {'from': 5, 'to': 7, 'var_index': 1}, {'from': 1, 'to': 2, 'var_index': 2}, {'from': 2, 'to': 3, 'var_index': 3}, {'from': 3, 'to': 4, 'var_index': 4}, {'from': 4, 'to': 5, 'var_index': 5}], 'node_id_map': {0: 1, 1: 2, 2: 3, 3: 4, 4: 5, 5: 6, 6: 7}}","[6, 1, 2, 3, 4, 5, 7]",6,csv,1
QSPP,QSPP,"Out on the bench there’s a single-route problem: route one signal from the input pad to the output pad by choosing a single directed chain of connections that’s allowed by the layout. Judge a candidate chain by summing each segment’s own leakage/resistance penalty and adding any extra penalties that come from every pair of segments on that chain interacting with each other — aim for the chain with the lowest overall sum. The result must be a single, unbroken sequence of locations starting at the input and ending at the output that steps only along valid directed links, and the specific map and numbers are shown below.

# total_locations=7
# total_segments=6
# location_ids=0, 1, 2, 3, 4, 5, 6
# input_pad=5
# output_pad=6

segment_from_location,segment_to_location,segment_id
5,0,0
4,6,1
0,1,2
1,2,3
2,3,4
3,4,5

segment_id,leakage_resistance_cost
0,9.0
1,2.0
2,5.0
3,9.0
4,4.0
5,7.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (segment_i_id, segment_j_id). If two segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| segment_i_id\segment_j_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 3.0 | 8.0 | 9.0 | 2.0 | 2.0 | 2.0 |
| 1 | 8.0 | 10.0 | 10.0 | 1.0 | 7.0 | 10.0 |
| 2 | 9.0 | 10.0 | 10.0 | 3.0 | 5.0 | 10.0 |
| 3 | 2.0 | 1.0 | 3.0 | 6.0 | 5.0 | 5.0 |
| 4 | 2.0 | 7.0 | 5.0 | 5.0 | 9.0 | 10.0 |
| 5 | 2.0 | 10.0 | 10.0 | 5.0 | 10.0 | 2.0 |

When you send back the chosen route, slip it into a tiny JSON snippet so it's easy to read and validate.

{
  ""solution"": []
}

The ""solution"" field is just an ordered list of node identifiers — the path from the input pad to the output pad. Treat it like a short form: list the starting location first, the ending location last, and put each intermediate location in order. This JSON is only a sketch of the expected shape, not the actual answer.

Please use the node identifiers exactly as they appear in the instance input — no renaming and no new labels. For example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6], 'edges': [{'from': 5, 'to': 0, 'var_index': 0}, {'from': 4, 'to': 6, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}], 'objective': {'constant': 0.0, 'linear': [9.0, 2.0, 5.0, 9.0, 4.0, 7.0], 'quadratic': [[3.0, 8.0, 9.0, 2.0, 2.0, 2.0], [8.0, 10.0, 10.0, 1.0, 7.0, 10.0], [9.0, 10.0, 10.0, 3.0, 5.0, 10.0], [2.0, 1.0, 3.0, 6.0, 5.0, 5.0], [2.0, 7.0, 5.0, 5.0, 9.0, 10.0], [2.0, 10.0, 10.0, 5.0, 10.0, 2.0]]}, 'source': 5, 'target': 6}","[5, 0, 1, 2, 3, 4, 6]",254.0,"{'problem_type': 'QSPP', 'num_nodes': 7, 'num_edges': 6, 'nodes': [0, 1, 2, 3, 4, 5, 6], 'source': 5, 'target': 6, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 9.0}, {'var_index': 1, 'linear_cost': 2.0}, {'var_index': 2, 'linear_cost': 5.0}, {'var_index': 3, 'linear_cost': 9.0}, {'var_index': 4, 'linear_cost': 4.0}, {'var_index': 5, 'linear_cost': 7.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 2.0}]}, 'edges': [{'from': 5, 'to': 0, 'var_index': 0}, {'from': 4, 'to': 6, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6}}","[5, 0, 1, 2, 3, 4, 6]",7,csv,0
QSPP,QSPP,"Back at the warehouse, the task is to send one robot from the pick area to the drop area along a single, allowed-direction aisle route and to spell out every location it passes. The trip time is built from the fixed time of each aisle segment on that route plus extra congestion penalties that apply whenever particular segment pairs are both present; a few segments also carry their own small extra time. The sensible plan is the one route whose combined time — base times plus any pairwise and per-segment penalties — is smallest, and the exact layout and penalty values are shown below.

# num_locations=8
# num_aisles=11
# locations_list=A, B, C, D, E, F, G, H
# pick_zone=G
# drop_zone=H

aisle_from,aisle_to,aisle_segment_id
G,A,0
G,D,1
C,H,2
F,H,3
A,B,4
A,D,5
B,C,6
B,E,7
C,F,8
D,E,9
E,F,10

aisle_segment_id,traversal_time
0,6.0
1,1.0
2,9.0
3,4.0
4,9.0
5,6.0
6,6.0
7,8.0
8,5.0
9,1.0
10,3.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (aisle_i_id, aisle_j_id). If two aisle_segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| aisle_i_id\aisle_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 7.0 | 2.0 | 7.0 | 6.0 | 10.0 | 2.0 | 3.0 | 3.0 | 10.0 | 10.0 | 6.0 |
| 1 | 2.0 | 1.0 | 7.0 | 6.0 | 8.0 | 1.0 | 1.0 | 10.0 | 3.0 | 2.0 | 3.0 |
| 2 | 7.0 | 7.0 | 6.0 | 2.0 | 7.0 | 6.0 | 1.0 | 10.0 | 5.0 | 1.0 | 6.0 |
| 3 | 6.0 | 6.0 | 2.0 | 4.0 | 4.0 | 7.0 | 5.0 | 4.0 | 1.0 | 5.0 | 4.0 |
| 4 | 10.0 | 8.0 | 7.0 | 4.0 | 3.0 | 2.0 | 3.0 | 9.0 | 2.0 | 2.0 | 3.0 |
| 5 | 2.0 | 1.0 | 6.0 | 7.0 | 2.0 | 8.0 | 9.0 | 5.0 | 10.0 | 4.0 | 4.0 |
| 6 | 3.0 | 1.0 | 1.0 | 5.0 | 3.0 | 9.0 | 3.0 | 10.0 | 9.0 | 5.0 | 7.0 |
| 7 | 3.0 | 10.0 | 10.0 | 4.0 | 9.0 | 5.0 | 10.0 | 2.0 | 1.0 | 2.0 | 1.0 |
| 8 | 10.0 | 3.0 | 5.0 | 1.0 | 2.0 | 10.0 | 9.0 | 1.0 | 5.0 | 3.0 | 3.0 |
| 9 | 10.0 | 2.0 | 1.0 | 5.0 | 2.0 | 4.0 | 5.0 | 2.0 | 3.0 | 2.0 | 10.0 |
| 10 | 6.0 | 3.0 | 6.0 | 4.0 | 3.0 | 4.0 | 7.0 | 1.0 | 3.0 | 10.0 | 2.0 |

Oh, and one small thing — when you send the chosen route, please put it into a tiny JSON object so it's easy to read and validate. The structure should look like this:

{
  ""solution"": []
}

The idea is simple: put the nodes, in order, inside that ""solution"" array — from the pick area (source) to the drop area (target). Keep it casual: just the node identifiers, nothing else (no edge IDs, no costs, no extra labels).

This JSON is just the sketch of the shape we want, not the actual answer itself.

Also, please use the node identifiers exactly as they appear in the instance input — do not rename them or invent new labels. For example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7], 'edges': [{'from': 6, 'to': 0, 'var_index': 0}, {'from': 6, 'to': 3, 'var_index': 1}, {'from': 2, 'to': 7, 'var_index': 2}, {'from': 5, 'to': 7, 'var_index': 3}, {'from': 0, 'to': 1, 'var_index': 4}, {'from': 0, 'to': 3, 'var_index': 5}, {'from': 1, 'to': 2, 'var_index': 6}, {'from': 1, 'to': 4, 'var_index': 7}, {'from': 2, 'to': 5, 'var_index': 8}, {'from': 3, 'to': 4, 'var_index': 9}, {'from': 4, 'to': 5, 'var_index': 10}], 'objective': {'constant': 0.0, 'linear': [6.0, 1.0, 9.0, 4.0, 9.0, 6.0, 6.0, 8.0, 5.0, 1.0, 3.0], 'quadratic': [[7.0, 2.0, 7.0, 6.0, 10.0, 2.0, 3.0, 3.0, 10.0, 10.0, 6.0], [2.0, 1.0, 7.0, 6.0, 8.0, 1.0, 1.0, 10.0, 3.0, 2.0, 3.0], [7.0, 7.0, 6.0, 2.0, 7.0, 6.0, 1.0, 10.0, 5.0, 1.0, 6.0], [6.0, 6.0, 2.0, 4.0, 4.0, 7.0, 5.0, 4.0, 1.0, 5.0, 4.0], [10.0, 8.0, 7.0, 4.0, 3.0, 2.0, 3.0, 9.0, 2.0, 2.0, 3.0], [2.0, 1.0, 6.0, 7.0, 2.0, 8.0, 9.0, 5.0, 10.0, 4.0, 4.0], [3.0, 1.0, 1.0, 5.0, 3.0, 9.0, 3.0, 10.0, 9.0, 5.0, 7.0], [3.0, 10.0, 10.0, 4.0, 9.0, 5.0, 10.0, 2.0, 1.0, 2.0, 1.0], [10.0, 3.0, 5.0, 1.0, 2.0, 10.0, 9.0, 1.0, 5.0, 3.0, 3.0], [10.0, 2.0, 1.0, 5.0, 2.0, 4.0, 5.0, 2.0, 3.0, 2.0, 10.0], [6.0, 3.0, 6.0, 4.0, 3.0, 4.0, 7.0, 1.0, 3.0, 10.0, 2.0]]}, 'source': 6, 'target': 7}","[6, 3, 4, 5, 7]",78.0,"{'problem_type': 'QSPP', 'num_nodes': 8, 'num_edges': 11, 'nodes': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H'], 'source': 'G', 'target': 'H', 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 6.0}, {'var_index': 1, 'linear_cost': 1.0}, {'var_index': 2, 'linear_cost': 9.0}, {'var_index': 3, 'linear_cost': 4.0}, {'var_index': 4, 'linear_cost': 9.0}, {'var_index': 5, 'linear_cost': 6.0}, {'var_index': 6, 'linear_cost': 6.0}, {'var_index': 7, 'linear_cost': 8.0}, {'var_index': 8, 'linear_cost': 5.0}, {'var_index': 9, 'linear_cost': 1.0}, {'var_index': 10, 'linear_cost': 3.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 7, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 7, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 8, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 8, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 8, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 8, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 8, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 8, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 8, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 9, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 9, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 9, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 9, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 9, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 10, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 10, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 10, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 10, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 10, 'var_j': 10, 'quadratic_cost': 2.0}]}, 'edges': [{'from': 'G', 'to': 'A', 'var_index': 0}, {'from': 'G', 'to': 'D', 'var_index': 1}, {'from': 'C', 'to': 'H', 'var_index': 2}, {'from': 'F', 'to': 'H', 'var_index': 3}, {'from': 'A', 'to': 'B', 'var_index': 4}, {'from': 'A', 'to': 'D', 'var_index': 5}, {'from': 'B', 'to': 'C', 'var_index': 6}, {'from': 'B', 'to': 'E', 'var_index': 7}, {'from': 'C', 'to': 'F', 'var_index': 8}, {'from': 'D', 'to': 'E', 'var_index': 9}, {'from': 'E', 'to': 'F', 'var_index': 10}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E', 5: 'F', 6: 'G', 7: 'H'}}","['G', 'D', 'E', 'F', 'H']",8,csv,names
QSPP,QSPP,"Someone in logistics sketched out a network of sea lanes where every segment has a basic tariff, but certain segment pairs together cause additional handling fees. The practical choice is to select a single legal, one-way path from the origin port to the destination and compute the total charge by summing each segment’s tariff and any extra pairwise charges that apply when both segments appear on the path. The selection must be one uninterrupted path along allowed lanes, beginning at the origin and ending at the destination, with no missing links or repeated corridor usage. The exact graph and fee numbers appear below.

The instance lists 5 ports (A, B, C, D, E), 4 directed corridors, with origin D and destination E.

| corridor_start_port | corridor_end_port | corridor_id |
|---|---|---|
| D | A | 0 |
| C | E | 1 |
| A | B | 2 |
| B | C | 3 |

| corridor_id | corridor_tariff |
|---|---|
| 0 | 1.0 |
| 1 | 2.0 |
| 2 | 9.0 |
| 3 | 1.0 |

*Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (corridor_i_id, corridor_j_id). If two corridors with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).*

**quadratic_costs**

| corridor_i_id\corridor_j_id | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| 0 | 9.0 | 2.0 | 2.0 | 3.0 |
| 1 | 2.0 | 5.0 | 9.0 | 3.0 |
| 2 | 2.0 | 9.0 | 1.0 | 2.0 |
| 3 | 3.0 | 3.0 | 2.0 | 7.0 |

Choose a single uninterrupted one-way path from D to E through the ports A, B, C, D, E; total charge equals summed corridor tariffs plus any applicable pairwise handling fees.

Also, when you give the actual answer, please stick to a tiny JSON shape so it’s easy to parse — nothing fancy, just a single top-level key called solution with the path inside. Here’s the little sketch I expect:

{
  ""solution"": []
}

In that sketch, ""solution"" should be a list containing the nodes of the chosen route in order, from the origin to the destination. Think of it like filling in a short form: one sequence of place names, nothing else — no edge identifiers, no costs, just the node names in path order. This JSON is only a template showing the expected shape, not the actual path.

Also be sure to use the node identifiers exactly as they appear in the instance input — don’t rename them or invent new labels. For example:
- Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'nodes': [0, 1, 2, 3, 4], 'edges': [{'from': 3, 'to': 0, 'var_index': 0}, {'from': 2, 'to': 4, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}], 'objective': {'constant': 0.0, 'linear': [1.0, 2.0, 9.0, 1.0], 'quadratic': [[9.0, 2.0, 2.0, 3.0], [2.0, 5.0, 9.0, 3.0], [2.0, 9.0, 1.0, 2.0], [3.0, 3.0, 2.0, 7.0]]}, 'source': 3, 'target': 4}","[3, 0, 1, 2, 4]",77.0,"{'problem_type': 'QSPP', 'num_nodes': 5, 'num_edges': 4, 'nodes': ['A', 'B', 'C', 'D', 'E'], 'source': 'D', 'target': 'E', 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 1.0}, {'var_index': 1, 'linear_cost': 2.0}, {'var_index': 2, 'linear_cost': 9.0}, {'var_index': 3, 'linear_cost': 1.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 7.0}]}, 'edges': [{'from': 'D', 'to': 'A', 'var_index': 0}, {'from': 'C', 'to': 'E', 'var_index': 1}, {'from': 'A', 'to': 'B', 'var_index': 2}, {'from': 'B', 'to': 'C', 'var_index': 3}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E'}}","['D', 'A', 'B', 'C', 'E']",9,markdown_table,names
QSPP,QSPP,"We’re organizing visitor flow and need to choose exactly one one-way path from the lobby to the keynote stage that follows the direction signs through the exhibit halls. Every hallway adds a base walking cost, some hallways have an extra obstacle cost when used, and certain hallway pairs create additional delay when both are included — so the “best” route is the one with the smallest total of all those pieces added together. The route must be a connected list of places, starting at the entrance and ending at the keynote, and the answer should only list location names in order (no corridor identifiers or cost figures). The specific map and numbers appear below.

We have 8 locations and 7 one-way corridors: 0, 1, 2, 3, 4, 5, 6, 7, with the entrance at 6 and the keynote at 7.
We list corridor 0 as running from 6 to 0.
We list corridor 1 as running from 5 to 7.
We list corridor 2 as running from 0 to 1.
We list corridor 3 as running from 1 to 2.
We list corridor 4 as running from 2 to 3.
We list corridor 5 as running from 3 to 4.
We list corridor 6 as running from 4 to 5.
We assign corridor 0 a base walking cost of 3.0.
We assign corridor 1 a base walking cost of 6.0.
We assign corridor 2 a base walking cost of 5.0.
We assign corridor 3 a base walking cost of 8.0.
We assign corridor 4 a base walking cost of 5.0.
We assign corridor 5 a base walking cost of 9.0.
We assign corridor 6 a base walking cost of 3.0.
Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (corridor_i_id, corridor_j_id). If two corridors with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
quadratic_costs:
| corridor_i_id\corridor_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| 0 | 10.0 | 1.0 | 8.0 | 1.0 | 3.0 | 2.0 | 1.0 |
| 1 | 1.0 | 10.0 | 6.0 | 10.0 | 6.0 | 4.0 | 7.0 |
| 2 | 8.0 | 6.0 | 2.0 | 7.0 | 5.0 | 9.0 | 4.0 |
| 3 | 1.0 | 10.0 | 7.0 | 8.0 | 1.0 | 7.0 | 3.0 |
| 4 | 3.0 | 6.0 | 5.0 | 1.0 | 7.0 | 5.0 | 10.0 |
| 5 | 2.0 | 4.0 | 9.0 | 7.0 | 5.0 | 1.0 | 1.0 |
| 6 | 1.0 | 7.0 | 4.0 | 3.0 | 10.0 | 1.0 | 10.0 |
When we pick the optimal route, we’ll output only the ordered location names from 6 to 7, omitting corridor IDs and cost figures.

Oh, and when you send back the route, please use this simple JSON layout so it's easy to check automatically:

{
  ""solution"": []
}

The ""solution"" array is where you put the ordered list of place names (the locations you walk through) from the entrance to the keynote stage. Keep it casual: just the location identifiers in order, nothing else — no corridor IDs, no cost numbers. This JSON is just a sketch of the shape I want, not the actual answer itself.

Use the node identifiers exactly as they appear in the instance input — no renaming and no new labels.  
Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7], 'edges': [{'from': 6, 'to': 0, 'var_index': 0}, {'from': 5, 'to': 7, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 4, 'to': 5, 'var_index': 6}], 'objective': {'constant': 0.0, 'linear': [3.0, 6.0, 5.0, 8.0, 5.0, 9.0, 3.0], 'quadratic': [[10.0, 1.0, 8.0, 1.0, 3.0, 2.0, 1.0], [1.0, 10.0, 6.0, 10.0, 6.0, 4.0, 7.0], [8.0, 6.0, 2.0, 7.0, 5.0, 9.0, 4.0], [1.0, 10.0, 7.0, 8.0, 1.0, 7.0, 3.0], [3.0, 6.0, 5.0, 1.0, 7.0, 5.0, 10.0], [2.0, 4.0, 9.0, 7.0, 5.0, 1.0, 1.0], [1.0, 7.0, 4.0, 3.0, 10.0, 1.0, 10.0]]}, 'source': 6, 'target': 7}","[6, 0, 1, 2, 3, 4, 5, 7]",289.0,"{'problem_type': 'QSPP', 'num_nodes': 8, 'num_edges': 7, 'nodes': [0, 1, 2, 3, 4, 5, 6, 7], 'source': 6, 'target': 7, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 3.0}, {'var_index': 1, 'linear_cost': 6.0}, {'var_index': 2, 'linear_cost': 5.0}, {'var_index': 3, 'linear_cost': 8.0}, {'var_index': 4, 'linear_cost': 5.0}, {'var_index': 5, 'linear_cost': 9.0}, {'var_index': 6, 'linear_cost': 3.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 10.0}]}, 'edges': [{'from': 6, 'to': 0, 'var_index': 0}, {'from': 5, 'to': 7, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 4, 'to': 5, 'var_index': 6}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7}}","[6, 0, 1, 2, 3, 4, 5, 7]",10,nl,0
QSPP,QSPP,"I’m the build engineer trying to stitch together a single chain of build steps from the root module to the final artifact, following every dependency in the right direction. The trick is that every step has its own compile time plus a little overhead whenever it runs, and certain pairs of steps cause extra cache-miss slowdowns if both of them end up in the chain (sometimes the slowdown depends on which one comes before the other). The whole point is to make the total build finish as fast as possible by picking one valid, dependency-respecting chain and adding up the per-step times, the per-step overheads, and any pairwise penalties that occur. Nothing in the chain can be skipped or duplicated — it has to be one continuous route from source to target. The concrete build graph and the exact times and penalties are shown below.

The concrete build graph below has 9 modules and 12 dependency edges; the modules are 1, 2, 3, 4, 5, 6, 7, 8, 9. I start at 1 and must end at 9.
I see a build step 0 that goes from module 1 to 2.
I see a build step 1 that goes from module 1 to 4.
I see a build step 2 that goes from module 2 to 3.
I see a build step 3 that goes from module 2 to 5.
I see a build step 4 that goes from module 3 to 6.
I see a build step 5 that goes from module 4 to 5.
I see a build step 6 that goes from module 4 to 7.
I see a build step 7 that goes from module 5 to 6.
I see a build step 8 that goes from module 5 to 8.
I see a build step 9 that goes from module 6 to 9.
I see a build step 10 that goes from module 7 to 8.
I see a build step 11 that goes from module 8 to 9.
For build step 0 I incur base compile time 7.0.
For build step 1 I incur base compile time 2.0.
For build step 2 I incur base compile time 4.0.
For build step 3 I incur base compile time 1.0.
For build step 4 I incur base compile time 7.0.
For build step 5 I incur base compile time 10.0.
For build step 6 I incur base compile time 3.0.
For build step 7 I incur base compile time 6.0.
For build step 8 I incur base compile time 10.0.
For build step 9 I incur base compile time 6.0.
For build step 10 I incur base compile time 8.0.
For build step 11 I incur base compile time 8.0.
Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (step_i_id, step_j_id). If two build_steps with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
quadratic_costs:
| step_i_id\step_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 7.0 | 5.0 | 9.0 | 7.0 | 10.0 | 10.0 | 5.0 | 4.0 | 6.0 | 3.0 | 3.0 | 7.0 |
| 1 | 5.0 | 9.0 | 9.0 | 4.0 | 8.0 | 1.0 | 2.0 | 10.0 | 3.0 | 5.0 | 10.0 | 2.0 |
| 2 | 9.0 | 9.0 | 8.0 | 8.0 | 9.0 | 3.0 | 4.0 | 2.0 | 6.0 | 3.0 | 5.0 | 3.0 |
| 3 | 7.0 | 4.0 | 8.0 | 6.0 | 6.0 | 4.0 | 10.0 | 10.0 | 5.0 | 8.0 | 7.0 | 8.0 |
| 4 | 10.0 | 8.0 | 9.0 | 6.0 | 9.0 | 8.0 | 10.0 | 6.0 | 6.0 | 10.0 | 7.0 | 5.0 |
| 5 | 10.0 | 1.0 | 3.0 | 4.0 | 8.0 | 6.0 | 6.0 | 1.0 | 10.0 | 7.0 | 6.0 | 6.0 |
| 6 | 5.0 | 2.0 | 4.0 | 10.0 | 10.0 | 6.0 | 1.0 | 3.0 | 7.0 | 5.0 | 3.0 | 8.0 |
| 7 | 4.0 | 10.0 | 2.0 | 10.0 | 6.0 | 1.0 | 3.0 | 3.0 | 5.0 | 6.0 | 9.0 | 4.0 |
| 8 | 6.0 | 3.0 | 6.0 | 5.0 | 6.0 | 10.0 | 7.0 | 5.0 | 4.0 | 2.0 | 3.0 | 2.0 |
| 9 | 3.0 | 5.0 | 3.0 | 8.0 | 10.0 | 7.0 | 5.0 | 6.0 | 2.0 | 5.0 | 5.0 | 6.0 |
| 10 | 3.0 | 10.0 | 5.0 | 7.0 | 7.0 | 6.0 | 3.0 | 9.0 | 3.0 | 5.0 | 3.0 | 5.0 |
| 11 | 7.0 | 2.0 | 3.0 | 8.0 | 5.0 | 6.0 | 8.0 | 4.0 | 2.0 | 6.0 | 5.0 | 1.0 |
I’ll choose one continuous, dependency-respecting route from 1 to 9 that minimizes the sum of per-step compile times, per-step overheads, and any cache-miss penalties.

Also, to keep things machine-friendly, please give the chosen chain in a tiny JSON layout — just a single key with the node sequence as the value.

{
  ""solution"": []
}

This little sketch shows the shape I expect: ""solution"" should hold the ordered list of node identifiers that form the chain from the root module to the final artifact. Think of it as the short form of a form field — just list the locations in order, start to finish. This is only a template showing the expected shape, not the actual path itself.

Please make sure to use the exact node identifiers from the instance input, with no renaming or invented labels. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'name': 'Rostami_Grid1_k3_seedNone', 'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8], 'edges': [{'from': 0, 'to': 1, 'var_index': 0}, {'from': 0, 'to': 3, 'var_index': 1}, {'from': 1, 'to': 2, 'var_index': 2}, {'from': 1, 'to': 4, 'var_index': 3}, {'from': 2, 'to': 5, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 3, 'to': 6, 'var_index': 6}, {'from': 4, 'to': 5, 'var_index': 7}, {'from': 4, 'to': 7, 'var_index': 8}, {'from': 5, 'to': 8, 'var_index': 9}, {'from': 6, 'to': 7, 'var_index': 10}, {'from': 7, 'to': 8, 'var_index': 11}], 'objective': {'constant': 0.0, 'linear': [7.0, 2.0, 4.0, 1.0, 7.0, 10.0, 3.0, 6.0, 10.0, 6.0, 8.0, 8.0], 'quadratic': [[7.0, 5.0, 9.0, 7.0, 10.0, 10.0, 5.0, 4.0, 6.0, 3.0, 3.0, 7.0], [5.0, 9.0, 9.0, 4.0, 8.0, 1.0, 2.0, 10.0, 3.0, 5.0, 10.0, 2.0], [9.0, 9.0, 8.0, 8.0, 9.0, 3.0, 4.0, 2.0, 6.0, 3.0, 5.0, 3.0], [7.0, 4.0, 8.0, 6.0, 6.0, 4.0, 10.0, 10.0, 5.0, 8.0, 7.0, 8.0], [10.0, 8.0, 9.0, 6.0, 9.0, 8.0, 10.0, 6.0, 6.0, 10.0, 7.0, 5.0], [10.0, 1.0, 3.0, 4.0, 8.0, 6.0, 6.0, 1.0, 10.0, 7.0, 6.0, 6.0], [5.0, 2.0, 4.0, 10.0, 10.0, 6.0, 1.0, 3.0, 7.0, 5.0, 3.0, 8.0], [4.0, 10.0, 2.0, 10.0, 6.0, 1.0, 3.0, 3.0, 5.0, 6.0, 9.0, 4.0], [6.0, 3.0, 6.0, 5.0, 6.0, 10.0, 7.0, 5.0, 4.0, 2.0, 3.0, 2.0], [3.0, 5.0, 3.0, 8.0, 10.0, 7.0, 5.0, 6.0, 2.0, 5.0, 5.0, 6.0], [3.0, 10.0, 5.0, 7.0, 7.0, 6.0, 3.0, 9.0, 3.0, 5.0, 3.0, 5.0], [7.0, 2.0, 3.0, 8.0, 5.0, 6.0, 8.0, 4.0, 2.0, 6.0, 5.0, 1.0]]}, 'source': 0, 'target': 8}","[0, 3, 6, 7, 8]",95.0,"{'problem_type': 'QSPP', 'num_nodes': 9, 'num_edges': 12, 'nodes': [1, 2, 3, 4, 5, 6, 7, 8, 9], 'source': 1, 'target': 9, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 7.0}, {'var_index': 1, 'linear_cost': 2.0}, {'var_index': 2, 'linear_cost': 4.0}, {'var_index': 3, 'linear_cost': 1.0}, {'var_index': 4, 'linear_cost': 7.0}, {'var_index': 5, 'linear_cost': 10.0}, {'var_index': 6, 'linear_cost': 3.0}, {'var_index': 7, 'linear_cost': 6.0}, {'var_index': 8, 'linear_cost': 10.0}, {'var_index': 9, 'linear_cost': 6.0}, {'var_index': 10, 'linear_cost': 8.0}, {'var_index': 11, 'linear_cost': 8.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 7, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 7, 'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 8, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 8, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 8, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 8, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 8, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 9, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 9, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 9, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 9, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 9, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 10, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 10, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 11, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 11, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 11, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 11, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 11, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 11, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 11, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 11, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 11, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 11, 'var_j': 11, 'quadratic_cost': 1.0}]}, 'edges': [{'from': 1, 'to': 2, 'var_index': 0}, {'from': 1, 'to': 4, 'var_index': 1}, {'from': 2, 'to': 3, 'var_index': 2}, {'from': 2, 'to': 5, 'var_index': 3}, {'from': 3, 'to': 6, 'var_index': 4}, {'from': 4, 'to': 5, 'var_index': 5}, {'from': 4, 'to': 7, 'var_index': 6}, {'from': 5, 'to': 6, 'var_index': 7}, {'from': 5, 'to': 8, 'var_index': 8}, {'from': 6, 'to': 9, 'var_index': 9}, {'from': 7, 'to': 8, 'var_index': 10}, {'from': 8, 'to': 9, 'var_index': 11}], 'node_id_map': {0: 1, 1: 2, 2: 3, 3: 4, 4: 5, 5: 6, 6: 7, 7: 8, 8: 9}}","[1, 4, 7, 8, 9]",11,nl,1
QSPP,QSPP,"I was sketching an evacuation plan the other day: imagine a building with one assembly area and one safe zone, and a web of one-way exit corridors between rooms. The job is to pick a single, continuous one-way route from the assembly area to the safe zone that actually follows those corridors step by step — no gaps, no branching, and each move must be along an existing directed corridor. Each corridor carries its own hazard surcharge, and some pairs of corridors trigger extra penalties when both are used on the same route (sometimes the extra hit depends on which corridor comes before the other, and some corridors even have an extra cost just for being used at all). The plan that works best is the one with the lowest total exposure when you add up every corridor’s base surcharge plus every extra penalty that applies because certain corridor combos appear together. The concrete map and the numbers for each corridor are shown below.

# total_rooms=7
# total_corridors=14
# room_list=0, 1, 2, 3, 4, 5, 6
# assembly_area_id=5
# safe_zone_id=6

corridor_from,corridor_to,corridor_id
5,0,0
5,1,1
5,2,2
5,3,3
5,4,4
0,6,5
1,6,6
2,6,7
3,6,8
4,6,9
0,1,10
1,2,11
2,3,12
3,4,13

corridor_ref,hazard_surcharge
0,6.0
1,4.0
2,9.0
3,3.0
4,8.0
5,1.0
6,5.0
7,10.0
8,5.0
9,5.0
10,3.0
11,4.0
12,4.0
13,6.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (corridor_i_ref, corridor_j_ref). If two corridors with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| corridor_i_ref\corridor_j_ref | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 6.0 | 8.0 | 8.0 | 7.0 | 7.0 | 1.0 | 5.0 | 3.0 | 1.0 | 4.0 | 2.0 | 1.0 | 2.0 | 10.0 |
| 1 | 8.0 | 9.0 | 8.0 | 3.0 | 5.0 | 3.0 | 7.0 | 10.0 | 1.0 | 2.0 | 10.0 | 10.0 | 9.0 | 8.0 |
| 2 | 8.0 | 8.0 | 4.0 | 3.0 | 9.0 | 5.0 | 10.0 | 7.0 | 7.0 | 6.0 | 9.0 | 10.0 | 8.0 | 1.0 |
| 3 | 7.0 | 3.0 | 3.0 | 9.0 | 2.0 | 7.0 | 9.0 | 1.0 | 8.0 | 3.0 | 7.0 | 8.0 | 8.0 | 7.0 |
| 4 | 7.0 | 5.0 | 9.0 | 2.0 | 9.0 | 3.0 | 2.0 | 4.0 | 3.0 | 6.0 | 7.0 | 6.0 | 2.0 | 8.0 |
| 5 | 1.0 | 3.0 | 5.0 | 7.0 | 3.0 | 2.0 | 7.0 | 8.0 | 1.0 | 5.0 | 6.0 | 10.0 | 6.0 | 8.0 |
| 6 | 5.0 | 7.0 | 10.0 | 9.0 | 2.0 | 7.0 | 8.0 | 10.0 | 7.0 | 10.0 | 8.0 | 8.0 | 9.0 | 2.0 |
| 7 | 3.0 | 10.0 | 7.0 | 1.0 | 4.0 | 8.0 | 10.0 | 6.0 | 2.0 | 7.0 | 9.0 | 6.0 | 5.0 | 8.0 |
| 8 | 1.0 | 1.0 | 7.0 | 8.0 | 3.0 | 1.0 | 7.0 | 2.0 | 1.0 | 8.0 | 2.0 | 1.0 | 3.0 | 9.0 |
| 9 | 4.0 | 2.0 | 6.0 | 3.0 | 6.0 | 5.0 | 10.0 | 7.0 | 8.0 | 8.0 | 6.0 | 9.0 | 1.0 | 5.0 |
| 10 | 2.0 | 10.0 | 9.0 | 7.0 | 7.0 | 6.0 | 8.0 | 9.0 | 2.0 | 6.0 | 1.0 | 8.0 | 1.0 | 7.0 |
| 11 | 1.0 | 10.0 | 10.0 | 8.0 | 6.0 | 10.0 | 8.0 | 6.0 | 1.0 | 9.0 | 8.0 | 1.0 | 10.0 | 1.0 |
| 12 | 2.0 | 9.0 | 8.0 | 8.0 | 2.0 | 6.0 | 9.0 | 5.0 | 3.0 | 1.0 | 1.0 | 10.0 | 6.0 | 4.0 |
| 13 | 10.0 | 8.0 | 1.0 | 7.0 | 8.0 | 8.0 | 2.0 | 8.0 | 9.0 | 5.0 | 7.0 | 1.0 | 4.0 | 1.0 |

Oh, and when you send the actual route back, please stick to a tiny, predictable JSON shape so it's easy to check automatically. Something casual like this is perfect:

{
  ""solution"": []
}

Here ""solution"" is just a single list where you'll put the nodes of the chosen route in order, from the assembly area (source) to the safe zone (target). Think of it as the one-line form field for the path — the example above is only the shape, not the answer itself. Please use the node labels exactly as they appear in the problem instance and don't invent or rename anything.

- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""

Keep it simple and readable, and I’ll take it from there.","{'nodes': [0, 1, 2, 3, 4, 5, 6], 'edges': [{'from': 5, 'to': 0, 'var_index': 0}, {'from': 5, 'to': 1, 'var_index': 1}, {'from': 5, 'to': 2, 'var_index': 2}, {'from': 5, 'to': 3, 'var_index': 3}, {'from': 5, 'to': 4, 'var_index': 4}, {'from': 0, 'to': 6, 'var_index': 5}, {'from': 1, 'to': 6, 'var_index': 6}, {'from': 2, 'to': 6, 'var_index': 7}, {'from': 3, 'to': 6, 'var_index': 8}, {'from': 4, 'to': 6, 'var_index': 9}, {'from': 0, 'to': 1, 'var_index': 10}, {'from': 1, 'to': 2, 'var_index': 11}, {'from': 2, 'to': 3, 'var_index': 12}, {'from': 3, 'to': 4, 'var_index': 13}], 'objective': {'constant': 0.0, 'linear': [6.0, 4.0, 9.0, 3.0, 8.0, 1.0, 5.0, 10.0, 5.0, 5.0, 3.0, 4.0, 4.0, 6.0], 'quadratic': [[6.0, 8.0, 8.0, 7.0, 7.0, 1.0, 5.0, 3.0, 1.0, 4.0, 2.0, 1.0, 2.0, 10.0], [8.0, 9.0, 8.0, 3.0, 5.0, 3.0, 7.0, 10.0, 1.0, 2.0, 10.0, 10.0, 9.0, 8.0], [8.0, 8.0, 4.0, 3.0, 9.0, 5.0, 10.0, 7.0, 7.0, 6.0, 9.0, 10.0, 8.0, 1.0], [7.0, 3.0, 3.0, 9.0, 2.0, 7.0, 9.0, 1.0, 8.0, 3.0, 7.0, 8.0, 8.0, 7.0], [7.0, 5.0, 9.0, 2.0, 9.0, 3.0, 2.0, 4.0, 3.0, 6.0, 7.0, 6.0, 2.0, 8.0], [1.0, 3.0, 5.0, 7.0, 3.0, 2.0, 7.0, 8.0, 1.0, 5.0, 6.0, 10.0, 6.0, 8.0], [5.0, 7.0, 10.0, 9.0, 2.0, 7.0, 8.0, 10.0, 7.0, 10.0, 8.0, 8.0, 9.0, 2.0], [3.0, 10.0, 7.0, 1.0, 4.0, 8.0, 10.0, 6.0, 2.0, 7.0, 9.0, 6.0, 5.0, 8.0], [1.0, 1.0, 7.0, 8.0, 3.0, 1.0, 7.0, 2.0, 1.0, 8.0, 2.0, 1.0, 3.0, 9.0], [4.0, 2.0, 6.0, 3.0, 6.0, 5.0, 10.0, 7.0, 8.0, 8.0, 6.0, 9.0, 1.0, 5.0], [2.0, 10.0, 9.0, 7.0, 7.0, 6.0, 8.0, 9.0, 2.0, 6.0, 1.0, 8.0, 1.0, 7.0], [1.0, 10.0, 10.0, 8.0, 6.0, 10.0, 8.0, 6.0, 1.0, 9.0, 8.0, 1.0, 10.0, 1.0], [2.0, 9.0, 8.0, 8.0, 2.0, 6.0, 9.0, 5.0, 3.0, 1.0, 1.0, 10.0, 6.0, 4.0], [10.0, 8.0, 1.0, 7.0, 8.0, 8.0, 2.0, 8.0, 9.0, 5.0, 7.0, 1.0, 4.0, 1.0]]}, 'source': 5, 'target': 6}","[5, 0, 6]",17.0,"{'problem_type': 'QSPP', 'num_nodes': 7, 'num_edges': 14, 'nodes': [0, 1, 2, 3, 4, 5, 6], 'source': 5, 'target': 6, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 6.0}, {'var_index': 1, 'linear_cost': 4.0}, {'var_index': 2, 'linear_cost': 9.0}, {'var_index': 3, 'linear_cost': 3.0}, {'var_index': 4, 'linear_cost': 8.0}, {'var_index': 5, 'linear_cost': 1.0}, {'var_index': 6, 'linear_cost': 5.0}, {'var_index': 7, 'linear_cost': 10.0}, {'var_index': 8, 'linear_cost': 5.0}, {'var_index': 9, 'linear_cost': 5.0}, {'var_index': 10, 'linear_cost': 3.0}, {'var_index': 11, 'linear_cost': 4.0}, {'var_index': 12, 'linear_cost': 4.0}, {'var_index': 13, 'linear_cost': 6.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 12, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 13, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 13, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 12, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 7, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 7, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 8, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 8, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 8, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 8, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 8, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 9, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 9, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 9, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 9, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 9, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 9, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 9, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 9, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 9, 'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 9, 'var_j': 13, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 10, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 10, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 10, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 10, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 10, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 10, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 10, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 10, 'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 10, 'var_j': 13, 'quadratic_cost': 7.0}, {'var_i': 11, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 11, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 11, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 11, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 11, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 11, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 11, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 11, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 11, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 11, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 11, 'var_j': 12, 'quadratic_cost': 10.0}, {'var_i': 11, 'var_j': 13, 'quadratic_cost': 1.0}, {'var_i': 12, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 12, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 12, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 12, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 12, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 12, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 12, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 12, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 12, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 12, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 12, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 12, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 12, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 12, 'var_j': 13, 'quadratic_cost': 4.0}, {'var_i': 13, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 13, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 13, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 13, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 13, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 13, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 13, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 13, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 13, 'var_j': 12, 'quadratic_cost': 4.0}, {'var_i': 13, 'var_j': 13, 'quadratic_cost': 1.0}]}, 'edges': [{'from': 5, 'to': 0, 'var_index': 0}, {'from': 5, 'to': 1, 'var_index': 1}, {'from': 5, 'to': 2, 'var_index': 2}, {'from': 5, 'to': 3, 'var_index': 3}, {'from': 5, 'to': 4, 'var_index': 4}, {'from': 0, 'to': 6, 'var_index': 5}, {'from': 1, 'to': 6, 'var_index': 6}, {'from': 2, 'to': 6, 'var_index': 7}, {'from': 3, 'to': 6, 'var_index': 8}, {'from': 4, 'to': 6, 'var_index': 9}, {'from': 0, 'to': 1, 'var_index': 10}, {'from': 1, 'to': 2, 'var_index': 11}, {'from': 2, 'to': 3, 'var_index': 12}, {'from': 3, 'to': 4, 'var_index': 13}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6}}","[5, 0, 6]",12,csv,0
QSPP,QSPP,"We were putting together a distribution map and needed exactly one directed chain from our content source to the audience endpoint. Every hop in that chain has a base activation fee, and certain combinations of hops cause extra overlap charges when both are used — those combination charges can be asymmetric, so if channel A and channel B are both in the chain you include A’s extra cost with B and B’s extra cost with A. The task is to choose one uninterrupted, direction-respecting route (start at the origin, end at the audience, and every consecutive pair must be a valid one-way connection) and keep everything in that single sequence — don’t split or create multiple routes. The winner is the route with the smallest total bill: sum all the individual activation fees plus all pairwise overlap costs for channels that appear together. Concrete channel names, fees, and overlap rules are listed below.

{
  ""num_locations"": 6,
  ""num_channel_hops"": 11,
  ""location_ids"": [
    0,
    1,
    2,
    3,
    4,
    5
  ],
  ""content_origin_node"": 4,
  ""audience_endpoint_node"": 5,
  ""edges"": [
    {
      ""hop_from_location"": 4,
      ""hop_to_location"": 0,
      ""channel_hop_id"": 0
    },
    {
      ""hop_from_location"": 4,
      ""hop_to_location"": 1,
      ""channel_hop_id"": 1
    },
    {
      ""hop_from_location"": 4,
      ""hop_to_location"": 2,
      ""channel_hop_id"": 2
    },
    {
      ""hop_from_location"": 4,
      ""hop_to_location"": 3,
      ""channel_hop_id"": 3
    },
    {
      ""hop_from_location"": 0,
      ""hop_to_location"": 5,
      ""channel_hop_id"": 4
    },
    {
      ""hop_from_location"": 1,
      ""hop_to_location"": 5,
      ""channel_hop_id"": 5
    },
    {
      ""hop_from_location"": 2,
      ""hop_to_location"": 5,
      ""channel_hop_id"": 6
    },
    {
      ""hop_from_location"": 3,
      ""hop_to_location"": 5,
      ""channel_hop_id"": 7
    },
    {
      ""hop_from_location"": 0,
      ""hop_to_location"": 1,
      ""channel_hop_id"": 8
    },
    {
      ""hop_from_location"": 1,
      ""hop_to_location"": 2,
      ""channel_hop_id"": 9
    },
    {
      ""hop_from_location"": 2,
      ""hop_to_location"": 3,
      ""channel_hop_id"": 10
    }
  ],
  ""linear_costs"": [
    {
      ""channel_hop_id"": 0,
      ""activation_fee"": 4.0
    },
    {
      ""channel_hop_id"": 1,
      ""activation_fee"": 3.0
    },
    {
      ""channel_hop_id"": 2,
      ""activation_fee"": 10.0
    },
    {
      ""channel_hop_id"": 3,
      ""activation_fee"": 8.0
    },
    {
      ""channel_hop_id"": 4,
      ""activation_fee"": 1.0
    },
    {
      ""channel_hop_id"": 5,
      ""activation_fee"": 9.0
    },
    {
      ""channel_hop_id"": 6,
      ""activation_fee"": 4.0
    },
    {
      ""channel_hop_id"": 7,
      ""activation_fee"": 2.0
    },
    {
      ""channel_hop_id"": 8,
      ""activation_fee"": 7.0
    },
    {
      ""channel_hop_id"": 9,
      ""activation_fee"": 9.0
    },
    {
      ""channel_hop_id"": 10,
      ""activation_fee"": 8.0
    }
  ]
}

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (channel_i_id, channel_j_id). If two channel_hops with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| channel_i_id\channel_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 7.0 | 5.0 | 9.0 | 1.0 | 3.0 | 2.0 | 2.0 | 5.0 | 2.0 | 8.0 | 7.0 |
| 1 | 5.0 | 3.0 | 4.0 | 2.0 | 4.0 | 7.0 | 9.0 | 4.0 | 3.0 | 6.0 | 2.0 |
| 2 | 9.0 | 4.0 | 10.0 | 4.0 | 5.0 | 6.0 | 6.0 | 5.0 | 6.0 | 8.0 | 5.0 |
| 3 | 1.0 | 2.0 | 4.0 | 9.0 | 1.0 | 9.0 | 8.0 | 4.0 | 6.0 | 10.0 | 1.0 |
| 4 | 3.0 | 4.0 | 5.0 | 1.0 | 10.0 | 1.0 | 1.0 | 1.0 | 10.0 | 3.0 | 4.0 |
| 5 | 2.0 | 7.0 | 6.0 | 9.0 | 1.0 | 1.0 | 2.0 | 7.0 | 9.0 | 7.0 | 9.0 |
| 6 | 2.0 | 9.0 | 6.0 | 8.0 | 1.0 | 2.0 | 10.0 | 4.0 | 6.0 | 8.0 | 1.0 |
| 7 | 5.0 | 4.0 | 5.0 | 4.0 | 1.0 | 7.0 | 4.0 | 2.0 | 2.0 | 3.0 | 9.0 |
| 8 | 2.0 | 3.0 | 6.0 | 6.0 | 10.0 | 9.0 | 6.0 | 2.0 | 8.0 | 3.0 | 7.0 |
| 9 | 8.0 | 6.0 | 8.0 | 10.0 | 3.0 | 7.0 | 8.0 | 3.0 | 3.0 | 1.0 | 7.0 |
| 10 | 7.0 | 2.0 | 5.0 | 1.0 | 4.0 | 9.0 | 1.0 | 9.0 | 7.0 | 7.0 | 8.0 |

Oh, and when you send back the final route, please drop it into this tiny JSON shape so it's easy to read and parse:

{
  ""solution"": []
}

Think of ""solution"" as the single ordered list of node names that form the path from the origin to the audience endpoint — just the node identifiers in order, nothing else. This JSON is just a sketch of the expected shape, not the actual answer; fill that array with the nodes of your chosen route.

Also, please use the node identifiers exactly as they appear in the instance input — no renaming and no new labels. For example:
- ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5], 'edges': [{'from': 4, 'to': 0, 'var_index': 0}, {'from': 4, 'to': 1, 'var_index': 1}, {'from': 4, 'to': 2, 'var_index': 2}, {'from': 4, 'to': 3, 'var_index': 3}, {'from': 0, 'to': 5, 'var_index': 4}, {'from': 1, 'to': 5, 'var_index': 5}, {'from': 2, 'to': 5, 'var_index': 6}, {'from': 3, 'to': 5, 'var_index': 7}, {'from': 0, 'to': 1, 'var_index': 8}, {'from': 1, 'to': 2, 'var_index': 9}, {'from': 2, 'to': 3, 'var_index': 10}], 'objective': {'constant': 0.0, 'linear': [4.0, 3.0, 10.0, 8.0, 1.0, 9.0, 4.0, 2.0, 7.0, 9.0, 8.0], 'quadratic': [[7.0, 5.0, 9.0, 1.0, 3.0, 2.0, 2.0, 5.0, 2.0, 8.0, 7.0], [5.0, 3.0, 4.0, 2.0, 4.0, 7.0, 9.0, 4.0, 3.0, 6.0, 2.0], [9.0, 4.0, 10.0, 4.0, 5.0, 6.0, 6.0, 5.0, 6.0, 8.0, 5.0], [1.0, 2.0, 4.0, 9.0, 1.0, 9.0, 8.0, 4.0, 6.0, 10.0, 1.0], [3.0, 4.0, 5.0, 1.0, 10.0, 1.0, 1.0, 1.0, 10.0, 3.0, 4.0], [2.0, 7.0, 6.0, 9.0, 1.0, 1.0, 2.0, 7.0, 9.0, 7.0, 9.0], [2.0, 9.0, 6.0, 8.0, 1.0, 2.0, 10.0, 4.0, 6.0, 8.0, 1.0], [5.0, 4.0, 5.0, 4.0, 1.0, 7.0, 4.0, 2.0, 2.0, 3.0, 9.0], [2.0, 3.0, 6.0, 6.0, 10.0, 9.0, 6.0, 2.0, 8.0, 3.0, 7.0], [8.0, 6.0, 8.0, 10.0, 3.0, 7.0, 8.0, 3.0, 3.0, 1.0, 7.0], [7.0, 2.0, 5.0, 1.0, 4.0, 9.0, 1.0, 9.0, 7.0, 7.0, 8.0]]}, 'source': 4, 'target': 5}","[4, 0, 5]",28.0,"{'problem_type': 'QSPP', 'num_nodes': 6, 'num_edges': 11, 'nodes': [0, 1, 2, 3, 4, 5], 'source': 4, 'target': 5, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 4.0}, {'var_index': 1, 'linear_cost': 3.0}, {'var_index': 2, 'linear_cost': 10.0}, {'var_index': 3, 'linear_cost': 8.0}, {'var_index': 4, 'linear_cost': 1.0}, {'var_index': 5, 'linear_cost': 9.0}, {'var_index': 6, 'linear_cost': 4.0}, {'var_index': 7, 'linear_cost': 2.0}, {'var_index': 8, 'linear_cost': 7.0}, {'var_index': 9, 'linear_cost': 9.0}, {'var_index': 10, 'linear_cost': 8.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 7, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 7, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 7, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 8, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 9, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 9, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 9, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 9, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 9, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 9, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 9, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 9, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 10, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 10, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 10, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 10, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 10, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 10, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 10, 'quadratic_cost': 8.0}]}, 'edges': [{'from': 4, 'to': 0, 'var_index': 0}, {'from': 4, 'to': 1, 'var_index': 1}, {'from': 4, 'to': 2, 'var_index': 2}, {'from': 4, 'to': 3, 'var_index': 3}, {'from': 0, 'to': 5, 'var_index': 4}, {'from': 1, 'to': 5, 'var_index': 5}, {'from': 2, 'to': 5, 'var_index': 6}, {'from': 3, 'to': 5, 'var_index': 7}, {'from': 0, 'to': 1, 'var_index': 8}, {'from': 1, 'to': 2, 'var_index': 9}, {'from': 2, 'to': 3, 'var_index': 10}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5}}","[4, 0, 5]",13,json,0
QSPP,QSPP,"Someone is routing a delivery drone: pick one one-way path from launch to landing that follows the allowed airways. Each airway has its own battery/wind penalty, and some have an extra built-in penalty when they’re used. Pairs of airways can also interact — if both are flown there’s an additional interference penalty, and that interaction can depend on which airway comes first in the trip. The idea is to choose the single legal route that ends up with the smallest total of all those penalties, computed by adding each airway’s individual penalty plus any extra penalties for every pair that appears on the trip. Concrete corridor choices and penalty values are shown below.

# total_locations_count=8
# total_corridors_count=17
# location_ids=0, 1, 2, 3, 4, 5, 6, 7
# launch_site=6
# landing_pad=7

corridor_tail,corridor_head,corridor_id
6,0,0
6,1,1
6,2,2
6,3,3
6,4,4
6,5,5
0,7,6
1,7,7
2,7,8
3,7,9
4,7,10
5,7,11
0,1,12
1,2,13
2,3,14
3,4,15
4,5,16

corridor_id,per_corridor_penalty
0,3.0
1,9.0
2,6.0
3,5.0
4,5.0
5,4.0
6,3.0
7,8.0
8,9.0
9,8.0
10,10.0
11,9.0
12,4.0
13,5.0
14,7.0
15,2.0
16,9.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (corridor_i_id, corridor_j_id). If two corridors with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| corridor_i_id\corridor_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 10.0 | 7.0 | 9.0 | 10.0 | 6.0 | 5.0 | 6.0 | 7.0 | 2.0 | 5.0 | 3.0 | 10.0 | 4.0 | 3.0 | 5.0 | 3.0 | 4.0 |
| 1 | 7.0 | 7.0 | 8.0 | 5.0 | 1.0 | 6.0 | 8.0 | 1.0 | 8.0 | 4.0 | 9.0 | 8.0 | 6.0 | 2.0 | 10.0 | 4.0 | 5.0 |
| 2 | 9.0 | 8.0 | 10.0 | 3.0 | 7.0 | 2.0 | 6.0 | 1.0 | 7.0 | 9.0 | 10.0 | 4.0 | 7.0 | 3.0 | 3.0 | 4.0 | 10.0 |
| 3 | 10.0 | 5.0 | 3.0 | 9.0 | 3.0 | 9.0 | 7.0 | 4.0 | 2.0 | 1.0 | 4.0 | 1.0 | 5.0 | 1.0 | 1.0 | 1.0 | 4.0 |
| 4 | 6.0 | 1.0 | 7.0 | 3.0 | 4.0 | 6.0 | 8.0 | 5.0 | 9.0 | 5.0 | 3.0 | 10.0 | 9.0 | 1.0 | 10.0 | 6.0 | 4.0 |
| 5 | 5.0 | 6.0 | 2.0 | 9.0 | 6.0 | 3.0 | 3.0 | 7.0 | 2.0 | 1.0 | 10.0 | 6.0 | 8.0 | 4.0 | 6.0 | 3.0 | 4.0 |
| 6 | 6.0 | 8.0 | 6.0 | 7.0 | 8.0 | 3.0 | 4.0 | 2.0 | 1.0 | 1.0 | 9.0 | 2.0 | 5.0 | 8.0 | 4.0 | 9.0 | 3.0 |
| 7 | 7.0 | 1.0 | 1.0 | 4.0 | 5.0 | 7.0 | 2.0 | 8.0 | 10.0 | 1.0 | 6.0 | 8.0 | 9.0 | 3.0 | 6.0 | 4.0 | 5.0 |
| 8 | 2.0 | 8.0 | 7.0 | 2.0 | 9.0 | 2.0 | 1.0 | 10.0 | 9.0 | 8.0 | 7.0 | 2.0 | 4.0 | 10.0 | 2.0 | 5.0 | 9.0 |
| 9 | 5.0 | 4.0 | 9.0 | 1.0 | 5.0 | 1.0 | 1.0 | 1.0 | 8.0 | 6.0 | 1.0 | 3.0 | 6.0 | 10.0 | 4.0 | 8.0 | 7.0 |
| 10 | 3.0 | 9.0 | 10.0 | 4.0 | 3.0 | 10.0 | 9.0 | 6.0 | 7.0 | 1.0 | 1.0 | 4.0 | 3.0 | 1.0 | 5.0 | 6.0 | 1.0 |
| 11 | 10.0 | 8.0 | 4.0 | 1.0 | 10.0 | 6.0 | 2.0 | 8.0 | 2.0 | 3.0 | 4.0 | 4.0 | 1.0 | 7.0 | 1.0 | 8.0 | 2.0 |
| 12 | 4.0 | 6.0 | 7.0 | 5.0 | 9.0 | 8.0 | 5.0 | 9.0 | 4.0 | 6.0 | 3.0 | 1.0 | 2.0 | 10.0 | 4.0 | 9.0 | 4.0 |
| 13 | 3.0 | 2.0 | 3.0 | 1.0 | 1.0 | 4.0 | 8.0 | 3.0 | 10.0 | 10.0 | 1.0 | 7.0 | 10.0 | 6.0 | 3.0 | 6.0 | 6.0 |
| 14 | 5.0 | 10.0 | 3.0 | 1.0 | 10.0 | 6.0 | 4.0 | 6.0 | 2.0 | 4.0 | 5.0 | 1.0 | 4.0 | 3.0 | 3.0 | 7.0 | 2.0 |
| 15 | 3.0 | 4.0 | 4.0 | 1.0 | 6.0 | 3.0 | 9.0 | 4.0 | 5.0 | 8.0 | 6.0 | 8.0 | 9.0 | 6.0 | 7.0 | 4.0 | 4.0 |
| 16 | 4.0 | 5.0 | 10.0 | 4.0 | 4.0 | 4.0 | 3.0 | 5.0 | 9.0 | 7.0 | 1.0 | 2.0 | 4.0 | 6.0 | 2.0 | 4.0 | 4.0 |

Oh, and when you reply with the chosen route, please use a tiny JSON layout so it's easy to check automatically — something like this:

{
  ""solution"": []
}

""solution"" should hold the route as an ordered list of node identifiers (launch point first, landing point last). Just list the node names in order — nothing else. This is only a sketch of the expected shape, not the actual answer.

Please use each node identifier exactly as it appears in the instance input — don't rename them or invent new labels.

- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7], 'edges': [{'from': 6, 'to': 0, 'var_index': 0}, {'from': 6, 'to': 1, 'var_index': 1}, {'from': 6, 'to': 2, 'var_index': 2}, {'from': 6, 'to': 3, 'var_index': 3}, {'from': 6, 'to': 4, 'var_index': 4}, {'from': 6, 'to': 5, 'var_index': 5}, {'from': 0, 'to': 7, 'var_index': 6}, {'from': 1, 'to': 7, 'var_index': 7}, {'from': 2, 'to': 7, 'var_index': 8}, {'from': 3, 'to': 7, 'var_index': 9}, {'from': 4, 'to': 7, 'var_index': 10}, {'from': 5, 'to': 7, 'var_index': 11}, {'from': 0, 'to': 1, 'var_index': 12}, {'from': 1, 'to': 2, 'var_index': 13}, {'from': 2, 'to': 3, 'var_index': 14}, {'from': 3, 'to': 4, 'var_index': 15}, {'from': 4, 'to': 5, 'var_index': 16}], 'objective': {'constant': 0.0, 'linear': [3.0, 9.0, 6.0, 5.0, 5.0, 4.0, 3.0, 8.0, 9.0, 8.0, 10.0, 9.0, 4.0, 5.0, 7.0, 2.0, 9.0], 'quadratic': [[10.0, 7.0, 9.0, 10.0, 6.0, 5.0, 6.0, 7.0, 2.0, 5.0, 3.0, 10.0, 4.0, 3.0, 5.0, 3.0, 4.0], [7.0, 7.0, 8.0, 5.0, 1.0, 6.0, 8.0, 1.0, 8.0, 4.0, 9.0, 8.0, 6.0, 2.0, 10.0, 4.0, 5.0], [9.0, 8.0, 10.0, 3.0, 7.0, 2.0, 6.0, 1.0, 7.0, 9.0, 10.0, 4.0, 7.0, 3.0, 3.0, 4.0, 10.0], [10.0, 5.0, 3.0, 9.0, 3.0, 9.0, 7.0, 4.0, 2.0, 1.0, 4.0, 1.0, 5.0, 1.0, 1.0, 1.0, 4.0], [6.0, 1.0, 7.0, 3.0, 4.0, 6.0, 8.0, 5.0, 9.0, 5.0, 3.0, 10.0, 9.0, 1.0, 10.0, 6.0, 4.0], [5.0, 6.0, 2.0, 9.0, 6.0, 3.0, 3.0, 7.0, 2.0, 1.0, 10.0, 6.0, 8.0, 4.0, 6.0, 3.0, 4.0], [6.0, 8.0, 6.0, 7.0, 8.0, 3.0, 4.0, 2.0, 1.0, 1.0, 9.0, 2.0, 5.0, 8.0, 4.0, 9.0, 3.0], [7.0, 1.0, 1.0, 4.0, 5.0, 7.0, 2.0, 8.0, 10.0, 1.0, 6.0, 8.0, 9.0, 3.0, 6.0, 4.0, 5.0], [2.0, 8.0, 7.0, 2.0, 9.0, 2.0, 1.0, 10.0, 9.0, 8.0, 7.0, 2.0, 4.0, 10.0, 2.0, 5.0, 9.0], [5.0, 4.0, 9.0, 1.0, 5.0, 1.0, 1.0, 1.0, 8.0, 6.0, 1.0, 3.0, 6.0, 10.0, 4.0, 8.0, 7.0], [3.0, 9.0, 10.0, 4.0, 3.0, 10.0, 9.0, 6.0, 7.0, 1.0, 1.0, 4.0, 3.0, 1.0, 5.0, 6.0, 1.0], 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{'var_i': 12, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 12, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 12, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 12, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 12, 'var_j': 12, 'quadratic_cost': 2.0}, {'var_i': 12, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 12, 'var_j': 14, 'quadratic_cost': 4.0}, {'var_i': 12, 'var_j': 15, 'quadratic_cost': 9.0}, {'var_i': 12, 'var_j': 16, 'quadratic_cost': 4.0}, {'var_i': 13, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 13, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 13, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 13, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 13, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 13, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 13, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 13, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 13, 'var_j': 12, 'quadratic_cost': 10.0}, {'var_i': 13, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 13, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 15, 'quadratic_cost': 6.0}, {'var_i': 13, 'var_j': 16, 'quadratic_cost': 6.0}, {'var_i': 14, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 14, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 14, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 14, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 14, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 14, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 14, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 14, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 14, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 14, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 14, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 14, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 14, 'var_j': 12, 'quadratic_cost': 4.0}, {'var_i': 14, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 14, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 14, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 14, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 15, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 15, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 15, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 15, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 15, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 15, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 15, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 15, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 15, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 15, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 15, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 15, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 15, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 15, 'var_j': 15, 'quadratic_cost': 4.0}, {'var_i': 15, 'var_j': 16, 'quadratic_cost': 4.0}, {'var_i': 16, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 16, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 16, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 16, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 16, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 16, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 16, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 16, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 16, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 16, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 16, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 16, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 16, 'var_j': 12, 'quadratic_cost': 4.0}, {'var_i': 16, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 16, 'var_j': 14, 'quadratic_cost': 2.0}, {'var_i': 16, 'var_j': 15, 'quadratic_cost': 4.0}, {'var_i': 16, 'var_j': 16, 'quadratic_cost': 4.0}]}, 'edges': [{'from': 6, 'to': 0, 'var_index': 0}, {'from': 6, 'to': 1, 'var_index': 1}, {'from': 6, 'to': 2, 'var_index': 2}, {'from': 6, 'to': 3, 'var_index': 3}, {'from': 6, 'to': 4, 'var_index': 4}, {'from': 6, 'to': 5, 'var_index': 5}, {'from': 0, 'to': 7, 'var_index': 6}, {'from': 1, 'to': 7, 'var_index': 7}, {'from': 2, 'to': 7, 'var_index': 8}, {'from': 3, 'to': 7, 'var_index': 9}, {'from': 4, 'to': 7, 'var_index': 10}, {'from': 5, 'to': 7, 'var_index': 11}, {'from': 0, 'to': 1, 'var_index': 12}, {'from': 1, 'to': 2, 'var_index': 13}, {'from': 2, 'to': 3, 'var_index': 14}, {'from': 3, 'to': 4, 'var_index': 15}, {'from': 4, 'to': 5, 'var_index': 16}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7}}","[6, 4, 7]",14,csv,0
QSPP,QSPP,"I’m putting together a single lesson run that starts at the intro topic and finishes at the wrap-up, and I need to pick one straight sequence of topics where each next topic is a valid follow-up to the one before. Every topic on that line adds some prep time, and some pairs of topics create extra work or awkward overlap if they both show up, so the best plan is the one that ends up with the least total prep when you add each topic’s prep plus any extra friction between pairs. Nothing can be skipped or taught twice — it has to be one continuous path from intro to summary that follows the prerequisite order. The concrete diagram and numbers will be shown below.

# num_topics=6
# num_transitions=11
# topic_ids=A, B, C, D, E, F
# intro_topic=E
# wrap_up_topic=F

prerequisite_topic,next_topic,transition_id
E,A,0
E,B,1
E,C,2
E,D,3
A,F,4
B,F,5
C,F,6
D,F,7
A,B,8
B,C,9
C,D,10

transition_id,prep_overhead
0,8.0
1,10.0
2,9.0
3,6.0
4,1.0
5,9.0
6,2.0
7,8.0
8,6.0
9,3.0
10,8.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (transition_i_id, transition_j_id). If two transitions with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| transition_i_id\transition_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 10.0 | 4.0 | 5.0 | 7.0 | 7.0 | 7.0 | 4.0 | 3.0 | 9.0 | 8.0 | 6.0 |
| 1 | 4.0 | 5.0 | 9.0 | 2.0 | 5.0 | 7.0 | 6.0 | 6.0 | 5.0 | 3.0 | 5.0 |
| 2 | 5.0 | 9.0 | 5.0 | 3.0 | 10.0 | 1.0 | 8.0 | 2.0 | 5.0 | 5.0 | 9.0 |
| 3 | 7.0 | 2.0 | 3.0 | 4.0 | 4.0 | 7.0 | 5.0 | 7.0 | 5.0 | 2.0 | 10.0 |
| 4 | 7.0 | 5.0 | 10.0 | 4.0 | 6.0 | 4.0 | 5.0 | 4.0 | 2.0 | 5.0 | 6.0 |
| 5 | 7.0 | 7.0 | 1.0 | 7.0 | 4.0 | 7.0 | 6.0 | 3.0 | 2.0 | 10.0 | 5.0 |
| 6 | 4.0 | 6.0 | 8.0 | 5.0 | 5.0 | 6.0 | 2.0 | 4.0 | 5.0 | 1.0 | 1.0 |
| 7 | 3.0 | 6.0 | 2.0 | 7.0 | 4.0 | 3.0 | 4.0 | 8.0 | 7.0 | 9.0 | 7.0 |
| 8 | 9.0 | 5.0 | 5.0 | 5.0 | 2.0 | 2.0 | 5.0 | 7.0 | 6.0 | 2.0 | 8.0 |
| 9 | 8.0 | 3.0 | 5.0 | 2.0 | 5.0 | 10.0 | 1.0 | 9.0 | 2.0 | 2.0 | 6.0 |
| 10 | 6.0 | 5.0 | 9.0 | 10.0 | 6.0 | 5.0 | 1.0 | 7.0 | 8.0 | 6.0 | 8.0 |

Oh, and one more thing — when you send the final pick, please put it in a tiny JSON sketch so I can read it cleanly. Something simple like this:

{
  ""solution"": []
}

Here ""solution"" is the spot where you’d list the chosen straight sequence of topic nodes (start with the intro node, end with the wrap-up node). Think of it like a short form: the array is just the ordered list of topic names in the path. This is just a template to show the expected shape, not the actual answer — fill that array with the nodes when you have the final path.

Please remember: use the exact identifiers from the instance input — don’t rename anything or invent new labels. For example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5], 'edges': [{'from': 4, 'to': 0, 'var_index': 0}, {'from': 4, 'to': 1, 'var_index': 1}, {'from': 4, 'to': 2, 'var_index': 2}, {'from': 4, 'to': 3, 'var_index': 3}, {'from': 0, 'to': 5, 'var_index': 4}, {'from': 1, 'to': 5, 'var_index': 5}, {'from': 2, 'to': 5, 'var_index': 6}, {'from': 3, 'to': 5, 'var_index': 7}, {'from': 0, 'to': 1, 'var_index': 8}, {'from': 1, 'to': 2, 'var_index': 9}, {'from': 2, 'to': 3, 'var_index': 10}], 'objective': {'constant': 0.0, 'linear': [8.0, 10.0, 9.0, 6.0, 1.0, 9.0, 2.0, 8.0, 6.0, 3.0, 8.0], 'quadratic': [[10.0, 4.0, 5.0, 7.0, 7.0, 7.0, 4.0, 3.0, 9.0, 8.0, 6.0], [4.0, 5.0, 9.0, 2.0, 5.0, 7.0, 6.0, 6.0, 5.0, 3.0, 5.0], [5.0, 9.0, 5.0, 3.0, 10.0, 1.0, 8.0, 2.0, 5.0, 5.0, 9.0], [7.0, 2.0, 3.0, 4.0, 4.0, 7.0, 5.0, 7.0, 5.0, 2.0, 10.0], [7.0, 5.0, 10.0, 4.0, 6.0, 4.0, 5.0, 4.0, 2.0, 5.0, 6.0], [7.0, 7.0, 1.0, 7.0, 4.0, 7.0, 6.0, 3.0, 2.0, 10.0, 5.0], [4.0, 6.0, 8.0, 5.0, 5.0, 6.0, 2.0, 4.0, 5.0, 1.0, 1.0], [3.0, 6.0, 2.0, 7.0, 4.0, 3.0, 4.0, 8.0, 7.0, 9.0, 7.0], [9.0, 5.0, 5.0, 5.0, 2.0, 2.0, 5.0, 7.0, 6.0, 2.0, 8.0], [8.0, 3.0, 5.0, 2.0, 5.0, 10.0, 1.0, 9.0, 2.0, 2.0, 6.0], [6.0, 5.0, 9.0, 10.0, 6.0, 5.0, 1.0, 7.0, 8.0, 6.0, 8.0]]}, 'source': 4, 'target': 5}","[4, 2, 5]",34.0,"{'problem_type': 'QSPP', 'num_nodes': 6, 'num_edges': 11, 'nodes': ['A', 'B', 'C', 'D', 'E', 'F'], 'source': 'E', 'target': 'F', 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 8.0}, {'var_index': 1, 'linear_cost': 10.0}, {'var_index': 2, 'linear_cost': 9.0}, {'var_index': 3, 'linear_cost': 6.0}, {'var_index': 4, 'linear_cost': 1.0}, {'var_index': 5, 'linear_cost': 9.0}, {'var_index': 6, 'linear_cost': 2.0}, {'var_index': 7, 'linear_cost': 8.0}, {'var_index': 8, 'linear_cost': 6.0}, {'var_index': 9, 'linear_cost': 3.0}, {'var_index': 10, 'linear_cost': 8.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 7, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 7, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 7, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 8, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 8, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 8, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 8, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 9, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 9, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 9, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 9, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 10, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 10, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 10, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 10, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 10, 'quadratic_cost': 8.0}]}, 'edges': [{'from': 'E', 'to': 'A', 'var_index': 0}, {'from': 'E', 'to': 'B', 'var_index': 1}, {'from': 'E', 'to': 'C', 'var_index': 2}, {'from': 'E', 'to': 'D', 'var_index': 3}, {'from': 'A', 'to': 'F', 'var_index': 4}, {'from': 'B', 'to': 'F', 'var_index': 5}, {'from': 'C', 'to': 'F', 'var_index': 6}, {'from': 'D', 'to': 'F', 'var_index': 7}, {'from': 'A', 'to': 'B', 'var_index': 8}, {'from': 'B', 'to': 'C', 'var_index': 9}, {'from': 'C', 'to': 'D', 'var_index': 10}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E', 5: 'F'}}","['E', 'C', 'F']",15,csv,names
QSPP,QSPP,"I can imagine the control plan as a little map story: send the batch from the intake valve to the delivery manifold along one directed route through the pipes. Every pipe piece in that route costs something to run and carries a per-piece maintenance surcharge, and whenever particular pieces are combined in the same run there can be extra coupling charges that apply only if both are included (and order can matter). The sensible way to pick is to sum each piece’s base fee plus its maintenance add-on, then include all the extra charges for every pair that’s used together — the route with the lowest total cost is the one to choose. The path must be continuous, start at intake and end at delivery, listed as locations only with nothing left out, and the concrete network and cost numbers are shown below.

{
  ""total_locations_count"": 5,
  ""total_pipeline_segments"": 4,
  ""location_ids"": [
    0,
    1,
    2,
    3,
    4
  ],
  ""intake_valve_location"": 3,
  ""delivery_manifold_location"": 4,
  ""edges"": [
    {
      ""segment_from_location"": 3,
      ""segment_to_location"": 0,
      ""segment_id"": 0
    },
    {
      ""segment_from_location"": 2,
      ""segment_to_location"": 4,
      ""segment_id"": 1
    },
    {
      ""segment_from_location"": 0,
      ""segment_to_location"": 1,
      ""segment_id"": 2
    },
    {
      ""segment_from_location"": 1,
      ""segment_to_location"": 2,
      ""segment_id"": 3
    }
  ],
  ""linear_costs"": [
    {
      ""segment_id"": 0,
      ""segment_operational_plus_maintenance_cost"": 2.0
    },
    {
      ""segment_id"": 1,
      ""segment_operational_plus_maintenance_cost"": 6.0
    },
    {
      ""segment_id"": 2,
      ""segment_operational_plus_maintenance_cost"": 7.0
    },
    {
      ""segment_id"": 3,
      ""segment_operational_plus_maintenance_cost"": 1.0
    }
  ]
}

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (segment_i_id, segment_j_id). If two segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| segment_i_id\segment_j_id | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| 0 | 8.0 | 8.0 | 8.0 | 8.0 |
| 1 | 8.0 | 6.0 | 3.0 | 10.0 |
| 2 | 8.0 | 3.0 | 5.0 | 7.0 |
| 3 | 8.0 | 10.0 | 7.0 | 8.0 |

Also, when you send back the path, please use a tiny JSON layout so it's clear and machine-friendly — just one top-level key called ""solution"" whose value is the ordered list of node names from intake to delivery.

{
  ""solution"": []
}

This ""solution"" array should hold the node sequence only (start at the intake/source, end at the delivery/target), nothing else — no edge identifiers, no costs. Think of the JSON above as a simple form: the field name tells you where to put the ordered list of locations, and the empty list is just a placeholder you should replace with the actual path when you submit it. It's just a sketch of the expected shape, not the answer itself.

Please be sure to use the exact node identifiers from the instance input — do not rename or invent labels. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4], 'edges': [{'from': 3, 'to': 0, 'var_index': 0}, {'from': 2, 'to': 4, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}], 'objective': {'constant': 0.0, 'linear': [2.0, 6.0, 7.0, 1.0], 'quadratic': [[8.0, 8.0, 8.0, 8.0], [8.0, 6.0, 3.0, 10.0], [8.0, 3.0, 5.0, 7.0], [8.0, 10.0, 7.0, 8.0]]}, 'source': 3, 'target': 4}","[3, 0, 1, 2, 4]",131.0,"{'problem_type': 'QSPP', 'num_nodes': 5, 'num_edges': 4, 'nodes': [0, 1, 2, 3, 4], 'source': 3, 'target': 4, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 2.0}, {'var_index': 1, 'linear_cost': 6.0}, {'var_index': 2, 'linear_cost': 7.0}, {'var_index': 3, 'linear_cost': 1.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 8.0}]}, 'edges': [{'from': 3, 'to': 0, 'var_index': 0}, {'from': 2, 'to': 4, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4}}","[3, 0, 1, 2, 4]",16,json,0
QSPP,QSPP,"Once there’s a panel and an outlet to link, the installer needs to pick exactly one route through the directed conduits that connect them. Every piece of conduit has a base material and connector cost, and some pieces also impose an extra cost simply for being in the route; beyond that, certain ordered pairs of pieces interact and add interference costs when both are used — since order can matter, the interference from a pair is made up of the contributions from both directions. The job is to lay out one continuous path from the panel to the outlet (no branching, no multiple runs) that results in the smallest possible total when adding up all segment fees and any interaction penalties. The full network and cost details will be provided below.

Below are the specifics: 5 locations, 4 directed conduit segments; location IDs A, B, C, D, E; panel at D; outlet at E.
Conduit segment 0 runs from D to A.
Conduit segment 1 runs from C to E.
Conduit segment 2 runs from A to B.
Conduit segment 3 runs from B to C.
The base material and connector fee for 0 is 1.0.
The base material and connector fee for 1 is 3.0.
The base material and connector fee for 2 is 9.0.
The base material and connector fee for 3 is 9.0.
Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (first_conduit_segment_id, second_conduit_segment_id). If two conduit_segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
quadratic_costs:
| first_conduit_segment_id\second_conduit_segment_id | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| 0 | 10.0 | 5.0 | 10.0 | 7.0 |
| 1 | 5.0 | 6.0 | 3.0 | 4.0 |
| 2 | 10.0 | 3.0 | 3.0 | 2.0 |
| 3 | 7.0 | 4.0 | 2.0 | 9.0 |
The installer will use these entries to select the single continuous path with the lowest total cost.

Oh — when you send me the final picked route, just tuck it into a tiny JSON wrapper so it's easy to read and check. Something like this:

{
  ""solution"": []
}

Here ""solution"" is where you'll list the path as a plain sequence of node identifiers, from the panel (source) to the outlet (target), in order. Think of it like filling in a short form: put each node name in the array, left-to-right along the route. This block is just a sketch of the shape I expect, not the actual answer — you'll replace the empty array with the actual node sequence.

Please use the node identifiers exactly as they appear in the instance input — don't rename them or invent new labels. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4], 'edges': [{'from': 3, 'to': 0, 'var_index': 0}, {'from': 2, 'to': 4, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}], 'objective': {'constant': 0.0, 'linear': [1.0, 3.0, 9.0, 9.0], 'quadratic': [[10.0, 5.0, 10.0, 7.0], [5.0, 6.0, 3.0, 4.0], [10.0, 3.0, 3.0, 2.0], [7.0, 4.0, 2.0, 9.0]]}, 'source': 3, 'target': 4}","[3, 0, 1, 2, 4]",112.0,"{'problem_type': 'QSPP', 'num_nodes': 5, 'num_edges': 4, 'nodes': ['A', 'B', 'C', 'D', 'E'], 'source': 'D', 'target': 'E', 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 1.0}, {'var_index': 1, 'linear_cost': 3.0}, {'var_index': 2, 'linear_cost': 9.0}, {'var_index': 3, 'linear_cost': 9.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 9.0}]}, 'edges': [{'from': 'D', 'to': 'A', 'var_index': 0}, {'from': 'C', 'to': 'E', 'var_index': 1}, {'from': 'A', 'to': 'B', 'var_index': 2}, {'from': 'B', 'to': 'C', 'var_index': 3}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E'}}","['D', 'A', 'B', 'C', 'E']",17,nl,names
QSPP,QSPP,"I’m imagining a lazy morning stroll from the city gate to the central plaza where the aim is simple: pick one continuous, one-way route that leaves the walker as comfortable as possible. Every block walked adds some base tiredness, some blocks are steep so they tack on an extra penalty if included, and certain combinations of streets make the walk noticeably worse when they’re both on the same route. The “better” route is just the one that ends up with the smallest total of those things — total base fatigue plus any steep-block penalties plus any extra pairwise awkwardness when two particular blocks are used together. The walk has to be a single, lawful path following the one-way lanes from gate to plaza without skipping or stitching together separate trips. The exact map and numbers are shown below.

Here the map shows 10 locations 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 23 directed blocks, and the walk starts at 8 and ends at 9.
Block 0 runs one-way from 8 to 0.
Block 1 runs one-way from 8 to 1.
Block 2 runs one-way from 8 to 2.
Block 3 runs one-way from 8 to 3.
Block 4 runs one-way from 8 to 4.
Block 5 runs one-way from 8 to 5.
Block 6 runs one-way from 8 to 6.
Block 7 runs one-way from 8 to 7.
Block 8 runs one-way from 0 to 9.
Block 9 runs one-way from 1 to 9.
Block 10 runs one-way from 2 to 9.
Block 11 runs one-way from 3 to 9.
Block 12 runs one-way from 4 to 9.
Block 13 runs one-way from 5 to 9.
Block 14 runs one-way from 6 to 9.
Block 15 runs one-way from 7 to 9.
Block 16 runs one-way from 0 to 1.
Block 17 runs one-way from 1 to 2.
Block 18 runs one-way from 2 to 3.
Block 19 runs one-way from 3 to 4.
Block 20 runs one-way from 4 to 5.
Block 21 runs one-way from 5 to 6.
Block 22 runs one-way from 6 to 7.
Including block 0 adds 5.0 base fatigue.
Including block 1 adds 6.0 base fatigue.
Including block 2 adds 10.0 base fatigue.
Including block 3 adds 3.0 base fatigue.
Including block 4 adds 3.0 base fatigue.
Including block 5 adds 8.0 base fatigue.
Including block 6 adds 7.0 base fatigue.
Including block 7 adds 4.0 base fatigue.
Including block 8 adds 1.0 base fatigue.
Including block 9 adds 4.0 base fatigue.
Including block 10 adds 7.0 base fatigue.
Including block 11 adds 2.0 base fatigue.
Including block 12 adds 8.0 base fatigue.
Including block 13 adds 4.0 base fatigue.
Including block 14 adds 9.0 base fatigue.
Including block 15 adds 3.0 base fatigue.
Including block 16 adds 2.0 base fatigue.
Including block 17 adds 7.0 base fatigue.
Including block 18 adds 5.0 base fatigue.
Including block 19 adds 4.0 base fatigue.
Including block 20 adds 6.0 base fatigue.
Including block 21 adds 5.0 base fatigue.
Including block 22 adds 8.0 base fatigue.
Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (first_block_identifier, second_block_identifier). If two block_identifiers with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
quadratic_costs:
| first_block_identifier\second_block_identifier | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 5.0 | 4.0 | 1.0 | 8.0 | 7.0 | 2.0 | 1.0 | 4.0 | 3.0 | 6.0 | 6.0 | 2.0 | 4.0 | 1.0 | 4.0 | 4.0 | 6.0 | 9.0 | 3.0 | 7.0 | 5.0 | 8.0 | 1.0 |
| 1 | 4.0 | 10.0 | 4.0 | 6.0 | 3.0 | 10.0 | 2.0 | 5.0 | 6.0 | 7.0 | 3.0 | 3.0 | 2.0 | 7.0 | 1.0 | 3.0 | 2.0 | 6.0 | 8.0 | 2.0 | 9.0 | 5.0 | 10.0 |
| 2 | 1.0 | 4.0 | 6.0 | 6.0 | 10.0 | 6.0 | 4.0 | 9.0 | 1.0 | 5.0 | 7.0 | 7.0 | 10.0 | 2.0 | 2.0 | 4.0 | 5.0 | 8.0 | 8.0 | 2.0 | 6.0 | 2.0 | 6.0 |
| 3 | 8.0 | 6.0 | 6.0 | 8.0 | 8.0 | 3.0 | 3.0 | 3.0 | 10.0 | 8.0 | 5.0 | 9.0 | 3.0 | 5.0 | 9.0 | 3.0 | 10.0 | 9.0 | 10.0 | 6.0 | 2.0 | 3.0 | 6.0 |
| 4 | 7.0 | 3.0 | 10.0 | 8.0 | 10.0 | 4.0 | 5.0 | 7.0 | 4.0 | 2.0 | 8.0 | 2.0 | 6.0 | 9.0 | 9.0 | 7.0 | 1.0 | 7.0 | 1.0 | 1.0 | 6.0 | 3.0 | 1.0 |
| 5 | 2.0 | 10.0 | 6.0 | 3.0 | 4.0 | 6.0 | 10.0 | 9.0 | 8.0 | 7.0 | 8.0 | 2.0 | 2.0 | 1.0 | 1.0 | 5.0 | 10.0 | 10.0 | 8.0 | 7.0 | 10.0 | 3.0 | 5.0 |
| 6 | 1.0 | 2.0 | 4.0 | 3.0 | 5.0 | 10.0 | 9.0 | 6.0 | 9.0 | 4.0 | 10.0 | 2.0 | 5.0 | 4.0 | 3.0 | 5.0 | 3.0 | 7.0 | 4.0 | 8.0 | 2.0 | 7.0 | 6.0 |
| 7 | 4.0 | 5.0 | 9.0 | 3.0 | 7.0 | 9.0 | 6.0 | 5.0 | 9.0 | 8.0 | 5.0 | 3.0 | 2.0 | 10.0 | 4.0 | 7.0 | 3.0 | 3.0 | 8.0 | 2.0 | 1.0 | 6.0 | 6.0 |
| 8 | 3.0 | 6.0 | 1.0 | 10.0 | 4.0 | 8.0 | 9.0 | 9.0 | 9.0 | 6.0 | 9.0 | 8.0 | 3.0 | 8.0 | 1.0 | 3.0 | 7.0 | 4.0 | 5.0 | 3.0 | 10.0 | 1.0 | 4.0 |
| 9 | 6.0 | 7.0 | 5.0 | 8.0 | 2.0 | 7.0 | 4.0 | 8.0 | 6.0 | 3.0 | 8.0 | 4.0 | 5.0 | 8.0 | 4.0 | 8.0 | 10.0 | 6.0 | 8.0 | 1.0 | 10.0 | 9.0 | 8.0 |
| 10 | 6.0 | 3.0 | 7.0 | 5.0 | 8.0 | 8.0 | 10.0 | 5.0 | 9.0 | 8.0 | 4.0 | 9.0 | 10.0 | 5.0 | 5.0 | 3.0 | 7.0 | 7.0 | 3.0 | 2.0 | 1.0 | 2.0 | 2.0 |
| 11 | 2.0 | 3.0 | 7.0 | 9.0 | 2.0 | 2.0 | 2.0 | 3.0 | 8.0 | 4.0 | 9.0 | 3.0 | 9.0 | 6.0 | 5.0 | 8.0 | 9.0 | 8.0 | 2.0 | 5.0 | 8.0 | 7.0 | 5.0 |
| 12 | 4.0 | 2.0 | 10.0 | 3.0 | 6.0 | 2.0 | 5.0 | 2.0 | 3.0 | 5.0 | 10.0 | 9.0 | 3.0 | 3.0 | 9.0 | 4.0 | 7.0 | 8.0 | 8.0 | 4.0 | 9.0 | 7.0 | 6.0 |
| 13 | 1.0 | 7.0 | 2.0 | 5.0 | 9.0 | 1.0 | 4.0 | 10.0 | 8.0 | 8.0 | 5.0 | 6.0 | 3.0 | 9.0 | 10.0 | 8.0 | 10.0 | 2.0 | 6.0 | 3.0 | 9.0 | 6.0 | 10.0 |
| 14 | 4.0 | 1.0 | 2.0 | 9.0 | 9.0 | 1.0 | 3.0 | 4.0 | 1.0 | 4.0 | 5.0 | 5.0 | 9.0 | 10.0 | 4.0 | 4.0 | 10.0 | 10.0 | 10.0 | 2.0 | 10.0 | 6.0 | 5.0 |
| 15 | 4.0 | 3.0 | 4.0 | 3.0 | 7.0 | 5.0 | 5.0 | 7.0 | 3.0 | 8.0 | 3.0 | 8.0 | 4.0 | 8.0 | 4.0 | 8.0 | 4.0 | 7.0 | 2.0 | 7.0 | 4.0 | 2.0 | 7.0 |
| 16 | 6.0 | 2.0 | 5.0 | 10.0 | 1.0 | 10.0 | 3.0 | 3.0 | 7.0 | 10.0 | 7.0 | 9.0 | 7.0 | 10.0 | 10.0 | 4.0 | 4.0 | 3.0 | 3.0 | 3.0 | 3.0 | 3.0 | 1.0 |
| 17 | 9.0 | 6.0 | 8.0 | 9.0 | 7.0 | 10.0 | 7.0 | 3.0 | 4.0 | 6.0 | 7.0 | 8.0 | 8.0 | 2.0 | 10.0 | 7.0 | 3.0 | 5.0 | 7.0 | 3.0 | 9.0 | 1.0 | 6.0 |
| 18 | 3.0 | 8.0 | 8.0 | 10.0 | 1.0 | 8.0 | 4.0 | 8.0 | 5.0 | 8.0 | 3.0 | 2.0 | 8.0 | 6.0 | 10.0 | 2.0 | 3.0 | 7.0 | 6.0 | 6.0 | 8.0 | 2.0 | 1.0 |
| 19 | 7.0 | 2.0 | 2.0 | 6.0 | 1.0 | 7.0 | 8.0 | 2.0 | 3.0 | 1.0 | 2.0 | 5.0 | 4.0 | 3.0 | 2.0 | 7.0 | 3.0 | 3.0 | 6.0 | 9.0 | 9.0 | 6.0 | 9.0 |
| 20 | 5.0 | 9.0 | 6.0 | 2.0 | 6.0 | 10.0 | 2.0 | 1.0 | 10.0 | 10.0 | 1.0 | 8.0 | 9.0 | 9.0 | 10.0 | 4.0 | 3.0 | 9.0 | 8.0 | 9.0 | 8.0 | 9.0 | 10.0 |
| 21 | 8.0 | 5.0 | 2.0 | 3.0 | 3.0 | 3.0 | 7.0 | 6.0 | 1.0 | 9.0 | 2.0 | 7.0 | 7.0 | 6.0 | 6.0 | 2.0 | 3.0 | 1.0 | 2.0 | 6.0 | 9.0 | 10.0 | 3.0 |
| 22 | 1.0 | 10.0 | 6.0 | 6.0 | 1.0 | 5.0 | 6.0 | 6.0 | 4.0 | 8.0 | 2.0 | 5.0 | 6.0 | 10.0 | 5.0 | 7.0 | 1.0 | 6.0 | 1.0 | 9.0 | 10.0 | 3.0 | 9.0 |
With those entries below, I’ll pick the single lawful route that minimizes the total fatigue and awkwardness.

While we’re at it, it’s handy to tuck the final path into a tiny JSON snippet so whatever reads this can pick it up easily — nothing fancy, just the shape below.

{
  ""solution"": []
}

Think of ""solution"" as the list where you’ll put the nodes in order from the city gate (source) to the central plaza (target). Keep it simple: an ordered array of NODE identifiers only, one after the other, like a little map trail. This JSON is just a sketch of the shape I want back, not the actual path answer itself.

Please be sure to use the node identifiers exactly as they appear in the instance input — don’t rename them or invent new labels.
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 'edges': [{'from': 8, 'to': 0, 'var_index': 0}, {'from': 8, 'to': 1, 'var_index': 1}, {'from': 8, 'to': 2, 'var_index': 2}, {'from': 8, 'to': 3, 'var_index': 3}, {'from': 8, 'to': 4, 'var_index': 4}, {'from': 8, 'to': 5, 'var_index': 5}, {'from': 8, 'to': 6, 'var_index': 6}, {'from': 8, 'to': 7, 'var_index': 7}, {'from': 0, 'to': 9, 'var_index': 8}, {'from': 1, 'to': 9, 'var_index': 9}, {'from': 2, 'to': 9, 'var_index': 10}, {'from': 3, 'to': 9, 'var_index': 11}, {'from': 4, 'to': 9, 'var_index': 12}, {'from': 5, 'to': 9, 'var_index': 13}, {'from': 6, 'to': 9, 'var_index': 14}, {'from': 7, 'to': 9, 'var_index': 15}, {'from': 0, 'to': 1, 'var_index': 16}, {'from': 1, 'to': 2, 'var_index': 17}, {'from': 2, 'to': 3, 'var_index': 18}, {'from': 3, 'to': 4, 'var_index': 19}, {'from': 4, 'to': 5, 'var_index': 20}, {'from': 5, 'to': 6, 'var_index': 21}, {'from': 6, 'to': 7, 'var_index': 22}], 'objective': {'constant': 0.0, 'linear': [5.0, 6.0, 10.0, 3.0, 3.0, 8.0, 7.0, 4.0, 1.0, 4.0, 7.0, 2.0, 8.0, 4.0, 9.0, 3.0, 2.0, 7.0, 5.0, 4.0, 6.0, 5.0, 8.0], 'quadratic': [[5.0, 4.0, 1.0, 8.0, 7.0, 2.0, 1.0, 4.0, 3.0, 6.0, 6.0, 2.0, 4.0, 1.0, 4.0, 4.0, 6.0, 9.0, 3.0, 7.0, 5.0, 8.0, 1.0], [4.0, 10.0, 4.0, 6.0, 3.0, 10.0, 2.0, 5.0, 6.0, 7.0, 3.0, 3.0, 2.0, 7.0, 1.0, 3.0, 2.0, 6.0, 8.0, 2.0, 9.0, 5.0, 10.0], [1.0, 4.0, 6.0, 6.0, 10.0, 6.0, 4.0, 9.0, 1.0, 5.0, 7.0, 7.0, 10.0, 2.0, 2.0, 4.0, 5.0, 8.0, 8.0, 2.0, 6.0, 2.0, 6.0], [8.0, 6.0, 6.0, 8.0, 8.0, 3.0, 3.0, 3.0, 10.0, 8.0, 5.0, 9.0, 3.0, 5.0, 9.0, 3.0, 10.0, 9.0, 10.0, 6.0, 2.0, 3.0, 6.0], [7.0, 3.0, 10.0, 8.0, 10.0, 4.0, 5.0, 7.0, 4.0, 2.0, 8.0, 2.0, 6.0, 9.0, 9.0, 7.0, 1.0, 7.0, 1.0, 1.0, 6.0, 3.0, 1.0], [2.0, 10.0, 6.0, 3.0, 4.0, 6.0, 10.0, 9.0, 8.0, 7.0, 8.0, 2.0, 2.0, 1.0, 1.0, 5.0, 10.0, 10.0, 8.0, 7.0, 10.0, 3.0, 5.0], [1.0, 2.0, 4.0, 3.0, 5.0, 10.0, 9.0, 6.0, 9.0, 4.0, 10.0, 2.0, 5.0, 4.0, 3.0, 5.0, 3.0, 7.0, 4.0, 8.0, 2.0, 7.0, 6.0], [4.0, 5.0, 9.0, 3.0, 7.0, 9.0, 6.0, 5.0, 9.0, 8.0, 5.0, 3.0, 2.0, 10.0, 4.0, 7.0, 3.0, 3.0, 8.0, 2.0, 1.0, 6.0, 6.0], [3.0, 6.0, 1.0, 10.0, 4.0, 8.0, 9.0, 9.0, 9.0, 6.0, 9.0, 8.0, 3.0, 8.0, 1.0, 3.0, 7.0, 4.0, 5.0, 3.0, 10.0, 1.0, 4.0], [6.0, 7.0, 5.0, 8.0, 2.0, 7.0, 4.0, 8.0, 6.0, 3.0, 8.0, 4.0, 5.0, 8.0, 4.0, 8.0, 10.0, 6.0, 8.0, 1.0, 10.0, 9.0, 8.0], [6.0, 3.0, 7.0, 5.0, 8.0, 8.0, 10.0, 5.0, 9.0, 8.0, 4.0, 9.0, 10.0, 5.0, 5.0, 3.0, 7.0, 7.0, 3.0, 2.0, 1.0, 2.0, 2.0], [2.0, 3.0, 7.0, 9.0, 2.0, 2.0, 2.0, 3.0, 8.0, 4.0, 9.0, 3.0, 9.0, 6.0, 5.0, 8.0, 9.0, 8.0, 2.0, 5.0, 8.0, 7.0, 5.0], [4.0, 2.0, 10.0, 3.0, 6.0, 2.0, 5.0, 2.0, 3.0, 5.0, 10.0, 9.0, 3.0, 3.0, 9.0, 4.0, 7.0, 8.0, 8.0, 4.0, 9.0, 7.0, 6.0], [1.0, 7.0, 2.0, 5.0, 9.0, 1.0, 4.0, 10.0, 8.0, 8.0, 5.0, 6.0, 3.0, 9.0, 10.0, 8.0, 10.0, 2.0, 6.0, 3.0, 9.0, 6.0, 10.0], [4.0, 1.0, 2.0, 9.0, 9.0, 1.0, 3.0, 4.0, 1.0, 4.0, 5.0, 5.0, 9.0, 10.0, 4.0, 4.0, 10.0, 10.0, 10.0, 2.0, 10.0, 6.0, 5.0], [4.0, 3.0, 4.0, 3.0, 7.0, 5.0, 5.0, 7.0, 3.0, 8.0, 3.0, 8.0, 4.0, 8.0, 4.0, 8.0, 4.0, 7.0, 2.0, 7.0, 4.0, 2.0, 7.0], [6.0, 2.0, 5.0, 10.0, 1.0, 10.0, 3.0, 3.0, 7.0, 10.0, 7.0, 9.0, 7.0, 10.0, 10.0, 4.0, 4.0, 3.0, 3.0, 3.0, 3.0, 3.0, 1.0], [9.0, 6.0, 8.0, 9.0, 7.0, 10.0, 7.0, 3.0, 4.0, 6.0, 7.0, 8.0, 8.0, 2.0, 10.0, 7.0, 3.0, 5.0, 7.0, 3.0, 9.0, 1.0, 6.0], [3.0, 8.0, 8.0, 10.0, 1.0, 8.0, 4.0, 8.0, 5.0, 8.0, 3.0, 2.0, 8.0, 6.0, 10.0, 2.0, 3.0, 7.0, 6.0, 6.0, 8.0, 2.0, 1.0], [7.0, 2.0, 2.0, 6.0, 1.0, 7.0, 8.0, 2.0, 3.0, 1.0, 2.0, 5.0, 4.0, 3.0, 2.0, 7.0, 3.0, 3.0, 6.0, 9.0, 9.0, 6.0, 9.0], [5.0, 9.0, 6.0, 2.0, 6.0, 10.0, 2.0, 1.0, 10.0, 10.0, 1.0, 8.0, 9.0, 9.0, 10.0, 4.0, 3.0, 9.0, 8.0, 9.0, 8.0, 9.0, 10.0], [8.0, 5.0, 2.0, 3.0, 3.0, 3.0, 7.0, 6.0, 1.0, 9.0, 2.0, 7.0, 7.0, 6.0, 6.0, 2.0, 3.0, 1.0, 2.0, 6.0, 9.0, 10.0, 3.0], [1.0, 10.0, 6.0, 6.0, 1.0, 5.0, 6.0, 6.0, 4.0, 8.0, 2.0, 5.0, 6.0, 10.0, 5.0, 7.0, 1.0, 6.0, 1.0, 9.0, 10.0, 3.0, 9.0]]}, 'source': 8, 'target': 9}","[8, 0, 9]",26.0,"{'problem_type': 'QSPP', 'num_nodes': 10, 'num_edges': 23, 'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 'source': 8, 'target': 9, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 5.0}, {'var_index': 1, 'linear_cost': 6.0}, {'var_index': 2, 'linear_cost': 10.0}, {'var_index': 3, 'linear_cost': 3.0}, {'var_index': 4, 'linear_cost': 3.0}, {'var_index': 5, 'linear_cost': 8.0}, {'var_index': 6, 'linear_cost': 7.0}, {'var_index': 7, 'linear_cost': 4.0}, {'var_index': 8, 'linear_cost': 1.0}, {'var_index': 9, 'linear_cost': 4.0}, {'var_index': 10, 'linear_cost': 7.0}, {'var_index': 11, 'linear_cost': 2.0}, {'var_index': 12, 'linear_cost': 8.0}, {'var_index': 13, 'linear_cost': 4.0}, {'var_index': 14, 'linear_cost': 9.0}, {'var_index': 15, 'linear_cost': 3.0}, {'var_index': 16, 'linear_cost': 2.0}, {'var_index': 17, 'linear_cost': 7.0}, {'var_index': 18, 'linear_cost': 5.0}, {'var_index': 19, 'linear_cost': 4.0}, {'var_index': 20, 'linear_cost': 6.0}, {'var_index': 21, 'linear_cost': 5.0}, {'var_index': 22, 'linear_cost': 8.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 12, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 13, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 14, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 15, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 16, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 17, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 18, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 19, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 20, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 21, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 22, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 12, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 13, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 14, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 15, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 17, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 18, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 19, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 20, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 21, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 22, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 12, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 14, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 15, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 16, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 17, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 18, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 19, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 20, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 21, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 22, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 13, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 15, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 16, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 17, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 18, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 19, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 20, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 21, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 22, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 4, 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10.0}, {'var_i': 16, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 16, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 16, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 16, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 16, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 16, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 16, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 16, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 16, 'var_j': 14, 'quadratic_cost': 10.0}, {'var_i': 16, 'var_j': 15, 'quadratic_cost': 4.0}, {'var_i': 16, 'var_j': 16, 'quadratic_cost': 4.0}, {'var_i': 16, 'var_j': 17, 'quadratic_cost': 3.0}, {'var_i': 16, 'var_j': 18, 'quadratic_cost': 3.0}, {'var_i': 16, 'var_j': 19, 'quadratic_cost': 3.0}, {'var_i': 16, 'var_j': 20, 'quadratic_cost': 3.0}, {'var_i': 16, 'var_j': 21, 'quadratic_cost': 3.0}, {'var_i': 16, 'var_j': 22, 'quadratic_cost': 1.0}, {'var_i': 17, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 17, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 17, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 17, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 17, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 17, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 17, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 17, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 17, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 17, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 17, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 17, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 17, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 17, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 17, 'var_j': 14, 'quadratic_cost': 10.0}, {'var_i': 17, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 17, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 17, 'var_j': 17, 'quadratic_cost': 5.0}, {'var_i': 17, 'var_j': 18, 'quadratic_cost': 7.0}, {'var_i': 17, 'var_j': 19, 'quadratic_cost': 3.0}, {'var_i': 17, 'var_j': 20, 'quadratic_cost': 9.0}, {'var_i': 17, 'var_j': 21, 'quadratic_cost': 1.0}, {'var_i': 17, 'var_j': 22, 'quadratic_cost': 6.0}, {'var_i': 18, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 18, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 18, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 18, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 18, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 18, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 18, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 18, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 18, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 18, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 18, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 18, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 18, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 18, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 18, 'var_j': 14, 'quadratic_cost': 10.0}, {'var_i': 18, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 18, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 18, 'var_j': 17, 'quadratic_cost': 7.0}, {'var_i': 18, 'var_j': 18, 'quadratic_cost': 6.0}, {'var_i': 18, 'var_j': 19, 'quadratic_cost': 6.0}, {'var_i': 18, 'var_j': 20, 'quadratic_cost': 8.0}, {'var_i': 18, 'var_j': 21, 'quadratic_cost': 2.0}, {'var_i': 18, 'var_j': 22, 'quadratic_cost': 1.0}, {'var_i': 19, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 19, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 19, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 19, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 19, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 19, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 19, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 19, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 19, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 19, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 19, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 19, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 19, 'var_j': 12, 'quadratic_cost': 4.0}, {'var_i': 19, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 19, 'var_j': 14, 'quadratic_cost': 2.0}, {'var_i': 19, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 19, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 19, 'var_j': 17, 'quadratic_cost': 3.0}, {'var_i': 19, 'var_j': 18, 'quadratic_cost': 6.0}, {'var_i': 19, 'var_j': 19, 'quadratic_cost': 9.0}, {'var_i': 19, 'var_j': 20, 'quadratic_cost': 9.0}, {'var_i': 19, 'var_j': 21, 'quadratic_cost': 6.0}, {'var_i': 19, 'var_j': 22, 'quadratic_cost': 9.0}, {'var_i': 20, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 20, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 20, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 20, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 20, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 20, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 20, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 20, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 20, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 20, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 20, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 20, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 20, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 20, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 20, 'var_j': 14, 'quadratic_cost': 10.0}, {'var_i': 20, 'var_j': 15, 'quadratic_cost': 4.0}, {'var_i': 20, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 20, 'var_j': 17, 'quadratic_cost': 9.0}, {'var_i': 20, 'var_j': 18, 'quadratic_cost': 8.0}, {'var_i': 20, 'var_j': 19, 'quadratic_cost': 9.0}, {'var_i': 20, 'var_j': 20, 'quadratic_cost': 8.0}, {'var_i': 20, 'var_j': 21, 'quadratic_cost': 9.0}, {'var_i': 20, 'var_j': 22, 'quadratic_cost': 10.0}, {'var_i': 21, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 21, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 21, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 21, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 21, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 21, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 21, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 21, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 21, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 21, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 21, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 21, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 21, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 21, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 21, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 21, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 21, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 21, 'var_j': 17, 'quadratic_cost': 1.0}, {'var_i': 21, 'var_j': 18, 'quadratic_cost': 2.0}, {'var_i': 21, 'var_j': 19, 'quadratic_cost': 6.0}, {'var_i': 21, 'var_j': 20, 'quadratic_cost': 9.0}, {'var_i': 21, 'var_j': 21, 'quadratic_cost': 10.0}, {'var_i': 21, 'var_j': 22, 'quadratic_cost': 3.0}, {'var_i': 22, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 22, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 22, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 22, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 22, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 22, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 22, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 22, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 22, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 22, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 22, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 22, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 22, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 22, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 22, 'var_j': 14, 'quadratic_cost': 5.0}, {'var_i': 22, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 22, 'var_j': 16, 'quadratic_cost': 1.0}, {'var_i': 22, 'var_j': 17, 'quadratic_cost': 6.0}, {'var_i': 22, 'var_j': 18, 'quadratic_cost': 1.0}, {'var_i': 22, 'var_j': 19, 'quadratic_cost': 9.0}, {'var_i': 22, 'var_j': 20, 'quadratic_cost': 10.0}, {'var_i': 22, 'var_j': 21, 'quadratic_cost': 3.0}, {'var_i': 22, 'var_j': 22, 'quadratic_cost': 9.0}]}, 'edges': [{'from': 8, 'to': 0, 'var_index': 0}, {'from': 8, 'to': 1, 'var_index': 1}, {'from': 8, 'to': 2, 'var_index': 2}, {'from': 8, 'to': 3, 'var_index': 3}, {'from': 8, 'to': 4, 'var_index': 4}, {'from': 8, 'to': 5, 'var_index': 5}, {'from': 8, 'to': 6, 'var_index': 6}, {'from': 8, 'to': 7, 'var_index': 7}, {'from': 0, 'to': 9, 'var_index': 8}, {'from': 1, 'to': 9, 'var_index': 9}, {'from': 2, 'to': 9, 'var_index': 10}, {'from': 3, 'to': 9, 'var_index': 11}, {'from': 4, 'to': 9, 'var_index': 12}, {'from': 5, 'to': 9, 'var_index': 13}, {'from': 6, 'to': 9, 'var_index': 14}, {'from': 7, 'to': 9, 'var_index': 15}, {'from': 0, 'to': 1, 'var_index': 16}, {'from': 1, 'to': 2, 'var_index': 17}, {'from': 2, 'to': 3, 'var_index': 18}, {'from': 3, 'to': 4, 'var_index': 19}, {'from': 4, 'to': 5, 'var_index': 20}, {'from': 5, 'to': 6, 'var_index': 21}, {'from': 6, 'to': 7, 'var_index': 22}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7, 8: 8, 9: 9}}","[8, 0, 9]",18,nl,0
QSPP,QSPP,"I walk the factory floor in my head: the inspector needs to pick one straight route from the start station to the final station that follows the conveyor flow, stepping only along the allowed connections. The “best” route is simply the one that ends up taking the least total time — that total is built from the travel time along each link, the setup time every time a station is inspected, and extra slowdowns that kick in when certain pairs of stations are both on the route (sometimes the order matters). The route has to be a single continuous path from the beginning to the end with no invented shortcuts, and the exact station map and times will be shown below.

{
  ""total_stations"": 8,
  ""total_transitions"": 7,
  ""station_ids"": [
    ""A"",
    ""B"",
    ""C"",
    ""D"",
    ""E"",
    ""F"",
    ""G"",
    ""H""
  ],
  ""start_station"": ""G"",
  ""final_station"": ""H"",
  ""edges"": [
    {
      ""transition_from_station"": ""G"",
      ""transition_to_station"": ""A"",
      ""transition_id"": 0
    },
    {
      ""transition_from_station"": ""F"",
      ""transition_to_station"": ""H"",
      ""transition_id"": 1
    },
    {
      ""transition_from_station"": ""A"",
      ""transition_to_station"": ""B"",
      ""transition_id"": 2
    },
    {
      ""transition_from_station"": ""B"",
      ""transition_to_station"": ""C"",
      ""transition_id"": 3
    },
    {
      ""transition_from_station"": ""C"",
      ""transition_to_station"": ""D"",
      ""transition_id"": 4
    },
    {
      ""transition_from_station"": ""D"",
      ""transition_to_station"": ""E"",
      ""transition_id"": 5
    },
    {
      ""transition_from_station"": ""E"",
      ""transition_to_station"": ""F"",
      ""transition_id"": 6
    }
  ],
  ""linear_costs"": [
    {
      ""transition_id"": 0,
      ""transition_base_time"": 1.0
    },
    {
      ""transition_id"": 1,
      ""transition_base_time"": 2.0
    },
    {
      ""transition_id"": 2,
      ""transition_base_time"": 3.0
    },
    {
      ""transition_id"": 3,
      ""transition_base_time"": 5.0
    },
    {
      ""transition_id"": 4,
      ""transition_base_time"": 8.0
    },
    {
      ""transition_id"": 5,
      ""transition_base_time"": 8.0
    },
    {
      ""transition_id"": 6,
      ""transition_base_time"": 3.0
    }
  ]
}

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (transition_i_id, transition_j_id). If two transitions with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| transition_i_id\transition_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| 0 | 4.0 | 7.0 | 6.0 | 10.0 | 7.0 | 1.0 | 9.0 |
| 1 | 7.0 | 2.0 | 7.0 | 3.0 | 5.0 | 7.0 | 9.0 |
| 2 | 6.0 | 7.0 | 3.0 | 10.0 | 4.0 | 8.0 | 8.0 |
| 3 | 10.0 | 3.0 | 10.0 | 7.0 | 8.0 | 4.0 | 4.0 |
| 4 | 7.0 | 5.0 | 4.0 | 8.0 | 2.0 | 5.0 | 1.0 |
| 5 | 1.0 | 7.0 | 8.0 | 4.0 | 5.0 | 6.0 | 10.0 |
| 6 | 9.0 | 9.0 | 8.0 | 4.0 | 1.0 | 10.0 | 5.0 |

Also, when you hand me the chosen route, tuck it into a tiny JSON envelope like this — nice and simple:

{
  ""solution"": []
}

""solution"" should be an array holding the node identifiers in order, from the start station to the final station. Think of it like filling in a short form: just list the station names (nodes) you walk through, in sequence. This block is only a sketch of the expected shape, not the actual answer itself.

Please use the node identifiers exactly as they appear in the instance input — do not rename them or introduce new labels, and do not include any edge IDs or cost tags (only node names belong in the path). 

Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7], 'edges': [{'from': 6, 'to': 0, 'var_index': 0}, {'from': 5, 'to': 7, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 4, 'to': 5, 'var_index': 6}], 'objective': {'constant': 0.0, 'linear': [1.0, 2.0, 3.0, 5.0, 8.0, 8.0, 3.0], 'quadratic': [[4.0, 7.0, 6.0, 10.0, 7.0, 1.0, 9.0], [7.0, 2.0, 7.0, 3.0, 5.0, 7.0, 9.0], [6.0, 7.0, 3.0, 10.0, 4.0, 8.0, 8.0], [10.0, 3.0, 10.0, 7.0, 8.0, 4.0, 4.0], [7.0, 5.0, 4.0, 8.0, 2.0, 5.0, 1.0], [1.0, 7.0, 8.0, 4.0, 5.0, 6.0, 10.0], [9.0, 9.0, 8.0, 4.0, 1.0, 10.0, 5.0]]}, 'source': 6, 'target': 7}","[6, 0, 1, 2, 3, 4, 5, 7]",325.0,"{'problem_type': 'QSPP', 'num_nodes': 8, 'num_edges': 7, 'nodes': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H'], 'source': 'G', 'target': 'H', 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 1.0}, {'var_index': 1, 'linear_cost': 2.0}, {'var_index': 2, 'linear_cost': 3.0}, {'var_index': 3, 'linear_cost': 5.0}, {'var_index': 4, 'linear_cost': 8.0}, {'var_index': 5, 'linear_cost': 8.0}, {'var_index': 6, 'linear_cost': 3.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 5.0}]}, 'edges': [{'from': 'G', 'to': 'A', 'var_index': 0}, {'from': 'F', 'to': 'H', 'var_index': 1}, {'from': 'A', 'to': 'B', 'var_index': 2}, {'from': 'B', 'to': 'C', 'var_index': 3}, {'from': 'C', 'to': 'D', 'var_index': 4}, {'from': 'D', 'to': 'E', 'var_index': 5}, {'from': 'E', 'to': 'F', 'var_index': 6}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E', 5: 'F', 6: 'G', 7: 'H'}}","['G', 'A', 'B', 'C', 'D', 'E', 'F', 'H']",19,json,names
QSPP,QSPP,"I need to map out one straight course sequence that starts at the intro seminar and ends at the capstone, following every prerequisite link like stepping stones. The plan is to pick a single chain of classes — no detours, no doubling back, no taking extra courses off the path — and for each class count its normal workload plus the admin fee that comes with signing up. Also watch out: some pairs of classes create extra friction when they’re both taken (and a few classes carry a little extra burden just by themselves), so the total effort is the sum of all those per-course loads and fees plus any extra pairwise difficulties. The goal is to make that total as small as possible. Concrete details about the courses, fees, and pairwise frictions are shown below.

# total_courses=7
# total_prereq_links=6
# course_node_ids=0, 1, 2, 3, 4, 5, 6
# intro_seminar_course=5
# capstone_course=6

prereq_from_course,prereq_to_course,prereq_link_id
5,0,0
4,6,1
0,1,2
1,2,3
2,3,4
3,4,5

prereq_link_id,course_workload_plus_admin_fee
0,7.0
1,1.0
2,9.0
3,10.0
4,8.0
5,5.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (prereq_link_i_id, prereq_link_j_id). If two prereq_links with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| prereq_link_i_id\prereq_link_j_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 1.0 | 4.0 | 7.0 | 1.0 | 1.0 | 3.0 |
| 1 | 4.0 | 3.0 | 5.0 | 9.0 | 5.0 | 7.0 |
| 2 | 7.0 | 5.0 | 2.0 | 4.0 | 9.0 | 1.0 |
| 3 | 1.0 | 9.0 | 4.0 | 4.0 | 6.0 | 9.0 |
| 4 | 1.0 | 5.0 | 9.0 | 6.0 | 6.0 | 10.0 |
| 5 | 3.0 | 7.0 | 1.0 | 9.0 | 10.0 | 8.0 |

Also, to keep things machine-friendly, please put the chosen course chain into a tiny JSON snippet like this:

{
  ""solution"": []
}

Here, ""solution"" should be a list of NODE identifiers only — the sequence of classes from the intro seminar to the capstone, in order. Think of it as a simple form: replace the empty array with the ordered list of nodes you picked. Don’t include any edge IDs, costs, or extra labels — just the node names, and make sure each consecutive pair is a real directed prerequisite link.

This JSON is just a sketch of the shape I expect, not the final answer itself. Also, use the identifiers exactly as they appear in the instance input — no renaming and no new labels. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6], 'edges': [{'from': 5, 'to': 0, 'var_index': 0}, {'from': 4, 'to': 6, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}], 'objective': {'constant': 0.0, 'linear': [7.0, 1.0, 9.0, 10.0, 8.0, 5.0], 'quadratic': [[1.0, 4.0, 7.0, 1.0, 1.0, 3.0], [4.0, 3.0, 5.0, 9.0, 5.0, 7.0], [7.0, 5.0, 2.0, 4.0, 9.0, 1.0], [1.0, 9.0, 4.0, 4.0, 6.0, 9.0], [1.0, 5.0, 9.0, 6.0, 6.0, 10.0], [3.0, 7.0, 1.0, 9.0, 10.0, 8.0]]}, 'source': 5, 'target': 6}","[5, 0, 1, 2, 3, 4, 6]",226.0,"{'problem_type': 'QSPP', 'num_nodes': 7, 'num_edges': 6, 'nodes': [0, 1, 2, 3, 4, 5, 6], 'source': 5, 'target': 6, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 7.0}, {'var_index': 1, 'linear_cost': 1.0}, {'var_index': 2, 'linear_cost': 9.0}, {'var_index': 3, 'linear_cost': 10.0}, {'var_index': 4, 'linear_cost': 8.0}, {'var_index': 5, 'linear_cost': 5.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 8.0}]}, 'edges': [{'from': 5, 'to': 0, 'var_index': 0}, {'from': 4, 'to': 6, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6}}","[5, 0, 1, 2, 3, 4, 6]",20,csv,0
QSPP,QSPP,"Someone made a map of one-way streets between home and the office and wants to pick exactly one route that keeps the total charges down. Every street on that map has a base toll; on top of that, certain street combinations trigger additional fees when both are used, and some streets can add a bit extra on their own. To judge any route, add together all the street tolls along it and then add any extra combination fees that apply — the lower the total, the better. The chosen route must follow actual one-way connections from the home node to the office node in order; the specific streets and their costs are listed below.

{
  ""total_intersections"": 8,
  ""total_one_way_streets"": 7,
  ""intersections"": [
    ""A"",
    ""B"",
    ""C"",
    ""D"",
    ""E"",
    ""F"",
    ""G"",
    ""H""
  ],
  ""home_intersection"": ""G"",
  ""office_intersection"": ""H"",
  ""edges"": [
    {
      ""street_from_intersection"": ""G"",
      ""street_to_intersection"": ""A"",
      ""street_id"": 0
    },
    {
      ""street_from_intersection"": ""F"",
      ""street_to_intersection"": ""H"",
      ""street_id"": 1
    },
    {
      ""street_from_intersection"": ""A"",
      ""street_to_intersection"": ""B"",
      ""street_id"": 2
    },
    {
      ""street_from_intersection"": ""B"",
      ""street_to_intersection"": ""C"",
      ""street_id"": 3
    },
    {
      ""street_from_intersection"": ""C"",
      ""street_to_intersection"": ""D"",
      ""street_id"": 4
    },
    {
      ""street_from_intersection"": ""D"",
      ""street_to_intersection"": ""E"",
      ""street_id"": 5
    },
    {
      ""street_from_intersection"": ""E"",
      ""street_to_intersection"": ""F"",
      ""street_id"": 6
    }
  ],
  ""linear_costs"": [
    {
      ""street_id_ref"": 0,
      ""base_toll"": 2.0
    },
    {
      ""street_id_ref"": 1,
      ""base_toll"": 9.0
    },
    {
      ""street_id_ref"": 2,
      ""base_toll"": 4.0
    },
    {
      ""street_id_ref"": 3,
      ""base_toll"": 2.0
    },
    {
      ""street_id_ref"": 4,
      ""base_toll"": 2.0
    },
    {
      ""street_id_ref"": 5,
      ""base_toll"": 6.0
    },
    {
      ""street_id_ref"": 6,
      ""base_toll"": 7.0
    }
  ]
}

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (street_i_ref, street_j_ref). If two streets with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| street_i_ref\street_j_ref | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| 0 | 3.0 | 10.0 | 8.0 | 9.0 | 7.0 | 1.0 | 1.0 |
| 1 | 10.0 | 10.0 | 4.0 | 6.0 | 7.0 | 3.0 | 9.0 |
| 2 | 8.0 | 4.0 | 4.0 | 4.0 | 9.0 | 1.0 | 9.0 |
| 3 | 9.0 | 6.0 | 4.0 | 7.0 | 2.0 | 7.0 | 2.0 |
| 4 | 7.0 | 7.0 | 9.0 | 2.0 | 3.0 | 1.0 | 1.0 |
| 5 | 1.0 | 3.0 | 1.0 | 7.0 | 1.0 | 9.0 | 4.0 |
| 6 | 1.0 | 9.0 | 9.0 | 2.0 | 1.0 | 4.0 | 1.0 |

If you want to hand me the route, just stick it in this simple JSON shape so I can read it easily:

{
  ""solution"": []
}

Think of ""solution"" as the place to list the route: a straight sequence of node identifiers (the home node first, the office node last), with each consecutive pair connected by an actual one-way street. This JSON is just a sketch of the expected shape — not your final answer — so replace that empty array with the path when you're ready.

Please use the node identifiers exactly as they appear in the instance input — don't rename them or invent new labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7], 'edges': [{'from': 6, 'to': 0, 'var_index': 0}, {'from': 5, 'to': 7, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 4, 'to': 5, 'var_index': 6}], 'objective': {'constant': 0.0, 'linear': [2.0, 9.0, 4.0, 2.0, 2.0, 6.0, 7.0], 'quadratic': [[3.0, 10.0, 8.0, 9.0, 7.0, 1.0, 1.0], [10.0, 10.0, 4.0, 6.0, 7.0, 3.0, 9.0], [8.0, 4.0, 4.0, 4.0, 9.0, 1.0, 9.0], [9.0, 6.0, 4.0, 7.0, 2.0, 7.0, 2.0], [7.0, 7.0, 9.0, 2.0, 3.0, 1.0, 1.0], [1.0, 3.0, 1.0, 7.0, 1.0, 9.0, 4.0], [1.0, 9.0, 9.0, 2.0, 1.0, 4.0, 1.0]]}, 'source': 6, 'target': 7}","[6, 0, 1, 2, 3, 4, 5, 7]",279.0,"{'problem_type': 'QSPP', 'num_nodes': 8, 'num_edges': 7, 'nodes': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H'], 'source': 'G', 'target': 'H', 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 2.0}, {'var_index': 1, 'linear_cost': 9.0}, {'var_index': 2, 'linear_cost': 4.0}, {'var_index': 3, 'linear_cost': 2.0}, {'var_index': 4, 'linear_cost': 2.0}, {'var_index': 5, 'linear_cost': 6.0}, {'var_index': 6, 'linear_cost': 7.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 1.0}]}, 'edges': [{'from': 'G', 'to': 'A', 'var_index': 0}, {'from': 'F', 'to': 'H', 'var_index': 1}, {'from': 'A', 'to': 'B', 'var_index': 2}, {'from': 'B', 'to': 'C', 'var_index': 3}, {'from': 'C', 'to': 'D', 'var_index': 4}, {'from': 'D', 'to': 'E', 'var_index': 5}, {'from': 'E', 'to': 'F', 'var_index': 6}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E', 5: 'F', 6: 'G', 7: 'H'}}","['G', 'A', 'B', 'C', 'D', 'E', 'F', 'H']",21,json,names
QSPP,QSPP,"Someone arranged the day so a driver has to pick one continuous path from the warehouse to a customer, obeying one-way streets. Every hop along the road schedule has a base fuel cost, and there are extra little penalties: some that apply just for taking a particular hop, and others that only come into play when two specific hops are both included (both directions of such a pair can contribute their own penalty if both hops are used). The smartest single-route choice is the one with the lowest total bill — get that bill by summing each hop’s fuel cost and then adding any applicable single-hop and pairwise penalties. The trip must be a single, legal one-way sequence from the warehouse to the customer, listed as the intersections encountered; the concrete map and cost figures are shown below.

# total_intersections=10
# total_one_way_segments=9
# intersection_list=A, B, C, D, E, F, G, H, I, J
# warehouse_intersection=I
# customer_intersection=J

segment_from,segment_to,segment_id
I,A,0
H,J,1
A,B,2
B,C,3
C,D,4
D,E,5
E,F,6
F,G,7
G,H,8

segment_id,fuel_cost
0,2.0
1,5.0
2,10.0
3,8.0
4,7.0
5,1.0
6,2.0
7,6.0
8,8.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (segment_i_id, segment_j_id). If two segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| segment_i_id\segment_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|---|
| 0 | 3.0 | 6.0 | 3.0 | 7.0 | 9.0 | 8.0 | 9.0 | 8.0 | 7.0 |
| 1 | 6.0 | 5.0 | 9.0 | 6.0 | 10.0 | 7.0 | 6.0 | 3.0 | 1.0 |
| 2 | 3.0 | 9.0 | 3.0 | 4.0 | 8.0 | 1.0 | 9.0 | 8.0 | 8.0 |
| 3 | 7.0 | 6.0 | 4.0 | 2.0 | 3.0 | 6.0 | 6.0 | 4.0 | 2.0 |
| 4 | 9.0 | 10.0 | 8.0 | 3.0 | 10.0 | 6.0 | 6.0 | 8.0 | 7.0 |
| 5 | 8.0 | 7.0 | 1.0 | 6.0 | 6.0 | 10.0 | 5.0 | 5.0 | 3.0 |
| 6 | 9.0 | 6.0 | 9.0 | 6.0 | 6.0 | 5.0 | 3.0 | 10.0 | 2.0 |
| 7 | 8.0 | 3.0 | 8.0 | 4.0 | 8.0 | 5.0 | 10.0 | 6.0 | 9.0 |
| 8 | 7.0 | 1.0 | 8.0 | 2.0 | 7.0 | 3.0 | 2.0 | 9.0 | 9.0 |

Also, when you send back the final chosen route, please put it in a tiny JSON snippet so it's easy to parse — just this shape:

{
  ""solution"": []
}

Here ""solution"" is meant to hold the ordered list of intersections (node names) you travel through, starting at the warehouse and ending at the customer. Keep it simple and human-friendly: just the nodes in order, nothing else. This JSON is just the sketch of the shape I expect, not the actual route.

Please be sure to use the exact identifiers given in the instance input — don't rename or invent labels. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 'edges': [{'from': 8, 'to': 0, 'var_index': 0}, {'from': 7, 'to': 9, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 4, 'to': 5, 'var_index': 6}, {'from': 5, 'to': 6, 'var_index': 7}, {'from': 6, 'to': 7, 'var_index': 8}], 'objective': {'constant': 0.0, 'linear': [2.0, 5.0, 10.0, 8.0, 7.0, 1.0, 2.0, 6.0, 8.0], 'quadratic': [[3.0, 6.0, 3.0, 7.0, 9.0, 8.0, 9.0, 8.0, 7.0], [6.0, 5.0, 9.0, 6.0, 10.0, 7.0, 6.0, 3.0, 1.0], [3.0, 9.0, 3.0, 4.0, 8.0, 1.0, 9.0, 8.0, 8.0], [7.0, 6.0, 4.0, 2.0, 3.0, 6.0, 6.0, 4.0, 2.0], [9.0, 10.0, 8.0, 3.0, 10.0, 6.0, 6.0, 8.0, 7.0], [8.0, 7.0, 1.0, 6.0, 6.0, 10.0, 5.0, 5.0, 3.0], [9.0, 6.0, 9.0, 6.0, 6.0, 5.0, 3.0, 10.0, 2.0], [8.0, 3.0, 8.0, 4.0, 8.0, 5.0, 10.0, 6.0, 9.0], [7.0, 1.0, 8.0, 2.0, 7.0, 3.0, 2.0, 9.0, 9.0]]}, 'source': 8, 'target': 9}","[8, 0, 1, 2, 3, 4, 5, 6, 7, 9]",538.0,"{'problem_type': 'QSPP', 'num_nodes': 10, 'num_edges': 9, 'nodes': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J'], 'source': 'I', 'target': 'J', 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 2.0}, {'var_index': 1, 'linear_cost': 5.0}, {'var_index': 2, 'linear_cost': 10.0}, {'var_index': 3, 'linear_cost': 8.0}, {'var_index': 4, 'linear_cost': 7.0}, {'var_index': 5, 'linear_cost': 1.0}, {'var_index': 6, 'linear_cost': 2.0}, {'var_index': 7, 'linear_cost': 6.0}, {'var_index': 8, 'linear_cost': 8.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 7, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 8, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 8, 'quadratic_cost': 9.0}]}, 'edges': [{'from': 'I', 'to': 'A', 'var_index': 0}, {'from': 'H', 'to': 'J', 'var_index': 1}, {'from': 'A', 'to': 'B', 'var_index': 2}, {'from': 'B', 'to': 'C', 'var_index': 3}, {'from': 'C', 'to': 'D', 'var_index': 4}, {'from': 'D', 'to': 'E', 'var_index': 5}, {'from': 'E', 'to': 'F', 'var_index': 6}, {'from': 'F', 'to': 'G', 'var_index': 7}, {'from': 'G', 'to': 'H', 'var_index': 8}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E', 5: 'F', 6: 'G', 7: 'H', 8: 'I', 9: 'J'}}","['I', 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'J']",22,csv,names
QSPP,QSPP,"Many people think routing is just finding a path, but in this setup each route has a little billing story: pick one one-way path from the entry location to the exit location, and remember that every link charges its own base cost. On top of that, whenever two links are both used there can be extra charges tied to that specific ordered pair — the order matters — and some links even add an extra charge just for being included. The score for a route is built by adding every link’s base cost and then adding every ordered-pair penalty for links on the route; the route with the lowest overall score is the one you want. The result must be a single valid directed path from start to finish and should be reported only as the sequence of locations (no link IDs or cost numbers). The detailed instance and costs come below.

# total_locations=9
# total_links=20
# location_ids=A, B, C, D, E, F, G, H, I
# ingress_node=H
# egress_node=I

link_tail_node,link_head_node,link_identifier
H,A,0
H,B,1
H,C,2
H,D,3
H,E,4
H,F,5
H,G,6
A,I,7
B,I,8
C,I,9
D,I,10
E,I,11
F,I,12
G,I,13
A,B,14
B,C,15
C,D,16
D,E,17
E,F,18
F,G,19

link_identifier,link_base_cost
0,8.0
1,2.0
2,10.0
3,6.0
4,5.0
5,3.0
6,4.0
7,1.0
8,9.0
9,3.0
10,5.0
11,7.0
12,1.0
13,3.0
14,4.0
15,10.0
16,2.0
17,8.0
18,8.0
19,10.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (ordered_link_i_id, ordered_link_j_id). If two link_identifiers with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| ordered_link_i_id\ordered_link_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 4.0 | 10.0 | 5.0 | 2.0 | 5.0 | 8.0 | 2.0 | 4.0 | 6.0 | 4.0 | 1.0 | 4.0 | 3.0 | 5.0 | 1.0 | 2.0 | 1.0 | 7.0 | 8.0 | 6.0 |
| 1 | 10.0 | 2.0 | 7.0 | 2.0 | 2.0 | 6.0 | 1.0 | 10.0 | 4.0 | 4.0 | 1.0 | 6.0 | 8.0 | 9.0 | 8.0 | 6.0 | 6.0 | 2.0 | 2.0 | 2.0 |
| 2 | 5.0 | 7.0 | 5.0 | 6.0 | 1.0 | 1.0 | 5.0 | 9.0 | 5.0 | 5.0 | 2.0 | 8.0 | 5.0 | 3.0 | 10.0 | 10.0 | 2.0 | 9.0 | 7.0 | 1.0 |
| 3 | 2.0 | 2.0 | 6.0 | 3.0 | 9.0 | 6.0 | 6.0 | 7.0 | 9.0 | 4.0 | 1.0 | 8.0 | 4.0 | 7.0 | 5.0 | 10.0 | 2.0 | 4.0 | 1.0 | 10.0 |
| 4 | 5.0 | 2.0 | 1.0 | 9.0 | 2.0 | 1.0 | 10.0 | 2.0 | 5.0 | 3.0 | 8.0 | 10.0 | 10.0 | 3.0 | 6.0 | 1.0 | 3.0 | 9.0 | 6.0 | 5.0 |
| 5 | 8.0 | 6.0 | 1.0 | 6.0 | 1.0 | 7.0 | 4.0 | 6.0 | 4.0 | 7.0 | 3.0 | 1.0 | 4.0 | 4.0 | 8.0 | 10.0 | 8.0 | 1.0 | 1.0 | 1.0 |
| 6 | 2.0 | 1.0 | 5.0 | 6.0 | 10.0 | 4.0 | 2.0 | 8.0 | 5.0 | 9.0 | 9.0 | 5.0 | 1.0 | 7.0 | 8.0 | 3.0 | 10.0 | 2.0 | 5.0 | 10.0 |
| 7 | 4.0 | 10.0 | 9.0 | 7.0 | 2.0 | 6.0 | 8.0 | 5.0 | 1.0 | 10.0 | 7.0 | 2.0 | 3.0 | 8.0 | 10.0 | 10.0 | 10.0 | 10.0 | 2.0 | 7.0 |
| 8 | 6.0 | 4.0 | 5.0 | 9.0 | 5.0 | 4.0 | 5.0 | 1.0 | 1.0 | 4.0 | 4.0 | 5.0 | 7.0 | 7.0 | 1.0 | 1.0 | 3.0 | 9.0 | 4.0 | 9.0 |
| 9 | 4.0 | 4.0 | 5.0 | 4.0 | 3.0 | 7.0 | 9.0 | 10.0 | 4.0 | 3.0 | 8.0 | 3.0 | 7.0 | 1.0 | 5.0 | 10.0 | 7.0 | 6.0 | 10.0 | 6.0 |
| 10 | 1.0 | 1.0 | 2.0 | 1.0 | 8.0 | 3.0 | 9.0 | 7.0 | 4.0 | 8.0 | 3.0 | 1.0 | 7.0 | 4.0 | 7.0 | 7.0 | 5.0 | 10.0 | 4.0 | 8.0 |
| 11 | 4.0 | 6.0 | 8.0 | 8.0 | 10.0 | 1.0 | 5.0 | 2.0 | 5.0 | 3.0 | 1.0 | 6.0 | 7.0 | 10.0 | 8.0 | 5.0 | 1.0 | 5.0 | 7.0 | 4.0 |
| 12 | 3.0 | 8.0 | 5.0 | 4.0 | 10.0 | 4.0 | 1.0 | 3.0 | 7.0 | 7.0 | 7.0 | 7.0 | 4.0 | 8.0 | 2.0 | 10.0 | 7.0 | 5.0 | 3.0 | 1.0 |
| 13 | 5.0 | 9.0 | 3.0 | 7.0 | 3.0 | 4.0 | 7.0 | 8.0 | 7.0 | 1.0 | 4.0 | 10.0 | 8.0 | 4.0 | 7.0 | 8.0 | 1.0 | 9.0 | 2.0 | 5.0 |
| 14 | 1.0 | 8.0 | 10.0 | 5.0 | 6.0 | 8.0 | 8.0 | 10.0 | 1.0 | 5.0 | 7.0 | 8.0 | 2.0 | 7.0 | 7.0 | 6.0 | 9.0 | 9.0 | 6.0 | 5.0 |
| 15 | 2.0 | 6.0 | 10.0 | 10.0 | 1.0 | 10.0 | 3.0 | 10.0 | 1.0 | 10.0 | 7.0 | 5.0 | 10.0 | 8.0 | 6.0 | 2.0 | 2.0 | 4.0 | 6.0 | 6.0 |
| 16 | 1.0 | 6.0 | 2.0 | 2.0 | 3.0 | 8.0 | 10.0 | 10.0 | 3.0 | 7.0 | 5.0 | 1.0 | 7.0 | 1.0 | 9.0 | 2.0 | 4.0 | 9.0 | 8.0 | 3.0 |
| 17 | 7.0 | 2.0 | 9.0 | 4.0 | 9.0 | 1.0 | 2.0 | 10.0 | 9.0 | 6.0 | 10.0 | 5.0 | 5.0 | 9.0 | 9.0 | 4.0 | 9.0 | 10.0 | 8.0 | 4.0 |
| 18 | 8.0 | 2.0 | 7.0 | 1.0 | 6.0 | 1.0 | 5.0 | 2.0 | 4.0 | 10.0 | 4.0 | 7.0 | 3.0 | 2.0 | 6.0 | 6.0 | 8.0 | 8.0 | 5.0 | 5.0 |
| 19 | 6.0 | 2.0 | 1.0 | 10.0 | 5.0 | 1.0 | 10.0 | 7.0 | 9.0 | 6.0 | 8.0 | 4.0 | 1.0 | 5.0 | 5.0 | 6.0 | 3.0 | 4.0 | 5.0 | 4.0 |

Also, to keep things tidy, please return your chosen path using this simple JSON layout:

{
  ""solution"": []
}

Think of ""solution"" as the little form field where you drop the ordered list of locations that make up your path — start node first, end node last, each entry a node label only (no link IDs, no costs). This JSON is just a sketch of the shape I expect, not the actual answer itself.

Please use the identifiers exactly as they appear in the instance input — don't rename them or invent new labels. For example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8], 'edges': [{'from': 7, 'to': 0, 'var_index': 0}, {'from': 7, 'to': 1, 'var_index': 1}, {'from': 7, 'to': 2, 'var_index': 2}, {'from': 7, 'to': 3, 'var_index': 3}, {'from': 7, 'to': 4, 'var_index': 4}, {'from': 7, 'to': 5, 'var_index': 5}, {'from': 7, 'to': 6, 'var_index': 6}, {'from': 0, 'to': 8, 'var_index': 7}, {'from': 1, 'to': 8, 'var_index': 8}, {'from': 2, 'to': 8, 'var_index': 9}, {'from': 3, 'to': 8, 'var_index': 10}, {'from': 4, 'to': 8, 'var_index': 11}, {'from': 5, 'to': 8, 'var_index': 12}, {'from': 6, 'to': 8, 'var_index': 13}, {'from': 0, 'to': 1, 'var_index': 14}, {'from': 1, 'to': 2, 'var_index': 15}, {'from': 2, 'to': 3, 'var_index': 16}, {'from': 3, 'to': 4, 'var_index': 17}, {'from': 4, 'to': 5, 'var_index': 18}, {'from': 5, 'to': 6, 'var_index': 19}], 'objective': {'constant': 0.0, 'linear': [8.0, 2.0, 10.0, 6.0, 5.0, 3.0, 4.0, 1.0, 9.0, 3.0, 5.0, 7.0, 1.0, 3.0, 4.0, 10.0, 2.0, 8.0, 8.0, 10.0], 'quadratic': [[4.0, 10.0, 5.0, 2.0, 5.0, 8.0, 2.0, 4.0, 6.0, 4.0, 1.0, 4.0, 3.0, 5.0, 1.0, 2.0, 1.0, 7.0, 8.0, 6.0], [10.0, 2.0, 7.0, 2.0, 2.0, 6.0, 1.0, 10.0, 4.0, 4.0, 1.0, 6.0, 8.0, 9.0, 8.0, 6.0, 6.0, 2.0, 2.0, 2.0], [5.0, 7.0, 5.0, 6.0, 1.0, 1.0, 5.0, 9.0, 5.0, 5.0, 2.0, 8.0, 5.0, 3.0, 10.0, 10.0, 2.0, 9.0, 7.0, 1.0], [2.0, 2.0, 6.0, 3.0, 9.0, 6.0, 6.0, 7.0, 9.0, 4.0, 1.0, 8.0, 4.0, 7.0, 5.0, 10.0, 2.0, 4.0, 1.0, 10.0], [5.0, 2.0, 1.0, 9.0, 2.0, 1.0, 10.0, 2.0, 5.0, 3.0, 8.0, 10.0, 10.0, 3.0, 6.0, 1.0, 3.0, 9.0, 6.0, 5.0], [8.0, 6.0, 1.0, 6.0, 1.0, 7.0, 4.0, 6.0, 4.0, 7.0, 3.0, 1.0, 4.0, 4.0, 8.0, 10.0, 8.0, 1.0, 1.0, 1.0], [2.0, 1.0, 5.0, 6.0, 10.0, 4.0, 2.0, 8.0, 5.0, 9.0, 9.0, 5.0, 1.0, 7.0, 8.0, 3.0, 10.0, 2.0, 5.0, 10.0], [4.0, 10.0, 9.0, 7.0, 2.0, 6.0, 8.0, 5.0, 1.0, 10.0, 7.0, 2.0, 3.0, 8.0, 10.0, 10.0, 10.0, 10.0, 2.0, 7.0], [6.0, 4.0, 5.0, 9.0, 5.0, 4.0, 5.0, 1.0, 1.0, 4.0, 4.0, 5.0, 7.0, 7.0, 1.0, 1.0, 3.0, 9.0, 4.0, 9.0], [4.0, 4.0, 5.0, 4.0, 3.0, 7.0, 9.0, 10.0, 4.0, 3.0, 8.0, 3.0, 7.0, 1.0, 5.0, 10.0, 7.0, 6.0, 10.0, 6.0], [1.0, 1.0, 2.0, 1.0, 8.0, 3.0, 9.0, 7.0, 4.0, 8.0, 3.0, 1.0, 7.0, 4.0, 7.0, 7.0, 5.0, 10.0, 4.0, 8.0], [4.0, 6.0, 8.0, 8.0, 10.0, 1.0, 5.0, 2.0, 5.0, 3.0, 1.0, 6.0, 7.0, 10.0, 8.0, 5.0, 1.0, 5.0, 7.0, 4.0], [3.0, 8.0, 5.0, 4.0, 10.0, 4.0, 1.0, 3.0, 7.0, 7.0, 7.0, 7.0, 4.0, 8.0, 2.0, 10.0, 7.0, 5.0, 3.0, 1.0], [5.0, 9.0, 3.0, 7.0, 3.0, 4.0, 7.0, 8.0, 7.0, 1.0, 4.0, 10.0, 8.0, 4.0, 7.0, 8.0, 1.0, 9.0, 2.0, 5.0], [1.0, 8.0, 10.0, 5.0, 6.0, 8.0, 8.0, 10.0, 1.0, 5.0, 7.0, 8.0, 2.0, 7.0, 7.0, 6.0, 9.0, 9.0, 6.0, 5.0], [2.0, 6.0, 10.0, 10.0, 1.0, 10.0, 3.0, 10.0, 1.0, 10.0, 7.0, 5.0, 10.0, 8.0, 6.0, 2.0, 2.0, 4.0, 6.0, 6.0], [1.0, 6.0, 2.0, 2.0, 3.0, 8.0, 10.0, 10.0, 3.0, 7.0, 5.0, 1.0, 7.0, 1.0, 9.0, 2.0, 4.0, 9.0, 8.0, 3.0], [7.0, 2.0, 9.0, 4.0, 9.0, 1.0, 2.0, 10.0, 9.0, 6.0, 10.0, 5.0, 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{'var_i': 11, 'var_j': 14, 'quadratic_cost': 8.0}, {'var_i': 11, 'var_j': 15, 'quadratic_cost': 5.0}, {'var_i': 11, 'var_j': 16, 'quadratic_cost': 1.0}, {'var_i': 11, 'var_j': 17, 'quadratic_cost': 5.0}, {'var_i': 11, 'var_j': 18, 'quadratic_cost': 7.0}, {'var_i': 11, 'var_j': 19, 'quadratic_cost': 4.0}, {'var_i': 12, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 12, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 12, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 12, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 12, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 12, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 12, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 12, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 12, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 12, 'quadratic_cost': 4.0}, {'var_i': 12, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 12, 'var_j': 14, 'quadratic_cost': 2.0}, {'var_i': 12, 'var_j': 15, 'quadratic_cost': 10.0}, {'var_i': 12, 'var_j': 16, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 17, 'quadratic_cost': 5.0}, {'var_i': 12, 'var_j': 18, 'quadratic_cost': 3.0}, {'var_i': 12, 'var_j': 19, 'quadratic_cost': 1.0}, {'var_i': 13, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 13, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 13, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 13, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 13, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 13, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 13, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 13, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 13, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 13, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 13, 'quadratic_cost': 4.0}, {'var_i': 13, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 13, 'var_j': 15, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 16, 'quadratic_cost': 1.0}, {'var_i': 13, 'var_j': 17, 'quadratic_cost': 9.0}, {'var_i': 13, 'var_j': 18, 'quadratic_cost': 2.0}, {'var_i': 13, 'var_j': 19, 'quadratic_cost': 5.0}, {'var_i': 14, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 14, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 14, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 14, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 14, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 14, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 14, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 14, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 14, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 14, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 14, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 14, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 14, 'var_j': 12, 'quadratic_cost': 2.0}, {'var_i': 14, 'var_j': 13, 'quadratic_cost': 7.0}, {'var_i': 14, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 14, 'var_j': 15, 'quadratic_cost': 6.0}, {'var_i': 14, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 14, 'var_j': 17, 'quadratic_cost': 9.0}, {'var_i': 14, 'var_j': 18, 'quadratic_cost': 6.0}, {'var_i': 14, 'var_j': 19, 'quadratic_cost': 5.0}, {'var_i': 15, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 15, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 15, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 15, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 15, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 15, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 15, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 15, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 15, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 15, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 15, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 15, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 15, 'var_j': 12, 'quadratic_cost': 10.0}, {'var_i': 15, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 15, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 15, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 15, 'var_j': 17, 'quadratic_cost': 4.0}, {'var_i': 15, 'var_j': 18, 'quadratic_cost': 6.0}, {'var_i': 15, 'var_j': 19, 'quadratic_cost': 6.0}, {'var_i': 16, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 16, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 16, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 16, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 16, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 16, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 16, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 16, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 16, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 16, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 16, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 16, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 16, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 16, 'var_j': 13, 'quadratic_cost': 1.0}, {'var_i': 16, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 16, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 16, 'var_j': 16, 'quadratic_cost': 4.0}, {'var_i': 16, 'var_j': 17, 'quadratic_cost': 9.0}, {'var_i': 16, 'var_j': 18, 'quadratic_cost': 8.0}, {'var_i': 16, 'var_j': 19, 'quadratic_cost': 3.0}, {'var_i': 17, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 17, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 17, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 17, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 17, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 17, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 17, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 17, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 17, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 17, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 17, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 17, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 17, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 17, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 17, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 17, 'var_j': 15, 'quadratic_cost': 4.0}, {'var_i': 17, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 17, 'var_j': 17, 'quadratic_cost': 10.0}, {'var_i': 17, 'var_j': 18, 'quadratic_cost': 8.0}, {'var_i': 17, 'var_j': 19, 'quadratic_cost': 4.0}, {'var_i': 18, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 18, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 18, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 18, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 18, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 18, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 18, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 18, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 18, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 18, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 18, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 18, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 18, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 18, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 18, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 18, 'var_j': 15, 'quadratic_cost': 6.0}, {'var_i': 18, 'var_j': 16, 'quadratic_cost': 8.0}, {'var_i': 18, 'var_j': 17, 'quadratic_cost': 8.0}, {'var_i': 18, 'var_j': 18, 'quadratic_cost': 5.0}, {'var_i': 18, 'var_j': 19, 'quadratic_cost': 5.0}, {'var_i': 19, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 19, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 19, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 19, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 19, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 19, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 19, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 19, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 19, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 19, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 19, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 19, 'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 19, 'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 19, 'var_j': 13, 'quadratic_cost': 5.0}, {'var_i': 19, 'var_j': 14, 'quadratic_cost': 5.0}, {'var_i': 19, 'var_j': 15, 'quadratic_cost': 6.0}, {'var_i': 19, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 19, 'var_j': 17, 'quadratic_cost': 4.0}, {'var_i': 19, 'var_j': 18, 'quadratic_cost': 5.0}, {'var_i': 19, 'var_j': 19, 'quadratic_cost': 4.0}]}, 'edges': [{'from': 'H', 'to': 'A', 'var_index': 0}, {'from': 'H', 'to': 'B', 'var_index': 1}, {'from': 'H', 'to': 'C', 'var_index': 2}, {'from': 'H', 'to': 'D', 'var_index': 3}, {'from': 'H', 'to': 'E', 'var_index': 4}, {'from': 'H', 'to': 'F', 'var_index': 5}, {'from': 'H', 'to': 'G', 'var_index': 6}, {'from': 'A', 'to': 'I', 'var_index': 7}, {'from': 'B', 'to': 'I', 'var_index': 8}, {'from': 'C', 'to': 'I', 'var_index': 9}, {'from': 'D', 'to': 'I', 'var_index': 10}, {'from': 'E', 'to': 'I', 'var_index': 11}, {'from': 'F', 'to': 'I', 'var_index': 12}, {'from': 'G', 'to': 'I', 'var_index': 13}, {'from': 'A', 'to': 'B', 'var_index': 14}, {'from': 'B', 'to': 'C', 'var_index': 15}, {'from': 'C', 'to': 'D', 'var_index': 16}, {'from': 'D', 'to': 'E', 'var_index': 17}, {'from': 'E', 'to': 'F', 'var_index': 18}, {'from': 'F', 'to': 'G', 'var_index': 19}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E', 5: 'F', 6: 'G', 7: 'H', 8: 'I'}}","['H', 'D', 'I']",23,csv,names
QSPP,QSPP,"Many people in the neighborhood treat picking a bike route like balancing a bill: start at the park, ride along allowed one-way lanes to the plaza, and each lane adds its usual delay while some lane pairings tack on extra delay when they appear together (some lanes even have their own extra cost just by being included). The trick is to choose one continuous route whose total — adding every lane’s base delay and all the extra delays caused by specific lane combinations — comes out the smallest. The route must be a legal directed path from park to plaza, spelled out as a sequence of place names with each step supported by an actual one-way lane, and the answer should contain only those place names (no lane codes). The specific map and delay details follow below.

# total_places_count=8
# total_one_way_lanes=11
# place_names=0, 1, 2, 3, 4, 5, 6, 7
# park_name=6
# plaza_name=7

lane_start_place,lane_end_place,lane_code
6,0,0
6,3,1
2,7,2
5,7,3
0,1,4
0,3,5
1,2,6
1,4,7
2,5,8
3,4,9
4,5,10

lane_code_for_linear,base_expected_delay
0,5.0
1,4.0
2,1.0
3,3.0
4,1.0
5,6.0
6,10.0
7,5.0
8,10.0
9,9.0
10,6.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (lane_i_code, lane_j_code). If two lane_codes with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| lane_i_code\lane_j_code | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 8.0 | 4.0 | 5.0 | 6.0 | 8.0 | 5.0 | 7.0 | 1.0 | 6.0 | 7.0 | 9.0 |
| 1 | 4.0 | 5.0 | 6.0 | 2.0 | 1.0 | 2.0 | 3.0 | 2.0 | 4.0 | 2.0 | 4.0 |
| 2 | 5.0 | 6.0 | 2.0 | 5.0 | 9.0 | 9.0 | 10.0 | 7.0 | 2.0 | 1.0 | 4.0 |
| 3 | 6.0 | 2.0 | 5.0 | 3.0 | 8.0 | 8.0 | 5.0 | 5.0 | 2.0 | 3.0 | 4.0 |
| 4 | 8.0 | 1.0 | 9.0 | 8.0 | 10.0 | 7.0 | 4.0 | 10.0 | 9.0 | 7.0 | 1.0 |
| 5 | 5.0 | 2.0 | 9.0 | 8.0 | 7.0 | 6.0 | 8.0 | 3.0 | 8.0 | 8.0 | 3.0 |
| 6 | 7.0 | 3.0 | 10.0 | 5.0 | 4.0 | 8.0 | 8.0 | 5.0 | 8.0 | 2.0 | 3.0 |
| 7 | 1.0 | 2.0 | 7.0 | 5.0 | 10.0 | 3.0 | 5.0 | 9.0 | 3.0 | 7.0 | 7.0 |
| 8 | 6.0 | 4.0 | 2.0 | 2.0 | 9.0 | 8.0 | 8.0 | 3.0 | 8.0 | 8.0 | 7.0 |
| 9 | 7.0 | 2.0 | 1.0 | 3.0 | 7.0 | 8.0 | 2.0 | 7.0 | 8.0 | 7.0 | 1.0 |
| 10 | 9.0 | 4.0 | 4.0 | 4.0 | 1.0 | 3.0 | 3.0 | 7.0 | 7.0 | 1.0 | 2.0 |

Oh, and when you send back the route, please stick to a tiny JSON sketch like this:

{
  ""solution"": []
}

""solution"" is just the ordered list of place names from the starting spot to the destination — fill it with the node names exactly as they appear on the map, one after another. Keep it to those place names only (don’t include lane codes, edge identifiers, costs, or anything else). This JSON is just the shape I’m expecting, not the actual answer itself.

Also, all identifiers must be used exactly as they appear in the instance input — no renaming and no new labels. For example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7], 'edges': [{'from': 6, 'to': 0, 'var_index': 0}, {'from': 6, 'to': 3, 'var_index': 1}, {'from': 2, 'to': 7, 'var_index': 2}, {'from': 5, 'to': 7, 'var_index': 3}, {'from': 0, 'to': 1, 'var_index': 4}, {'from': 0, 'to': 3, 'var_index': 5}, {'from': 1, 'to': 2, 'var_index': 6}, {'from': 1, 'to': 4, 'var_index': 7}, {'from': 2, 'to': 5, 'var_index': 8}, {'from': 3, 'to': 4, 'var_index': 9}, {'from': 4, 'to': 5, 'var_index': 10}], 'objective': {'constant': 0.0, 'linear': [5.0, 4.0, 1.0, 3.0, 1.0, 6.0, 10.0, 5.0, 10.0, 9.0, 6.0], 'quadratic': [[8.0, 4.0, 5.0, 6.0, 8.0, 5.0, 7.0, 1.0, 6.0, 7.0, 9.0], [4.0, 5.0, 6.0, 2.0, 1.0, 2.0, 3.0, 2.0, 4.0, 2.0, 4.0], [5.0, 6.0, 2.0, 5.0, 9.0, 9.0, 10.0, 7.0, 2.0, 1.0, 4.0], [6.0, 2.0, 5.0, 3.0, 8.0, 8.0, 5.0, 5.0, 2.0, 3.0, 4.0], [8.0, 1.0, 9.0, 8.0, 10.0, 7.0, 4.0, 10.0, 9.0, 7.0, 1.0], [5.0, 2.0, 9.0, 8.0, 7.0, 6.0, 8.0, 3.0, 8.0, 8.0, 3.0], [7.0, 3.0, 10.0, 5.0, 4.0, 8.0, 8.0, 5.0, 8.0, 2.0, 3.0], [1.0, 2.0, 7.0, 5.0, 10.0, 3.0, 5.0, 9.0, 3.0, 7.0, 7.0], [6.0, 4.0, 2.0, 2.0, 9.0, 8.0, 8.0, 3.0, 8.0, 8.0, 7.0], [7.0, 2.0, 1.0, 3.0, 7.0, 8.0, 2.0, 7.0, 8.0, 7.0, 1.0], [9.0, 4.0, 4.0, 4.0, 1.0, 3.0, 3.0, 7.0, 7.0, 1.0, 2.0]]}, 'source': 6, 'target': 7}","[6, 3, 4, 5, 7]",71.0,"{'problem_type': 'QSPP', 'num_nodes': 8, 'num_edges': 11, 'nodes': [0, 1, 2, 3, 4, 5, 6, 7], 'source': 6, 'target': 7, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 5.0}, {'var_index': 1, 'linear_cost': 4.0}, {'var_index': 2, 'linear_cost': 1.0}, {'var_index': 3, 'linear_cost': 3.0}, {'var_index': 4, 'linear_cost': 1.0}, {'var_index': 5, 'linear_cost': 6.0}, {'var_index': 6, 'linear_cost': 10.0}, {'var_index': 7, 'linear_cost': 5.0}, {'var_index': 8, 'linear_cost': 10.0}, {'var_index': 9, 'linear_cost': 9.0}, {'var_index': 10, 'linear_cost': 6.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 7, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 8, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 9, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 9, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 9, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 9, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 9, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 9, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 9, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 10, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 10, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 10, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 10, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 10, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 10, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 10, 'var_j': 10, 'quadratic_cost': 2.0}]}, 'edges': [{'from': 6, 'to': 0, 'var_index': 0}, {'from': 6, 'to': 3, 'var_index': 1}, {'from': 2, 'to': 7, 'var_index': 2}, {'from': 5, 'to': 7, 'var_index': 3}, {'from': 0, 'to': 1, 'var_index': 4}, {'from': 0, 'to': 3, 'var_index': 5}, {'from': 1, 'to': 2, 'var_index': 6}, {'from': 1, 'to': 4, 'var_index': 7}, {'from': 2, 'to': 5, 'var_index': 8}, {'from': 3, 'to': 4, 'var_index': 9}, {'from': 4, 'to': 5, 'var_index': 10}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7}}","[6, 3, 4, 5, 7]",24,csv,0
QSPP,QSPP,"There’s a scenario at the harbor where the operator has to send a ferry along one directed waterway from the entrance to the pier, using only the permitted one-way channels. Each channel carries a base fee, and whenever two particular channels end up used in sequence there can be an extra surcharge — so cost is the sum of the channel fees plus any surcharges for those ordered channel pairs that appear on the trip. The goal is to choose the single continuous route that comes out cheapest by that accounting. The route must be continuous and legal (entrance first, pier last, every hop along an allowed direction) and the response should list only the locations visited in order. The concrete map and charges are shown below.

The map contains 5 locations and 8 directed channels: 1, 2, 3, 4, 5. The trip must begin at 4 and end at 5.
Channel 0 runs from 4 to 1.
Channel 1 runs from 4 to 2.
Channel 2 runs from 4 to 3.
Channel 3 runs from 1 to 5.
Channel 4 runs from 2 to 5.
Channel 5 runs from 3 to 5.
Channel 6 runs from 1 to 2.
Channel 7 runs from 2 to 3.
Using 0 incurs a base fee of 10.0.
Using 1 incurs a base fee of 3.0.
Using 2 incurs a base fee of 3.0.
Using 3 incurs a base fee of 8.0.
Using 4 incurs a base fee of 4.0.
Using 5 incurs a base fee of 1.0.
Using 6 incurs a base fee of 4.0.
Using 7 incurs a base fee of 6.0.
Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (first_channel_id, second_channel_id). If two channels with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
quadratic_costs:
| first_channel_id\second_channel_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|---|
| 0 | 5.0 | 6.0 | 4.0 | 10.0 | 10.0 | 5.0 | 10.0 | 2.0 |
| 1 | 6.0 | 2.0 | 1.0 | 9.0 | 1.0 | 2.0 | 3.0 | 2.0 |
| 2 | 4.0 | 1.0 | 5.0 | 3.0 | 2.0 | 8.0 | 10.0 | 6.0 |
| 3 | 10.0 | 9.0 | 3.0 | 7.0 | 6.0 | 10.0 | 6.0 | 6.0 |
| 4 | 10.0 | 1.0 | 2.0 | 6.0 | 7.0 | 5.0 | 7.0 | 3.0 |
| 5 | 5.0 | 2.0 | 8.0 | 10.0 | 5.0 | 3.0 | 5.0 | 5.0 |
| 6 | 10.0 | 3.0 | 10.0 | 6.0 | 7.0 | 5.0 | 7.0 | 8.0 |
| 7 | 2.0 | 2.0 | 6.0 | 6.0 | 3.0 | 5.0 | 8.0 | 3.0 |
The operator should list only the locations visited in order for the single cheapest legal route.

Also, when you send your chosen route back, please use the little JSON layout below so it's easy to parse — just a single top-level object with a solution array containing the visited locations in order.

{
  ""solution"": []
}

This JSON is just a simple sketch: ""solution"" should hold a list of the place names (nodes) you visit from the entrance to the pier, in order. Keep it casual — just the locations, nothing about channel IDs, costs, or surcharges. The JSON above shows the shape your answer should follow, but it's not the actual path.

One important note: use the exact identifiers from the problem input with no renaming and no new labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'nodes': [0, 1, 2, 3, 4], 'edges': [{'from': 3, 'to': 0, 'var_index': 0}, {'from': 3, 'to': 1, 'var_index': 1}, {'from': 3, 'to': 2, 'var_index': 2}, {'from': 0, 'to': 4, 'var_index': 3}, {'from': 1, 'to': 4, 'var_index': 4}, {'from': 2, 'to': 4, 'var_index': 5}, {'from': 0, 'to': 1, 'var_index': 6}, {'from': 1, 'to': 2, 'var_index': 7}], 'objective': {'constant': 0.0, 'linear': [10.0, 3.0, 3.0, 8.0, 4.0, 1.0, 4.0, 6.0], 'quadratic': [[5.0, 6.0, 4.0, 10.0, 10.0, 5.0, 10.0, 2.0], [6.0, 2.0, 1.0, 9.0, 1.0, 2.0, 3.0, 2.0], [4.0, 1.0, 5.0, 3.0, 2.0, 8.0, 10.0, 6.0], [10.0, 9.0, 3.0, 7.0, 6.0, 10.0, 6.0, 6.0], [10.0, 1.0, 2.0, 6.0, 7.0, 5.0, 7.0, 3.0], [5.0, 2.0, 8.0, 10.0, 5.0, 3.0, 5.0, 5.0], [10.0, 3.0, 10.0, 6.0, 7.0, 5.0, 7.0, 8.0], [2.0, 2.0, 6.0, 6.0, 3.0, 5.0, 8.0, 3.0]]}, 'source': 3, 'target': 4}","[3, 1, 4]",18.0,"{'problem_type': 'QSPP', 'num_nodes': 5, 'num_edges': 8, 'nodes': [1, 2, 3, 4, 5], 'source': 4, 'target': 5, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 10.0}, {'var_index': 1, 'linear_cost': 3.0}, {'var_index': 2, 'linear_cost': 3.0}, {'var_index': 3, 'linear_cost': 8.0}, {'var_index': 4, 'linear_cost': 4.0}, {'var_index': 5, 'linear_cost': 1.0}, {'var_index': 6, 'linear_cost': 4.0}, {'var_index': 7, 'linear_cost': 6.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 7, 'quadratic_cost': 3.0}]}, 'edges': [{'from': 4, 'to': 1, 'var_index': 0}, {'from': 4, 'to': 2, 'var_index': 1}, {'from': 4, 'to': 3, 'var_index': 2}, {'from': 1, 'to': 5, 'var_index': 3}, {'from': 2, 'to': 5, 'var_index': 4}, {'from': 3, 'to': 5, 'var_index': 5}, {'from': 1, 'to': 2, 'var_index': 6}, {'from': 2, 'to': 3, 'var_index': 7}], 'node_id_map': {0: 1, 1: 2, 2: 3, 3: 4, 4: 5}}","[4, 2, 5]",25,nl,1
QSPP,QSPP,"I was asked to send a single maintenance crew from the gate to the machinery room using only the approved one-way service corridors. The crew has to pick one continuous route that follows the arrows from start to finish — no side trips, no skipping segments, and the route must begin at the gate and end at the machinery room. Each corridor has a regular access charge and also its own little surcharge just for being used, and some specific pairs of corridors add extra fees when both are taken (sometimes the extra depends on which corridor comes first). The goal is to pick the route that makes the total bill as small as possible by adding up each corridor’s access charge, any per-corridor surcharges, and every extra fee caused by any used corridor pairs. The exact layout and numbers will be shown below.

# total_locations=6
# total_corridors=8
# location_ids=0, 1, 2, 3, 4, 5
# gate_location=4
# machinery_room_location=5

corridor_from,corridor_to,corridor_id
4,0,0
4,2,1
1,5,2
3,5,3
0,1,4
0,2,5
1,3,6
2,3,7

corridor_id,access_charge
0,6.0
1,4.0
2,8.0
3,4.0
4,7.0
5,3.0
6,10.0
7,4.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (corridor_i_id, corridor_j_id). If two corridors with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| corridor_i_id\corridor_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|---|
| 0 | 5.0 | 9.0 | 5.0 | 7.0 | 9.0 | 5.0 | 3.0 | 5.0 |
| 1 | 9.0 | 5.0 | 2.0 | 5.0 | 3.0 | 5.0 | 8.0 | 7.0 |
| 2 | 5.0 | 2.0 | 1.0 | 5.0 | 10.0 | 1.0 | 8.0 | 4.0 |
| 3 | 7.0 | 5.0 | 5.0 | 5.0 | 4.0 | 5.0 | 6.0 | 2.0 |
| 4 | 9.0 | 3.0 | 10.0 | 4.0 | 10.0 | 6.0 | 4.0 | 6.0 |
| 5 | 5.0 | 5.0 | 1.0 | 5.0 | 6.0 | 2.0 | 4.0 | 9.0 |
| 6 | 3.0 | 8.0 | 8.0 | 6.0 | 4.0 | 4.0 | 3.0 | 8.0 |
| 7 | 5.0 | 7.0 | 4.0 | 2.0 | 6.0 | 9.0 | 8.0 | 2.0 |

Also, when you send back the chosen route, you can use a tiny JSON layout so it's easy to parse—nothing fancy, just drop the path into this shape:

{
  ""solution"": []
}

Think of the ""solution"" array as the place to list the corridor stops in order: start with the gate, then each location you pass through, and finish with the machinery room. It's just a simple form to fill out with the node names in sequence.

This JSON is only a sketch of the expected shape — you'll replace the empty array with the actual path when you give the answer.

Also, please use the node identifiers exactly as they appear in the instance input — no renaming and no new labels. For example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""

Don't include edge IDs or any cost labels in the response; just the sequence of node identifiers.","{'nodes': [0, 1, 2, 3, 4, 5], 'edges': [{'from': 4, 'to': 0, 'var_index': 0}, {'from': 4, 'to': 2, 'var_index': 1}, {'from': 1, 'to': 5, 'var_index': 2}, {'from': 3, 'to': 5, 'var_index': 3}, {'from': 0, 'to': 1, 'var_index': 4}, {'from': 0, 'to': 2, 'var_index': 5}, {'from': 1, 'to': 3, 'var_index': 6}, {'from': 2, 'to': 3, 'var_index': 7}], 'objective': {'constant': 0.0, 'linear': [6.0, 4.0, 8.0, 4.0, 7.0, 3.0, 10.0, 4.0], 'quadratic': [[5.0, 9.0, 5.0, 7.0, 9.0, 5.0, 3.0, 5.0], [9.0, 5.0, 2.0, 5.0, 3.0, 5.0, 8.0, 7.0], [5.0, 2.0, 1.0, 5.0, 10.0, 1.0, 8.0, 4.0], [7.0, 5.0, 5.0, 5.0, 4.0, 5.0, 6.0, 2.0], [9.0, 3.0, 10.0, 4.0, 10.0, 6.0, 4.0, 6.0], [5.0, 5.0, 1.0, 5.0, 6.0, 2.0, 4.0, 9.0], [3.0, 8.0, 8.0, 6.0, 4.0, 4.0, 3.0, 8.0], [5.0, 7.0, 4.0, 2.0, 6.0, 9.0, 8.0, 2.0]]}, 'source': 4, 'target': 5}","[4, 2, 3, 5]",52.0,"{'problem_type': 'QSPP', 'num_nodes': 6, 'num_edges': 8, 'nodes': [0, 1, 2, 3, 4, 5], 'source': 4, 'target': 5, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 6.0}, {'var_index': 1, 'linear_cost': 4.0}, {'var_index': 2, 'linear_cost': 8.0}, {'var_index': 3, 'linear_cost': 4.0}, {'var_index': 4, 'linear_cost': 7.0}, {'var_index': 5, 'linear_cost': 3.0}, {'var_index': 6, 'linear_cost': 10.0}, {'var_index': 7, 'linear_cost': 4.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 7, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 7, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 7, 'quadratic_cost': 2.0}]}, 'edges': [{'from': 4, 'to': 0, 'var_index': 0}, {'from': 4, 'to': 2, 'var_index': 1}, {'from': 1, 'to': 5, 'var_index': 2}, {'from': 3, 'to': 5, 'var_index': 3}, {'from': 0, 'to': 1, 'var_index': 4}, {'from': 0, 'to': 2, 'var_index': 5}, {'from': 1, 'to': 3, 'var_index': 6}, {'from': 2, 'to': 3, 'var_index': 7}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5}}","[4, 2, 3, 5]",26,csv,0
QSPP,QSPP,"Many people treat this like picking a single subway path from the entry concourse to the platform: follow the one-way tracks, hop from station to station, and don’t split the trip. Each track segment charges a base fee, some segments tack on an extra surcharge when they’re used, and some particular combos of segments create additional penalties that only count if both are on the trip. The aim is to choose exactly one legal route, obeying the track directions and starting and ending in the right places, so that when all base fees, surcharges, and combo penalties are summed the total is as small as possible. The detailed map and the fee schedule are provided below.

Below are the 6 station locations and 8 one-way track segments, listed as station identifiers 1, 2, 3, 4, 5, 6; the commuter starts at 5 and finishes at 6.
Segment 0: departs 5 and arrives at 1.
Segment 1: departs 5 and arrives at 3.
Segment 2: departs 2 and arrives at 6.
Segment 3: departs 4 and arrives at 6.
Segment 4: departs 1 and arrives at 2.
Segment 5: departs 1 and arrives at 3.
Segment 6: departs 2 and arrives at 4.
Segment 7: departs 3 and arrives at 4.
Segment 0 carries a base fee of 2.0 when used.
Segment 1 carries a base fee of 8.0 when used.
Segment 2 carries a base fee of 5.0 when used.
Segment 3 carries a base fee of 8.0 when used.
Segment 4 carries a base fee of 4.0 when used.
Segment 5 carries a base fee of 10.0 when used.
Segment 6 carries a base fee of 1.0 when used.
Segment 7 carries a base fee of 2.0 when used.
Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (segment_i_id, segment_j_id). If two segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
quadratic_costs:
| segment_i_id\segment_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|---|
| 0 | 5.0 | 10.0 | 4.0 | 5.0 | 10.0 | 6.0 | 4.0 | 7.0 |
| 1 | 10.0 | 1.0 | 4.0 | 6.0 | 7.0 | 3.0 | 5.0 | 2.0 |
| 2 | 4.0 | 4.0 | 4.0 | 6.0 | 6.0 | 8.0 | 1.0 | 5.0 |
| 3 | 5.0 | 6.0 | 6.0 | 8.0 | 2.0 | 1.0 | 3.0 | 8.0 |
| 4 | 10.0 | 7.0 | 6.0 | 2.0 | 3.0 | 9.0 | 10.0 | 10.0 |
| 5 | 6.0 | 3.0 | 8.0 | 1.0 | 9.0 | 7.0 | 5.0 | 3.0 |
| 6 | 4.0 | 5.0 | 1.0 | 3.0 | 10.0 | 5.0 | 5.0 | 7.0 |
| 7 | 7.0 | 2.0 | 5.0 | 8.0 | 10.0 | 3.0 | 7.0 | 9.0 |
Sum base fees, surcharges, and pairwise penalties for any candidate route to obtain its total fare.

Oh, and one more practical thing: when you send back the path, please put it into a tiny JSON object like this.

{
  ""solution"": []
}

The ""solution"" array is where you list the nodes of your chosen route in order — like station names: the first entry is the start, the last entry is the finish, and each pair of neighbors in the list must correspond to a legal one-way link on the map. Think of this JSON as just the simple form I want to see filled in, not the route itself.

Please use the exact node labels from the instance input — don’t rename them or invent new ones. 
- For example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5], 'edges': [{'from': 4, 'to': 0, 'var_index': 0}, {'from': 4, 'to': 2, 'var_index': 1}, {'from': 1, 'to': 5, 'var_index': 2}, {'from': 3, 'to': 5, 'var_index': 3}, {'from': 0, 'to': 1, 'var_index': 4}, {'from': 0, 'to': 2, 'var_index': 5}, {'from': 1, 'to': 3, 'var_index': 6}, {'from': 2, 'to': 3, 'var_index': 7}], 'objective': {'constant': 0.0, 'linear': [2.0, 8.0, 5.0, 8.0, 4.0, 10.0, 1.0, 2.0], 'quadratic': [[5.0, 10.0, 4.0, 5.0, 10.0, 6.0, 4.0, 7.0], [10.0, 1.0, 4.0, 6.0, 7.0, 3.0, 5.0, 2.0], [4.0, 4.0, 4.0, 6.0, 6.0, 8.0, 1.0, 5.0], [5.0, 6.0, 6.0, 8.0, 2.0, 1.0, 3.0, 8.0], [10.0, 7.0, 6.0, 2.0, 3.0, 9.0, 10.0, 10.0], [6.0, 3.0, 8.0, 1.0, 9.0, 7.0, 5.0, 3.0], [4.0, 5.0, 1.0, 3.0, 10.0, 5.0, 5.0, 7.0], [7.0, 2.0, 5.0, 8.0, 10.0, 3.0, 7.0, 9.0]]}, 'source': 4, 'target': 5}","[4, 0, 1, 5]",63.0,"{'problem_type': 'QSPP', 'num_nodes': 6, 'num_edges': 8, 'nodes': [1, 2, 3, 4, 5, 6], 'source': 5, 'target': 6, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 2.0}, {'var_index': 1, 'linear_cost': 8.0}, {'var_index': 2, 'linear_cost': 5.0}, {'var_index': 3, 'linear_cost': 8.0}, {'var_index': 4, 'linear_cost': 4.0}, {'var_index': 5, 'linear_cost': 10.0}, {'var_index': 6, 'linear_cost': 1.0}, {'var_index': 7, 'linear_cost': 2.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 7, 'quadratic_cost': 9.0}]}, 'edges': [{'from': 5, 'to': 1, 'var_index': 0}, {'from': 5, 'to': 3, 'var_index': 1}, {'from': 2, 'to': 6, 'var_index': 2}, {'from': 4, 'to': 6, 'var_index': 3}, {'from': 1, 'to': 2, 'var_index': 4}, {'from': 1, 'to': 3, 'var_index': 5}, {'from': 2, 'to': 4, 'var_index': 6}, {'from': 3, 'to': 4, 'var_index': 7}], 'node_id_map': {0: 1, 1: 2, 2: 3, 3: 4, 4: 5, 5: 6}}","[5, 1, 2, 6]",27,nl,1
QSPP,QSPP,"Someone is trying to pick a single one-way plumbing run from the inlet to the outlet through a maze of pipes. Each pipe carries a handling cost, and whenever certain pipes are used together they produce extra losses — even a lone pipe can have its own extra hit. The task is to select one continuous route (begin at the inlet, finish at the outlet, step along existing directed connections) so that the final tally — add every pipe’s base fee and add every extra penalty for each pair of pipes that both show up on the route — is as small as possible. The exact network and the numbers for each pipe and pair are shown below.

{
  ""total_junctions"": 5,
  ""total_pipes"": 4,
  ""junction_ids"": [
    ""A"",
    ""B"",
    ""C"",
    ""D"",
    ""E""
  ],
  ""inlet_junction"": ""D"",
  ""outlet_junction"": ""E"",
  ""edges"": [
    {
      ""pipe_from_junction"": ""D"",
      ""pipe_to_junction"": ""A"",
      ""pipe_id"": 0
    },
    {
      ""pipe_from_junction"": ""C"",
      ""pipe_to_junction"": ""E"",
      ""pipe_id"": 1
    },
    {
      ""pipe_from_junction"": ""A"",
      ""pipe_to_junction"": ""B"",
      ""pipe_id"": 2
    },
    {
      ""pipe_from_junction"": ""B"",
      ""pipe_to_junction"": ""C"",
      ""pipe_id"": 3
    }
  ],
  ""linear_costs"": [
    {
      ""pipe_id"": 0,
      ""pipe_handling_fee"": 4.0
    },
    {
      ""pipe_id"": 1,
      ""pipe_handling_fee"": 10.0
    },
    {
      ""pipe_id"": 2,
      ""pipe_handling_fee"": 4.0
    },
    {
      ""pipe_id"": 3,
      ""pipe_handling_fee"": 7.0
    }
  ]
}

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (pipe_i_id, pipe_j_id). If two pipes with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| pipe_i_id\pipe_j_id | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| 0 | 10.0 | 1.0 | 5.0 | 3.0 |
| 1 | 1.0 | 10.0 | 5.0 | 1.0 |
| 2 | 5.0 | 5.0 | 2.0 | 1.0 |
| 3 | 3.0 | 1.0 | 1.0 | 1.0 |

When you're ready, just reply with the chosen node sequence in a tiny JSON object — super simple, just a single field called solution that holds the list of nodes along the route. For example:

{
  ""solution"": []
}

Here ""solution"" is the list of node identifiers in order from the inlet to the outlet (first entry is the inlet, last is the outlet). Treat this JSON like a short form you fill out—it's only a sketch of the expected shape, not the actual answer itself.

Please use node identifiers exactly as they appear in the instance input — no renaming, no made-up labels. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4], 'edges': [{'from': 3, 'to': 0, 'var_index': 0}, {'from': 2, 'to': 4, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}], 'objective': {'constant': 0.0, 'linear': [4.0, 10.0, 4.0, 7.0], 'quadratic': [[10.0, 1.0, 5.0, 3.0], [1.0, 10.0, 5.0, 1.0], [5.0, 5.0, 2.0, 1.0], [3.0, 1.0, 1.0, 1.0]]}, 'source': 3, 'target': 4}","[3, 0, 1, 2, 4]",80.0,"{'problem_type': 'QSPP', 'num_nodes': 5, 'num_edges': 4, 'nodes': ['A', 'B', 'C', 'D', 'E'], 'source': 'D', 'target': 'E', 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 4.0}, {'var_index': 1, 'linear_cost': 10.0}, {'var_index': 2, 'linear_cost': 4.0}, {'var_index': 3, 'linear_cost': 7.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 1.0}]}, 'edges': [{'from': 'D', 'to': 'A', 'var_index': 0}, {'from': 'C', 'to': 'E', 'var_index': 1}, {'from': 'A', 'to': 'B', 'var_index': 2}, {'from': 'B', 'to': 'C', 'var_index': 3}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E'}}","['D', 'A', 'B', 'C', 'E']",28,json,names
QSPP,QSPP,"I’m helping out an event planner who has to pick one clear route to move all guests from the lobby into the banquet hall using the venue’s one-way corridors. Each corridor has a basic inconvenience — like how narrow, long, or awkward it is — and some corridor combinations make things worse when used together (maybe they create pinch points or confusing turns). The aim is to pick the single continuous route that causes the least total hassle, where the total hassle is just the sum of each corridor’s basic cost plus any extra friction that arises if certain corridors are used in combination. The route has to start in the lobby, end in the banquet room, follow the direction of the passageways at every step, and be a single, unbroken sequence (no splitting guests across multiple routes or skipping/making up connections). The exact map and the numbers for each corridor and combination are shown below.

# total_locations=6
# total_corridors=5
# location_ids=0, 1, 2, 3, 4, 5
# lobby_node=4
# banquet_hall_node=5

corridor_from_location,corridor_to_location,corridor_id
4,0,0
3,5,1
0,1,2
1,2,3
2,3,4

corridor_id_ref,base_inconvenience
0,7.0
1,4.0
2,3.0
3,6.0
4,2.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (corridor_i_id, corridor_j_id). If two corridors with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| corridor_i_id\corridor_j_id | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| 0 | 2.0 | 7.0 | 4.0 | 6.0 | 1.0 |
| 1 | 7.0 | 7.0 | 6.0 | 10.0 | 9.0 |
| 2 | 4.0 | 6.0 | 7.0 | 5.0 | 4.0 |
| 3 | 6.0 | 10.0 | 5.0 | 1.0 | 6.0 |
| 4 | 1.0 | 9.0 | 4.0 | 6.0 | 2.0 |

Oh, and to keep things easy to parse, please put the chosen route into a tiny JSON snippet like this:

{
  ""solution"": []
}

Here, ""solution"" is where you’ll list the route as an ordered array of NODE identifiers only (start with the lobby, end with the banquet room, and make sure each step follows an existing one-way corridor). This JSON is just a sketch of the shape I expect — not the actual answer itself.

Please use identifiers exactly as they appear in the instance input — no renaming and no made-up labels. Valid identifiers look like plain numbers such as ""1"" or ""23"", single capital letters like ""A"" or ""B"", or a capital letter followed by digits like ""A1"" or ""X7"".

Also, don’t include corridor/edge identifiers or any cost numbers in the path — just the node names.","{'nodes': [0, 1, 2, 3, 4, 5], 'edges': [{'from': 4, 'to': 0, 'var_index': 0}, {'from': 3, 'to': 5, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}], 'objective': {'constant': 0.0, 'linear': [7.0, 4.0, 3.0, 6.0, 2.0], 'quadratic': [[2.0, 7.0, 4.0, 6.0, 1.0], [7.0, 7.0, 6.0, 10.0, 9.0], [4.0, 6.0, 7.0, 5.0, 4.0], [6.0, 10.0, 5.0, 1.0, 6.0], [1.0, 9.0, 4.0, 6.0, 2.0]]}, 'source': 4, 'target': 5}","[4, 0, 1, 2, 3, 5]",157.0,"{'problem_type': 'QSPP', 'num_nodes': 6, 'num_edges': 5, 'nodes': [0, 1, 2, 3, 4, 5], 'source': 4, 'target': 5, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 7.0}, {'var_index': 1, 'linear_cost': 4.0}, {'var_index': 2, 'linear_cost': 3.0}, {'var_index': 3, 'linear_cost': 6.0}, {'var_index': 4, 'linear_cost': 2.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 2.0}]}, 'edges': [{'from': 4, 'to': 0, 'var_index': 0}, {'from': 3, 'to': 5, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5}}","[4, 0, 1, 2, 3, 5]",29,csv,0
QSPP,QSPP,"Out in town a carrier needed to pick a single, legal one-way path from the depot to a mailbox. Every street costs something to serve, some streets have extra charges that kick in when they’re used, and some pairs of streets add an extra penalty if both are included on the run. The idea is to find one continuous path that ends at the mailbox and gives the lowest total bill — add up every street’s cost, any individual extra charges, and every extra penalty for street pairs that both appear on the trip. Each step must be an actual allowed one-way move from one spot to the next, and the full route must go straight from depot to mailbox. The detailed map and cost numbers are shown below.

The map shows 6 locations (0, 1, 2, 3, 4, 5) and 5 one-way streets; the depot is 4 and the mailbox is 5.

| street_from | street_to | street_id |
|---|---|---|
| 4 | 0 | 0 |
| 3 | 5 | 1 |
| 0 | 1 | 2 |
| 1 | 2 | 3 |
| 2 | 3 | 4 |

| street_id | street_service_cost |
|---|---|
| 0 | 10.0 |
| 1 | 5.0 |
| 2 | 7.0 |
| 3 | 4.0 |
| 4 | 9.0 |

*Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (street_i_id, street_j_id). If two streets with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).*

**quadratic_costs**

| street_i_id\street_j_id | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| 0 | 10.0 | 4.0 | 8.0 | 3.0 | 9.0 |
| 1 | 4.0 | 6.0 | 6.0 | 10.0 | 10.0 |
| 2 | 8.0 | 6.0 | 1.0 | 4.0 | 1.0 |
| 3 | 3.0 | 10.0 | 4.0 | 10.0 | 5.0 |
| 4 | 9.0 | 10.0 | 1.0 | 5.0 | 6.0 |

Use these entries to pick the single legal one-way route from 4 to 5 that yields the lowest total cost.

And here's the tiny bit of structure I want you to follow for your reply — just a simple JSON shape that holds the route.

{
  ""solution"": []
}

""solution"" is where you put the chosen path as an ordered list of node identifiers, starting at the depot and ending at the mailbox. Think of it like filling in a short form: list each location you pass through in order, and make sure every step is a legal one-way move on the map. This JSON is just a sketch of the expected shape, not the actual route answer.

Please use the exact identifiers from the instance input — do not rename them or invent new labels. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""

Keep it simple and exact, and I'll check the path you drop into that ""solution"" array.","{'nodes': [0, 1, 2, 3, 4, 5], 'edges': [{'from': 4, 'to': 0, 'var_index': 0}, {'from': 3, 'to': 5, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}], 'objective': {'constant': 0.0, 'linear': [10.0, 5.0, 7.0, 4.0, 9.0], 'quadratic': [[10.0, 4.0, 8.0, 3.0, 9.0], [4.0, 6.0, 6.0, 10.0, 10.0], [8.0, 6.0, 1.0, 4.0, 1.0], [3.0, 10.0, 4.0, 10.0, 5.0], [9.0, 10.0, 1.0, 5.0, 6.0]]}, 'source': 4, 'target': 5}","[4, 0, 1, 2, 3, 5]",188.0,"{'problem_type': 'QSPP', 'num_nodes': 6, 'num_edges': 5, 'nodes': [0, 1, 2, 3, 4, 5], 'source': 4, 'target': 5, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 10.0}, {'var_index': 1, 'linear_cost': 5.0}, {'var_index': 2, 'linear_cost': 7.0}, {'var_index': 3, 'linear_cost': 4.0}, {'var_index': 4, 'linear_cost': 9.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 6.0}]}, 'edges': [{'from': 4, 'to': 0, 'var_index': 0}, {'from': 3, 'to': 5, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5}}","[4, 0, 1, 2, 3, 5]",30,markdown_table,0
QSPP,QSPP,"Many people on the team treat it like a little puzzle: program a single, one-way trip for the robot from its charger to the workbench using only the approved directional lanes. Each lane adds its own energy cost, and some lane pairs introduce extra penalties when they both show up in that exact order, so the trip’s total cost is the sum of the lane energies plus any such ordered penalties. The best trip is the one with the lowest total, and the recorded answer should be just the sequence of locations from start to finish—every consecutive pair must be a real lane, with nothing else tacked on. The full map and cost numbers are given below.

{
  ""num_locations"": 6,
  ""num_lanes"": 11,
  ""location_ids"": [
    ""A"",
    ""B"",
    ""C"",
    ""D"",
    ""E"",
    ""F""
  ],
  ""recharge_station_id"": ""E"",
  ""workbench_id"": ""F"",
  ""edges"": [
    {
      ""lane_tail_location"": ""E"",
      ""lane_head_location"": ""A"",
      ""lane_id"": 0
    },
    {
      ""lane_tail_location"": ""E"",
      ""lane_head_location"": ""B"",
      ""lane_id"": 1
    },
    {
      ""lane_tail_location"": ""E"",
      ""lane_head_location"": ""C"",
      ""lane_id"": 2
    },
    {
      ""lane_tail_location"": ""E"",
      ""lane_head_location"": ""D"",
      ""lane_id"": 3
    },
    {
      ""lane_tail_location"": ""A"",
      ""lane_head_location"": ""F"",
      ""lane_id"": 4
    },
    {
      ""lane_tail_location"": ""B"",
      ""lane_head_location"": ""F"",
      ""lane_id"": 5
    },
    {
      ""lane_tail_location"": ""C"",
      ""lane_head_location"": ""F"",
      ""lane_id"": 6
    },
    {
      ""lane_tail_location"": ""D"",
      ""lane_head_location"": ""F"",
      ""lane_id"": 7
    },
    {
      ""lane_tail_location"": ""A"",
      ""lane_head_location"": ""B"",
      ""lane_id"": 8
    },
    {
      ""lane_tail_location"": ""B"",
      ""lane_head_location"": ""C"",
      ""lane_id"": 9
    },
    {
      ""lane_tail_location"": ""C"",
      ""lane_head_location"": ""D"",
      ""lane_id"": 10
    }
  ],
  ""linear_costs"": [
    {
      ""lane_id"": 0,
      ""lane_energy_cost"": 6.0
    },
    {
      ""lane_id"": 1,
      ""lane_energy_cost"": 1.0
    },
    {
      ""lane_id"": 2,
      ""lane_energy_cost"": 5.0
    },
    {
      ""lane_id"": 3,
      ""lane_energy_cost"": 5.0
    },
    {
      ""lane_id"": 4,
      ""lane_energy_cost"": 6.0
    },
    {
      ""lane_id"": 5,
      ""lane_energy_cost"": 4.0
    },
    {
      ""lane_id"": 6,
      ""lane_energy_cost"": 8.0
    },
    {
      ""lane_id"": 7,
      ""lane_energy_cost"": 7.0
    },
    {
      ""lane_id"": 8,
      ""lane_energy_cost"": 6.0
    },
    {
      ""lane_id"": 9,
      ""lane_energy_cost"": 5.0
    },
    {
      ""lane_id"": 10,
      ""lane_energy_cost"": 4.0
    }
  ]
}

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (first_lane_id, second_lane_id). If two lanes with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| first_lane_id\second_lane_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 9.0 | 5.0 | 9.0 | 6.0 | 10.0 | 3.0 | 1.0 | 10.0 | 5.0 | 2.0 | 6.0 |
| 1 | 5.0 | 3.0 | 5.0 | 10.0 | 4.0 | 9.0 | 5.0 | 8.0 | 5.0 | 5.0 | 1.0 |
| 2 | 9.0 | 5.0 | 9.0 | 4.0 | 2.0 | 10.0 | 7.0 | 10.0 | 5.0 | 2.0 | 2.0 |
| 3 | 6.0 | 10.0 | 4.0 | 9.0 | 9.0 | 5.0 | 6.0 | 6.0 | 8.0 | 2.0 | 2.0 |
| 4 | 10.0 | 4.0 | 2.0 | 9.0 | 10.0 | 5.0 | 3.0 | 2.0 | 2.0 | 3.0 | 7.0 |
| 5 | 3.0 | 9.0 | 10.0 | 5.0 | 5.0 | 6.0 | 10.0 | 5.0 | 6.0 | 8.0 | 8.0 |
| 6 | 1.0 | 5.0 | 7.0 | 6.0 | 3.0 | 10.0 | 3.0 | 5.0 | 6.0 | 2.0 | 2.0 |
| 7 | 10.0 | 8.0 | 10.0 | 6.0 | 2.0 | 5.0 | 5.0 | 6.0 | 4.0 | 3.0 | 3.0 |
| 8 | 5.0 | 5.0 | 5.0 | 8.0 | 2.0 | 6.0 | 6.0 | 4.0 | 8.0 | 8.0 | 3.0 |
| 9 | 2.0 | 5.0 | 2.0 | 2.0 | 3.0 | 8.0 | 2.0 | 3.0 | 8.0 | 1.0 | 10.0 |
| 10 | 6.0 | 1.0 | 2.0 | 2.0 | 7.0 | 8.0 | 2.0 | 3.0 | 3.0 | 10.0 | 7.0 |

Also, when you send back the chosen trip, please drop it into a tiny JSON snippet so it's easy to read and parse. A relaxed example of the shape I expect is below.

{
  ""solution"": []
}

Think of ""solution"" as the ordered list of locations you want the robot to drive through — just the node names from start to finish, in order. This JSON is only a sketch of the shape I want, not the actual answer itself.

Please use the node identifiers exactly as they appear in the input — do not rename them or invent new labels. For example, valid identifiers look like plain numbers such as ""1"" or ""23"", single capital letters like ""A"" or ""B"", or a capital letter followed by digits like ""A1"" or ""X7"".","{'nodes': [0, 1, 2, 3, 4, 5], 'edges': [{'from': 4, 'to': 0, 'var_index': 0}, {'from': 4, 'to': 1, 'var_index': 1}, {'from': 4, 'to': 2, 'var_index': 2}, {'from': 4, 'to': 3, 'var_index': 3}, {'from': 0, 'to': 5, 'var_index': 4}, {'from': 1, 'to': 5, 'var_index': 5}, {'from': 2, 'to': 5, 'var_index': 6}, {'from': 3, 'to': 5, 'var_index': 7}, {'from': 0, 'to': 1, 'var_index': 8}, {'from': 1, 'to': 2, 'var_index': 9}, {'from': 2, 'to': 3, 'var_index': 10}], 'objective': {'constant': 0.0, 'linear': [6.0, 1.0, 5.0, 5.0, 6.0, 4.0, 8.0, 7.0, 6.0, 5.0, 4.0], 'quadratic': [[9.0, 5.0, 9.0, 6.0, 10.0, 3.0, 1.0, 10.0, 5.0, 2.0, 6.0], [5.0, 3.0, 5.0, 10.0, 4.0, 9.0, 5.0, 8.0, 5.0, 5.0, 1.0], [9.0, 5.0, 9.0, 4.0, 2.0, 10.0, 7.0, 10.0, 5.0, 2.0, 2.0], [6.0, 10.0, 4.0, 9.0, 9.0, 5.0, 6.0, 6.0, 8.0, 2.0, 2.0], [10.0, 4.0, 2.0, 9.0, 10.0, 5.0, 3.0, 2.0, 2.0, 3.0, 7.0], [3.0, 9.0, 10.0, 5.0, 5.0, 6.0, 10.0, 5.0, 6.0, 8.0, 8.0], [1.0, 5.0, 7.0, 6.0, 3.0, 10.0, 3.0, 5.0, 6.0, 2.0, 2.0], [10.0, 8.0, 10.0, 6.0, 2.0, 5.0, 5.0, 6.0, 4.0, 3.0, 3.0], [5.0, 5.0, 5.0, 8.0, 2.0, 6.0, 6.0, 4.0, 8.0, 8.0, 3.0], [2.0, 5.0, 2.0, 2.0, 3.0, 8.0, 2.0, 3.0, 8.0, 1.0, 10.0], [6.0, 1.0, 2.0, 2.0, 7.0, 8.0, 2.0, 3.0, 3.0, 10.0, 7.0]]}, 'source': 4, 'target': 5}","[4, 1, 5]",32.0,"{'problem_type': 'QSPP', 'num_nodes': 6, 'num_edges': 11, 'nodes': ['A', 'B', 'C', 'D', 'E', 'F'], 'source': 'E', 'target': 'F', 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 6.0}, {'var_index': 1, 'linear_cost': 1.0}, {'var_index': 2, 'linear_cost': 5.0}, {'var_index': 3, 'linear_cost': 5.0}, {'var_index': 4, 'linear_cost': 6.0}, {'var_index': 5, 'linear_cost': 4.0}, {'var_index': 6, 'linear_cost': 8.0}, {'var_index': 7, 'linear_cost': 7.0}, {'var_index': 8, 'linear_cost': 6.0}, {'var_index': 9, 'linear_cost': 5.0}, {'var_index': 10, 'linear_cost': 4.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 7, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 8, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 8, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 8, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 8, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 9, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 9, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 9, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 9, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 10, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 10, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 10, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 10, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 10, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 10, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 10, 'var_j': 10, 'quadratic_cost': 7.0}]}, 'edges': [{'from': 'E', 'to': 'A', 'var_index': 0}, {'from': 'E', 'to': 'B', 'var_index': 1}, {'from': 'E', 'to': 'C', 'var_index': 2}, {'from': 'E', 'to': 'D', 'var_index': 3}, {'from': 'A', 'to': 'F', 'var_index': 4}, {'from': 'B', 'to': 'F', 'var_index': 5}, {'from': 'C', 'to': 'F', 'var_index': 6}, {'from': 'D', 'to': 'F', 'var_index': 7}, {'from': 'A', 'to': 'B', 'var_index': 8}, {'from': 'B', 'to': 'C', 'var_index': 9}, {'from': 'C', 'to': 'D', 'var_index': 10}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E', 5: 'F'}}","['E', 'B', 'F']",31,json,names
QSPP,QSPP,"There's a simple scene: a visitor wants to go from the museum entrance to the viewpoint using the one-way promenades, and only one path is allowed. That path must be continuous and follow the direction signs the whole way — no splitting the trip or leaving out any segments. Each promenade costs some walking effort, some segments bring their own extra awkwardness even alone, and any time two specific promenades appear together they may add extra combined discomfort (both sides of their interaction are added up). So the trick is to pick the single allowed route that minimizes the sum of all individual efforts plus any extra awkwardness from chosen pairings. The full map with the walkway details and numbers is shown below.

# num_locations=9
# num_promenades=12
# location_ids=1, 2, 3, 4, 5, 6, 7, 8, 9
# museum_entrance_id=1
# viewpoint_id=9

promenade_tail_location,promenade_head_location,promenade_id
1,2,0
1,4,1
2,3,2
2,5,3
3,6,4
4,5,5
4,7,6
5,6,7
5,8,8
6,9,9
7,8,10
8,9,11

promenade_id,walking_effort
0,4.0
1,9.0
2,5.0
3,9.0
4,3.0
5,7.0
6,8.0
7,2.0
8,3.0
9,8.0
10,2.0
11,5.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (promenade_i_id, promenade_j_id). If two promenades with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| promenade_i_id\promenade_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 5.0 | 4.0 | 6.0 | 10.0 | 1.0 | 10.0 | 6.0 | 1.0 | 5.0 | 2.0 | 6.0 | 3.0 |
| 1 | 4.0 | 7.0 | 8.0 | 7.0 | 7.0 | 4.0 | 1.0 | 4.0 | 3.0 | 2.0 | 5.0 | 4.0 |
| 2 | 6.0 | 8.0 | 4.0 | 8.0 | 8.0 | 9.0 | 5.0 | 10.0 | 6.0 | 2.0 | 9.0 | 3.0 |
| 3 | 10.0 | 7.0 | 8.0 | 8.0 | 4.0 | 7.0 | 3.0 | 2.0 | 1.0 | 2.0 | 5.0 | 10.0 |
| 4 | 1.0 | 7.0 | 8.0 | 4.0 | 2.0 | 4.0 | 10.0 | 7.0 | 3.0 | 3.0 | 1.0 | 8.0 |
| 5 | 10.0 | 4.0 | 9.0 | 7.0 | 4.0 | 1.0 | 7.0 | 7.0 | 9.0 | 4.0 | 3.0 | 5.0 |
| 6 | 6.0 | 1.0 | 5.0 | 3.0 | 10.0 | 7.0 | 1.0 | 4.0 | 3.0 | 9.0 | 5.0 | 3.0 |
| 7 | 1.0 | 4.0 | 10.0 | 2.0 | 7.0 | 7.0 | 4.0 | 5.0 | 10.0 | 2.0 | 9.0 | 2.0 |
| 8 | 5.0 | 3.0 | 6.0 | 1.0 | 3.0 | 9.0 | 3.0 | 10.0 | 4.0 | 10.0 | 10.0 | 2.0 |
| 9 | 2.0 | 2.0 | 2.0 | 2.0 | 3.0 | 4.0 | 9.0 | 2.0 | 10.0 | 1.0 | 9.0 | 6.0 |
| 10 | 6.0 | 5.0 | 9.0 | 5.0 | 1.0 | 3.0 | 5.0 | 9.0 | 10.0 | 9.0 | 4.0 | 5.0 |
| 11 | 3.0 | 4.0 | 3.0 | 10.0 | 8.0 | 5.0 | 3.0 | 2.0 | 2.0 | 6.0 | 5.0 | 9.0 |

When you send back the single chosen promenade, just drop it into a tiny JSON sketch like this so it's easy to parse — nothing fancy, just the shape I expect:

{
  ""solution"": []
}

Think of ""solution"" as the ordered list of NODE names only: start at the museum entrance and list each node you pass through until the viewpoint, in order. Keep it human-readable and simple (for example, [""Entrance"",""A"",""Viewpoint""]), and remember this block is only a template showing the expected shape, not the actual answer.

Please use the node identifiers exactly as they appear in the instance input — don't rename them or invent new labels. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'name': 'Rostami_Grid1_k3_seedNone', 'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8], 'edges': [{'from': 0, 'to': 1, 'var_index': 0}, {'from': 0, 'to': 3, 'var_index': 1}, {'from': 1, 'to': 2, 'var_index': 2}, {'from': 1, 'to': 4, 'var_index': 3}, {'from': 2, 'to': 5, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 3, 'to': 6, 'var_index': 6}, {'from': 4, 'to': 5, 'var_index': 7}, {'from': 4, 'to': 7, 'var_index': 8}, {'from': 5, 'to': 8, 'var_index': 9}, {'from': 6, 'to': 7, 'var_index': 10}, {'from': 7, 'to': 8, 'var_index': 11}], 'objective': {'constant': 0.0, 'linear': [4.0, 9.0, 5.0, 9.0, 3.0, 7.0, 8.0, 2.0, 3.0, 8.0, 2.0, 5.0], 'quadratic': [[5.0, 4.0, 6.0, 10.0, 1.0, 10.0, 6.0, 1.0, 5.0, 2.0, 6.0, 3.0], [4.0, 7.0, 8.0, 7.0, 7.0, 4.0, 1.0, 4.0, 3.0, 2.0, 5.0, 4.0], [6.0, 8.0, 4.0, 8.0, 8.0, 9.0, 5.0, 10.0, 6.0, 2.0, 9.0, 3.0], [10.0, 7.0, 8.0, 8.0, 4.0, 7.0, 3.0, 2.0, 1.0, 2.0, 5.0, 10.0], [1.0, 7.0, 8.0, 4.0, 2.0, 4.0, 10.0, 7.0, 3.0, 3.0, 1.0, 8.0], [10.0, 4.0, 9.0, 7.0, 4.0, 1.0, 7.0, 7.0, 9.0, 4.0, 3.0, 5.0], [6.0, 1.0, 5.0, 3.0, 10.0, 7.0, 1.0, 4.0, 3.0, 9.0, 5.0, 3.0], [1.0, 4.0, 10.0, 2.0, 7.0, 7.0, 4.0, 5.0, 10.0, 2.0, 9.0, 2.0], [5.0, 3.0, 6.0, 1.0, 3.0, 9.0, 3.0, 10.0, 4.0, 10.0, 10.0, 2.0], [2.0, 2.0, 2.0, 2.0, 3.0, 4.0, 9.0, 2.0, 10.0, 1.0, 9.0, 6.0], [6.0, 5.0, 9.0, 5.0, 1.0, 3.0, 5.0, 9.0, 10.0, 9.0, 4.0, 5.0], [3.0, 4.0, 3.0, 10.0, 8.0, 5.0, 3.0, 2.0, 2.0, 6.0, 5.0, 9.0]]}, 'source': 0, 'target': 8}","[0, 1, 2, 5, 8]",76.0,"{'problem_type': 'QSPP', 'num_nodes': 9, 'num_edges': 12, 'nodes': [1, 2, 3, 4, 5, 6, 7, 8, 9], 'source': 1, 'target': 9, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 4.0}, {'var_index': 1, 'linear_cost': 9.0}, {'var_index': 2, 'linear_cost': 5.0}, {'var_index': 3, 'linear_cost': 9.0}, {'var_index': 4, 'linear_cost': 3.0}, {'var_index': 5, 'linear_cost': 7.0}, {'var_index': 6, 'linear_cost': 8.0}, {'var_index': 7, 'linear_cost': 2.0}, {'var_index': 8, 'linear_cost': 3.0}, {'var_index': 9, 'linear_cost': 8.0}, {'var_index': 10, 'linear_cost': 2.0}, {'var_index': 11, 'linear_cost': 5.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 7, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 7, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 7, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 8, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 8, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 8, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 8, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 8, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 8, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 9, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 9, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 9, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 9, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 9, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 9, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 10, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 10, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 10, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 10, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 10, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 10, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 11, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 11, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 11, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 11, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 11, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 11, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 11, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 11, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 11, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 11, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 11, 'var_j': 11, 'quadratic_cost': 9.0}]}, 'edges': [{'from': 1, 'to': 2, 'var_index': 0}, {'from': 1, 'to': 4, 'var_index': 1}, {'from': 2, 'to': 3, 'var_index': 2}, {'from': 2, 'to': 5, 'var_index': 3}, {'from': 3, 'to': 6, 'var_index': 4}, {'from': 4, 'to': 5, 'var_index': 5}, {'from': 4, 'to': 7, 'var_index': 6}, {'from': 5, 'to': 6, 'var_index': 7}, {'from': 5, 'to': 8, 'var_index': 8}, {'from': 6, 'to': 9, 'var_index': 9}, {'from': 7, 'to': 8, 'var_index': 10}, {'from': 8, 'to': 9, 'var_index': 11}], 'node_id_map': {0: 1, 1: 2, 2: 3, 3: 4, 4: 5, 5: 6, 6: 7, 7: 8, 8: 9}}","[1, 2, 3, 6, 9]",32,csv,1
QSPP,QSPP,"At the station they want one clear path for the ambulance to follow from base to the incident, using only legal one-way streets, and the preference is the path that yields the lowest total trip time. Each street in that path brings a basic travel time, and there are extra slowdowns associated with some streets individually or when certain streets appear together, so the trip’s total time is the sum of the street times plus any applicable added delays. The chosen route should be written as a single list of locations—starting at the emergency center, ending at the scene—where each consecutive pair matches a real one-way street; the detailed map and costs are provided below.

The map below lists 8 locations and 17 one-way streets: 0, 1, 2, 3, 4, 5, 6, 7. The ambulance starts at 6 and must end at 7.
Street 0 runs from 6 to 0.
Street 1 runs from 6 to 1.
Street 2 runs from 6 to 2.
Street 3 runs from 6 to 3.
Street 4 runs from 6 to 4.
Street 5 runs from 6 to 5.
Street 6 runs from 0 to 7.
Street 7 runs from 1 to 7.
Street 8 runs from 2 to 7.
Street 9 runs from 3 to 7.
Street 10 runs from 4 to 7.
Street 11 runs from 5 to 7.
Street 12 runs from 0 to 1.
Street 13 runs from 1 to 2.
Street 14 runs from 2 to 3.
Street 15 runs from 3 to 4.
Street 16 runs from 4 to 5.
Street 0 carries a base travel time of 6.0.
Street 1 carries a base travel time of 1.0.
Street 2 carries a base travel time of 8.0.
Street 3 carries a base travel time of 3.0.
Street 4 carries a base travel time of 7.0.
Street 5 carries a base travel time of 10.0.
Street 6 carries a base travel time of 2.0.
Street 7 carries a base travel time of 1.0.
Street 8 carries a base travel time of 3.0.
Street 9 carries a base travel time of 10.0.
Street 10 carries a base travel time of 9.0.
Street 11 carries a base travel time of 9.0.
Street 12 carries a base travel time of 5.0.
Street 13 carries a base travel time of 8.0.
Street 14 carries a base travel time of 8.0.
Street 15 carries a base travel time of 3.0.
Street 16 carries a base travel time of 8.0.
Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (street_i_id, street_j_id). If two streets with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
quadratic_costs:
| street_i_id\street_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 5.0 | 6.0 | 9.0 | 7.0 | 2.0 | 6.0 | 4.0 | 6.0 | 2.0 | 7.0 | 10.0 | 9.0 | 6.0 | 5.0 | 3.0 | 1.0 | 9.0 |
| 1 | 6.0 | 4.0 | 9.0 | 1.0 | 8.0 | 1.0 | 4.0 | 2.0 | 5.0 | 9.0 | 7.0 | 2.0 | 6.0 | 4.0 | 1.0 | 9.0 | 7.0 |
| 2 | 9.0 | 9.0 | 1.0 | 2.0 | 9.0 | 8.0 | 6.0 | 10.0 | 7.0 | 1.0 | 1.0 | 9.0 | 5.0 | 5.0 | 6.0 | 8.0 | 5.0 |
| 3 | 7.0 | 1.0 | 2.0 | 7.0 | 6.0 | 6.0 | 5.0 | 6.0 | 3.0 | 8.0 | 6.0 | 4.0 | 6.0 | 3.0 | 8.0 | 9.0 | 9.0 |
| 4 | 2.0 | 8.0 | 9.0 | 6.0 | 1.0 | 1.0 | 8.0 | 3.0 | 10.0 | 3.0 | 10.0 | 9.0 | 4.0 | 7.0 | 4.0 | 6.0 | 5.0 |
| 5 | 6.0 | 1.0 | 8.0 | 6.0 | 1.0 | 8.0 | 4.0 | 10.0 | 4.0 | 10.0 | 7.0 | 8.0 | 8.0 | 9.0 | 9.0 | 8.0 | 2.0 |
| 6 | 4.0 | 4.0 | 6.0 | 5.0 | 8.0 | 4.0 | 2.0 | 6.0 | 5.0 | 4.0 | 7.0 | 10.0 | 1.0 | 1.0 | 1.0 | 10.0 | 2.0 |
| 7 | 6.0 | 2.0 | 10.0 | 6.0 | 3.0 | 10.0 | 6.0 | 9.0 | 10.0 | 7.0 | 4.0 | 5.0 | 10.0 | 6.0 | 4.0 | 6.0 | 10.0 |
| 8 | 2.0 | 5.0 | 7.0 | 3.0 | 10.0 | 4.0 | 5.0 | 10.0 | 9.0 | 6.0 | 5.0 | 10.0 | 8.0 | 8.0 | 5.0 | 5.0 | 1.0 |
| 9 | 7.0 | 9.0 | 1.0 | 8.0 | 3.0 | 10.0 | 4.0 | 7.0 | 6.0 | 7.0 | 9.0 | 9.0 | 8.0 | 6.0 | 3.0 | 1.0 | 1.0 |
| 10 | 10.0 | 7.0 | 1.0 | 6.0 | 10.0 | 7.0 | 7.0 | 4.0 | 5.0 | 9.0 | 10.0 | 9.0 | 8.0 | 1.0 | 6.0 | 8.0 | 4.0 |
| 11 | 9.0 | 2.0 | 9.0 | 4.0 | 9.0 | 8.0 | 10.0 | 5.0 | 10.0 | 9.0 | 9.0 | 9.0 | 10.0 | 5.0 | 2.0 | 6.0 | 7.0 |
| 12 | 6.0 | 6.0 | 5.0 | 6.0 | 4.0 | 8.0 | 1.0 | 10.0 | 8.0 | 8.0 | 8.0 | 10.0 | 1.0 | 9.0 | 1.0 | 4.0 | 8.0 |
| 13 | 5.0 | 4.0 | 5.0 | 3.0 | 7.0 | 9.0 | 1.0 | 6.0 | 8.0 | 6.0 | 1.0 | 5.0 | 9.0 | 3.0 | 2.0 | 6.0 | 6.0 |
| 14 | 3.0 | 1.0 | 6.0 | 8.0 | 4.0 | 9.0 | 1.0 | 4.0 | 5.0 | 3.0 | 6.0 | 2.0 | 1.0 | 2.0 | 5.0 | 4.0 | 5.0 |
| 15 | 1.0 | 9.0 | 8.0 | 9.0 | 6.0 | 8.0 | 10.0 | 6.0 | 5.0 | 1.0 | 8.0 | 6.0 | 4.0 | 6.0 | 4.0 | 9.0 | 7.0 |
| 16 | 9.0 | 7.0 | 5.0 | 9.0 | 5.0 | 2.0 | 2.0 | 10.0 | 1.0 | 1.0 | 4.0 | 7.0 | 8.0 | 6.0 | 5.0 | 7.0 | 10.0 |
They expect the chosen route to be given as a single ordered list of locations from 6 to 7.

Also, to keep things machine-friendly, please give the chosen route in a tiny JSON snippet — nothing fancy — like this:

{
  ""solution"": []
}

Think of ""solution"" as the single list of locations (nodes) starting at the emergency center and ending at the scene; replace the empty array with the sequence of node identifiers in order. This JSON is just a sketch of the shape I expect, not the answer itself.

A quick note: use only node identifiers exactly as they appear in the instance input — no renaming, no invented labels, and do not include edge identifiers or any cost labels in the path. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7], 'edges': [{'from': 6, 'to': 0, 'var_index': 0}, {'from': 6, 'to': 1, 'var_index': 1}, {'from': 6, 'to': 2, 'var_index': 2}, {'from': 6, 'to': 3, 'var_index': 3}, {'from': 6, 'to': 4, 'var_index': 4}, {'from': 6, 'to': 5, 'var_index': 5}, {'from': 0, 'to': 7, 'var_index': 6}, {'from': 1, 'to': 7, 'var_index': 7}, {'from': 2, 'to': 7, 'var_index': 8}, {'from': 3, 'to': 7, 'var_index': 9}, {'from': 4, 'to': 7, 'var_index': 10}, {'from': 5, 'to': 7, 'var_index': 11}, {'from': 0, 'to': 1, 'var_index': 12}, {'from': 1, 'to': 2, 'var_index': 13}, {'from': 2, 'to': 3, 'var_index': 14}, {'from': 3, 'to': 4, 'var_index': 15}, {'from': 4, 'to': 5, 'var_index': 16}], 'objective': {'constant': 0.0, 'linear': [6.0, 1.0, 8.0, 3.0, 7.0, 10.0, 2.0, 1.0, 3.0, 10.0, 9.0, 9.0, 5.0, 8.0, 8.0, 3.0, 8.0], 'quadratic': [[5.0, 6.0, 9.0, 7.0, 2.0, 6.0, 4.0, 6.0, 2.0, 7.0, 10.0, 9.0, 6.0, 5.0, 3.0, 1.0, 9.0], [6.0, 4.0, 9.0, 1.0, 8.0, 1.0, 4.0, 2.0, 5.0, 9.0, 7.0, 2.0, 6.0, 4.0, 1.0, 9.0, 7.0], [9.0, 9.0, 1.0, 2.0, 9.0, 8.0, 6.0, 10.0, 7.0, 1.0, 1.0, 9.0, 5.0, 5.0, 6.0, 8.0, 5.0], [7.0, 1.0, 2.0, 7.0, 6.0, 6.0, 5.0, 6.0, 3.0, 8.0, 6.0, 4.0, 6.0, 3.0, 8.0, 9.0, 9.0], [2.0, 8.0, 9.0, 6.0, 1.0, 1.0, 8.0, 3.0, 10.0, 3.0, 10.0, 9.0, 4.0, 7.0, 4.0, 6.0, 5.0], [6.0, 1.0, 8.0, 6.0, 1.0, 8.0, 4.0, 10.0, 4.0, 10.0, 7.0, 8.0, 8.0, 9.0, 9.0, 8.0, 2.0], [4.0, 4.0, 6.0, 5.0, 8.0, 4.0, 2.0, 6.0, 5.0, 4.0, 7.0, 10.0, 1.0, 1.0, 1.0, 10.0, 2.0], [6.0, 2.0, 10.0, 6.0, 3.0, 10.0, 6.0, 9.0, 10.0, 7.0, 4.0, 5.0, 10.0, 6.0, 4.0, 6.0, 10.0], [2.0, 5.0, 7.0, 3.0, 10.0, 4.0, 5.0, 10.0, 9.0, 6.0, 5.0, 10.0, 8.0, 8.0, 5.0, 5.0, 1.0], [7.0, 9.0, 1.0, 8.0, 3.0, 10.0, 4.0, 7.0, 6.0, 7.0, 9.0, 9.0, 8.0, 6.0, 3.0, 1.0, 1.0], [10.0, 7.0, 1.0, 6.0, 10.0, 7.0, 7.0, 4.0, 5.0, 9.0, 10.0, 9.0, 8.0, 1.0, 6.0, 8.0, 4.0], [9.0, 2.0, 9.0, 4.0, 9.0, 8.0, 10.0, 5.0, 10.0, 9.0, 9.0, 9.0, 10.0, 5.0, 2.0, 6.0, 7.0], [6.0, 6.0, 5.0, 6.0, 4.0, 8.0, 1.0, 10.0, 8.0, 8.0, 8.0, 10.0, 1.0, 9.0, 1.0, 4.0, 8.0], [5.0, 4.0, 5.0, 3.0, 7.0, 9.0, 1.0, 6.0, 8.0, 6.0, 1.0, 5.0, 9.0, 3.0, 2.0, 6.0, 6.0], [3.0, 1.0, 6.0, 8.0, 4.0, 9.0, 1.0, 4.0, 5.0, 3.0, 6.0, 2.0, 1.0, 2.0, 5.0, 4.0, 5.0], [1.0, 9.0, 8.0, 9.0, 6.0, 8.0, 10.0, 6.0, 5.0, 1.0, 8.0, 6.0, 4.0, 6.0, 4.0, 9.0, 7.0], [9.0, 7.0, 5.0, 9.0, 5.0, 2.0, 2.0, 10.0, 1.0, 1.0, 4.0, 7.0, 8.0, 6.0, 5.0, 7.0, 10.0]]}, 'source': 6, 'target': 7}","[6, 1, 7]",19.0,"{'problem_type': 'QSPP', 'num_nodes': 8, 'num_edges': 17, 'nodes': [0, 1, 2, 3, 4, 5, 6, 7], 'source': 6, 'target': 7, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 6.0}, {'var_index': 1, 'linear_cost': 1.0}, {'var_index': 2, 'linear_cost': 8.0}, {'var_index': 3, 'linear_cost': 3.0}, {'var_index': 4, 'linear_cost': 7.0}, {'var_index': 5, 'linear_cost': 10.0}, {'var_index': 6, 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'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 14, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 14, 'var_j': 14, 'quadratic_cost': 5.0}, {'var_i': 14, 'var_j': 15, 'quadratic_cost': 4.0}, {'var_i': 14, 'var_j': 16, 'quadratic_cost': 5.0}, {'var_i': 15, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 15, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 15, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 15, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 15, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 15, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 15, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 15, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 15, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 15, 'var_j': 12, 'quadratic_cost': 4.0}, {'var_i': 15, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 15, 'var_j': 14, 'quadratic_cost': 4.0}, {'var_i': 15, 'var_j': 15, 'quadratic_cost': 9.0}, {'var_i': 15, 'var_j': 16, 'quadratic_cost': 7.0}, {'var_i': 16, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 16, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 16, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 16, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 16, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 16, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 16, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 16, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 16, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 16, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 16, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 16, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 16, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 16, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 16, 'var_j': 14, 'quadratic_cost': 5.0}, {'var_i': 16, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 16, 'var_j': 16, 'quadratic_cost': 10.0}]}, 'edges': [{'from': 6, 'to': 0, 'var_index': 0}, {'from': 6, 'to': 1, 'var_index': 1}, {'from': 6, 'to': 2, 'var_index': 2}, {'from': 6, 'to': 3, 'var_index': 3}, {'from': 6, 'to': 4, 'var_index': 4}, {'from': 6, 'to': 5, 'var_index': 5}, {'from': 0, 'to': 7, 'var_index': 6}, {'from': 1, 'to': 7, 'var_index': 7}, {'from': 2, 'to': 7, 'var_index': 8}, {'from': 3, 'to': 7, 'var_index': 9}, {'from': 4, 'to': 7, 'var_index': 10}, {'from': 5, 'to': 7, 'var_index': 11}, {'from': 0, 'to': 1, 'var_index': 12}, {'from': 1, 'to': 2, 'var_index': 13}, {'from': 2, 'to': 3, 'var_index': 14}, {'from': 3, 'to': 4, 'var_index': 15}, {'from': 4, 'to': 5, 'var_index': 16}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7}}","[6, 1, 7]",33,nl,0
QSPP,QSPP,"Backstage there’s a request to route supplies along a single, permitted route from the service gate to the stage, following only the designated one‑way pathways. Each pathway has a normal cost, and certain pathways, or particular pairs of pathways used together, add extra penalties to the bill, so the final cost is simply the sum of every pathway’s base charge plus any extra charges that apply when specific pathways coincide. The job is to pick one uninterrupted chain of locations — start at the gate, move along real one‑way links step by step, finish at the staging area — that produces the smallest possible total when all those costs are added. The full map and the numeric details are available below.

{
  ""total_locations"": 10,
  ""total_thoroughfares"": 9,
  ""location_ids"": [
    ""A"",
    ""B"",
    ""C"",
    ""D"",
    ""E"",
    ""F"",
    ""G"",
    ""H"",
    ""I"",
    ""J""
  ],
  ""service_gate"": ""I"",
  ""staging_area"": ""J"",
  ""edges"": [
    {
      ""thoroughfare_start_location"": ""I"",
      ""thoroughfare_end_location"": ""A"",
      ""thoroughfare_id"": 0
    },
    {
      ""thoroughfare_start_location"": ""H"",
      ""thoroughfare_end_location"": ""J"",
      ""thoroughfare_id"": 1
    },
    {
      ""thoroughfare_start_location"": ""A"",
      ""thoroughfare_end_location"": ""B"",
      ""thoroughfare_id"": 2
    },
    {
      ""thoroughfare_start_location"": ""B"",
      ""thoroughfare_end_location"": ""C"",
      ""thoroughfare_id"": 3
    },
    {
      ""thoroughfare_start_location"": ""C"",
      ""thoroughfare_end_location"": ""D"",
      ""thoroughfare_id"": 4
    },
    {
      ""thoroughfare_start_location"": ""D"",
      ""thoroughfare_end_location"": ""E"",
      ""thoroughfare_id"": 5
    },
    {
      ""thoroughfare_start_location"": ""E"",
      ""thoroughfare_end_location"": ""F"",
      ""thoroughfare_id"": 6
    },
    {
      ""thoroughfare_start_location"": ""F"",
      ""thoroughfare_end_location"": ""G"",
      ""thoroughfare_id"": 7
    },
    {
      ""thoroughfare_start_location"": ""G"",
      ""thoroughfare_end_location"": ""H"",
      ""thoroughfare_id"": 8
    }
  ],
  ""linear_costs"": [
    {
      ""thoroughfare_id"": 0,
      ""base_transport_cost"": 2.0
    },
    {
      ""thoroughfare_id"": 1,
      ""base_transport_cost"": 5.0
    },
    {
      ""thoroughfare_id"": 2,
      ""base_transport_cost"": 3.0
    },
    {
      ""thoroughfare_id"": 3,
      ""base_transport_cost"": 5.0
    },
    {
      ""thoroughfare_id"": 4,
      ""base_transport_cost"": 10.0
    },
    {
      ""thoroughfare_id"": 5,
      ""base_transport_cost"": 6.0
    },
    {
      ""thoroughfare_id"": 6,
      ""base_transport_cost"": 10.0
    },
    {
      ""thoroughfare_id"": 7,
      ""base_transport_cost"": 7.0
    },
    {
      ""thoroughfare_id"": 8,
      ""base_transport_cost"": 3.0
    }
  ]
}

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (thoroughfare_i_id, thoroughfare_j_id). If two thoroughfares with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| thoroughfare_i_id\thoroughfare_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|---|
| 0 | 5.0 | 5.0 | 8.0 | 7.0 | 2.0 | 7.0 | 3.0 | 8.0 | 6.0 |
| 1 | 5.0 | 2.0 | 1.0 | 2.0 | 4.0 | 7.0 | 1.0 | 9.0 | 6.0 |
| 2 | 8.0 | 1.0 | 1.0 | 5.0 | 2.0 | 3.0 | 6.0 | 8.0 | 1.0 |
| 3 | 7.0 | 2.0 | 5.0 | 9.0 | 3.0 | 7.0 | 10.0 | 9.0 | 3.0 |
| 4 | 2.0 | 4.0 | 2.0 | 3.0 | 8.0 | 7.0 | 7.0 | 6.0 | 4.0 |
| 5 | 7.0 | 7.0 | 3.0 | 7.0 | 7.0 | 10.0 | 9.0 | 5.0 | 9.0 |
| 6 | 3.0 | 1.0 | 6.0 | 10.0 | 7.0 | 9.0 | 9.0 | 10.0 | 3.0 |
| 7 | 8.0 | 9.0 | 8.0 | 9.0 | 6.0 | 5.0 | 10.0 | 7.0 | 10.0 |
| 8 | 6.0 | 6.0 | 1.0 | 3.0 | 4.0 | 9.0 | 3.0 | 10.0 | 3.0 |

Also, when you give the final reply, please put the chosen route into a tiny JSON layout — nothing fancy, just a single top-level key called ""solution"" whose value is the path as an array.

{
  ""solution"": []
}

This little block is just a sketch of the shape I expect: the ""solution"" array is where you'll list the chain of locations from the service gate to the stage, in order, using node identifiers only (start node first, end node last). Think of it like filling in a short form — the JSON shows the fields, but it's not the actual answer until you fill that array with the nodes of the path.

One more thing: use the node identifiers exactly as they appear in the instance input — don't rename them or invent new labels. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7"".""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 'edges': [{'from': 8, 'to': 0, 'var_index': 0}, {'from': 7, 'to': 9, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 4, 'to': 5, 'var_index': 6}, {'from': 5, 'to': 6, 'var_index': 7}, {'from': 6, 'to': 7, 'var_index': 8}], 'objective': {'constant': 0.0, 'linear': [2.0, 5.0, 3.0, 5.0, 10.0, 6.0, 10.0, 7.0, 3.0], 'quadratic': [[5.0, 5.0, 8.0, 7.0, 2.0, 7.0, 3.0, 8.0, 6.0], [5.0, 2.0, 1.0, 2.0, 4.0, 7.0, 1.0, 9.0, 6.0], [8.0, 1.0, 1.0, 5.0, 2.0, 3.0, 6.0, 8.0, 1.0], [7.0, 2.0, 5.0, 9.0, 3.0, 7.0, 10.0, 9.0, 3.0], [2.0, 4.0, 2.0, 3.0, 8.0, 7.0, 7.0, 6.0, 4.0], [7.0, 7.0, 3.0, 7.0, 7.0, 10.0, 9.0, 5.0, 9.0], [3.0, 1.0, 6.0, 10.0, 7.0, 9.0, 9.0, 10.0, 3.0], [8.0, 9.0, 8.0, 9.0, 6.0, 5.0, 10.0, 7.0, 10.0], [6.0, 6.0, 1.0, 3.0, 4.0, 9.0, 3.0, 10.0, 3.0]]}, 'source': 8, 'target': 9}","[8, 0, 1, 2, 3, 4, 5, 6, 7, 9]",511.0,"{'problem_type': 'QSPP', 'num_nodes': 10, 'num_edges': 9, 'nodes': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J'], 'source': 'I', 'target': 'J', 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 2.0}, {'var_index': 1, 'linear_cost': 5.0}, {'var_index': 2, 'linear_cost': 3.0}, {'var_index': 3, 'linear_cost': 5.0}, {'var_index': 4, 'linear_cost': 10.0}, {'var_index': 5, 'linear_cost': 6.0}, {'var_index': 6, 'linear_cost': 10.0}, {'var_index': 7, 'linear_cost': 7.0}, {'var_index': 8, 'linear_cost': 3.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 7, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 7, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 8, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 8, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 8, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 8, 'var_j': 8, 'quadratic_cost': 3.0}]}, 'edges': [{'from': 'I', 'to': 'A', 'var_index': 0}, {'from': 'H', 'to': 'J', 'var_index': 1}, {'from': 'A', 'to': 'B', 'var_index': 2}, {'from': 'B', 'to': 'C', 'var_index': 3}, {'from': 'C', 'to': 'D', 'var_index': 4}, {'from': 'D', 'to': 'E', 'var_index': 5}, {'from': 'E', 'to': 'F', 'var_index': 6}, {'from': 'F', 'to': 'G', 'var_index': 7}, {'from': 'G', 'to': 'H', 'var_index': 8}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E', 5: 'F', 6: 'G', 7: 'H', 8: 'I', 9: 'J'}}","['I', 'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'J']",34,json,names
QSPP,QSPP,"Someone on the team needs to commit to one specific path a user would take from the landing page to checkout — no branching, no skipping, just one continuous set of clicks following the site’s links. Each click has a baseline cost in friction, and when certain clicks are combined the pair can cause additional losses (order can matter, and some clicks even carry an extra standalone penalty). The idea is to pick the one route that ends up with the least total friction by summing all individual frictions and any extra pairwise hits. The chosen route must begin at landing, end at checkout, only follow existing links in sequence, and the actual page map and cost numbers appear below.

The actual page map and cost numbers appear below: 9 total pages, 12 directed links, page IDs 1, 2, 3, 4, 5, 6, 7, 8, 9, landing page 1, checkout page 9.

| link_from_page | link_to_page | link_identifier |
|---|---|---|
| 1 | 2 | 0 |
| 1 | 4 | 1 |
| 2 | 3 | 2 |
| 2 | 5 | 3 |
| 3 | 6 | 4 |
| 4 | 5 | 5 |
| 4 | 7 | 6 |
| 5 | 6 | 7 |
| 5 | 8 | 8 |
| 6 | 9 | 9 |
| 7 | 8 | 10 |
| 8 | 9 | 11 |

| link_id_for_cost | click_friction |
|---|---|
| 0 | 2.0 |
| 1 | 3.0 |
| 2 | 10.0 |
| 3 | 1.0 |
| 4 | 2.0 |
| 5 | 1.0 |
| 6 | 2.0 |
| 7 | 1.0 |
| 8 | 1.0 |
| 9 | 9.0 |
| 10 | 7.0 |
| 11 | 9.0 |

*Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (first_link_in_pair, second_link_in_pair). If two link_identifiers with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).*

**quadratic_costs**

| first_link_in_pair\second_link_in_pair | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1.0 | 9.0 | 7.0 | 9.0 | 1.0 | 9.0 | 9.0 | 3.0 | 2.0 | 6.0 | 8.0 | 2.0 |
| 1 | 9.0 | 6.0 | 4.0 | 10.0 | 7.0 | 8.0 | 1.0 | 3.0 | 7.0 | 5.0 | 5.0 | 3.0 |
| 2 | 7.0 | 4.0 | 3.0 | 6.0 | 10.0 | 4.0 | 7.0 | 8.0 | 7.0 | 1.0 | 1.0 | 1.0 |
| 3 | 9.0 | 10.0 | 6.0 | 2.0 | 4.0 | 2.0 | 9.0 | 3.0 | 7.0 | 5.0 | 9.0 | 8.0 |
| 4 | 1.0 | 7.0 | 10.0 | 4.0 | 9.0 | 10.0 | 8.0 | 1.0 | 4.0 | 1.0 | 6.0 | 7.0 |
| 5 | 9.0 | 8.0 | 4.0 | 2.0 | 10.0 | 4.0 | 4.0 | 3.0 | 6.0 | 6.0 | 7.0 | 6.0 |
| 6 | 9.0 | 1.0 | 7.0 | 9.0 | 8.0 | 4.0 | 7.0 | 2.0 | 3.0 | 10.0 | 3.0 | 6.0 |
| 7 | 3.0 | 3.0 | 8.0 | 3.0 | 1.0 | 3.0 | 2.0 | 5.0 | 9.0 | 3.0 | 8.0 | 2.0 |
| 8 | 2.0 | 7.0 | 7.0 | 7.0 | 4.0 | 6.0 | 3.0 | 9.0 | 9.0 | 3.0 | 3.0 | 4.0 |
| 9 | 6.0 | 5.0 | 1.0 | 5.0 | 1.0 | 6.0 | 10.0 | 3.0 | 3.0 | 9.0 | 1.0 | 6.0 |
| 10 | 8.0 | 5.0 | 1.0 | 9.0 | 6.0 | 7.0 | 3.0 | 8.0 | 3.0 | 1.0 | 9.0 | 7.0 |
| 11 | 2.0 | 3.0 | 1.0 | 8.0 | 7.0 | 6.0 | 6.0 | 2.0 | 4.0 | 6.0 | 7.0 | 2.0 |

Someone on the team must pick the single path from 1 to 9 that minimizes total friction across the 9 pages and 12 links.

Also, when you send back the specific route you picked, please put it in a tiny JSON snippet so it's easy to read and machine-friendly. Just drop the sequence of page NODE names into the solution array, like this:

{
  ""solution"": []
}

The idea: ""solution"" should be the ordered list of pages (node identifiers) from the landing page to checkout — just the page names in order, nothing else. Treat the JSON above like a simple form: solution = [first page, next page, ..., checkout]. This is just a sketch of the shape I expect, not the actual answer.

One more thing — use the exact identifiers as they appear in the instance input. Do not rename them or invent new labels. Valid identifiers look like:
- plain numbers such as ""1"" or ""23""
- single capital letters like ""A"" or ""B""
- a capital letter followed by digits like ""A1"" or ""X7""","{'name': 'Rostami_Grid1_k3_seedNone', 'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8], 'edges': [{'from': 0, 'to': 1, 'var_index': 0}, {'from': 0, 'to': 3, 'var_index': 1}, {'from': 1, 'to': 2, 'var_index': 2}, {'from': 1, 'to': 4, 'var_index': 3}, {'from': 2, 'to': 5, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 3, 'to': 6, 'var_index': 6}, {'from': 4, 'to': 5, 'var_index': 7}, {'from': 4, 'to': 7, 'var_index': 8}, {'from': 5, 'to': 8, 'var_index': 9}, {'from': 6, 'to': 7, 'var_index': 10}, {'from': 7, 'to': 8, 'var_index': 11}], 'objective': {'constant': 0.0, 'linear': [2.0, 3.0, 10.0, 1.0, 2.0, 1.0, 2.0, 1.0, 1.0, 9.0, 7.0, 9.0], 'quadratic': [[1.0, 9.0, 7.0, 9.0, 1.0, 9.0, 9.0, 3.0, 2.0, 6.0, 8.0, 2.0], [9.0, 6.0, 4.0, 10.0, 7.0, 8.0, 1.0, 3.0, 7.0, 5.0, 5.0, 3.0], [7.0, 4.0, 3.0, 6.0, 10.0, 4.0, 7.0, 8.0, 7.0, 1.0, 1.0, 1.0], [9.0, 10.0, 6.0, 2.0, 4.0, 2.0, 9.0, 3.0, 7.0, 5.0, 9.0, 8.0], [1.0, 7.0, 10.0, 4.0, 9.0, 10.0, 8.0, 1.0, 4.0, 1.0, 6.0, 7.0], [9.0, 8.0, 4.0, 2.0, 10.0, 4.0, 4.0, 3.0, 6.0, 6.0, 7.0, 6.0], [9.0, 1.0, 7.0, 9.0, 8.0, 4.0, 7.0, 2.0, 3.0, 10.0, 3.0, 6.0], [3.0, 3.0, 8.0, 3.0, 1.0, 3.0, 2.0, 5.0, 9.0, 3.0, 8.0, 2.0], [2.0, 7.0, 7.0, 7.0, 4.0, 6.0, 3.0, 9.0, 9.0, 3.0, 3.0, 4.0], [6.0, 5.0, 1.0, 5.0, 1.0, 6.0, 10.0, 3.0, 3.0, 9.0, 1.0, 6.0], [8.0, 5.0, 1.0, 9.0, 6.0, 7.0, 3.0, 8.0, 3.0, 1.0, 9.0, 7.0], [2.0, 3.0, 1.0, 8.0, 7.0, 6.0, 6.0, 2.0, 4.0, 6.0, 7.0, 2.0]]}, 'source': 0, 'target': 8}","[0, 1, 4, 5, 8]",88.0,"{'problem_type': 'QSPP', 'num_nodes': 9, 'num_edges': 12, 'nodes': [1, 2, 3, 4, 5, 6, 7, 8, 9], 'source': 1, 'target': 9, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 2.0}, {'var_index': 1, 'linear_cost': 3.0}, {'var_index': 2, 'linear_cost': 10.0}, {'var_index': 3, 'linear_cost': 1.0}, {'var_index': 4, 'linear_cost': 2.0}, {'var_index': 5, 'linear_cost': 1.0}, {'var_index': 6, 'linear_cost': 2.0}, {'var_index': 7, 'linear_cost': 1.0}, {'var_index': 8, 'linear_cost': 1.0}, {'var_index': 9, 'linear_cost': 9.0}, {'var_index': 10, 'linear_cost': 7.0}, {'var_index': 11, 'linear_cost': 9.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 7, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 8, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 9, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 9, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 9, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 9, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 9, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 9, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 9, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 9, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 9, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 9, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 10, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 10, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 10, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 10, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 10, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 10, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 11, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 11, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 11, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 11, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 11, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 11, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 11, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 11, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 11, 'var_j': 11, 'quadratic_cost': 2.0}]}, 'edges': [{'from': 1, 'to': 2, 'var_index': 0}, {'from': 1, 'to': 4, 'var_index': 1}, {'from': 2, 'to': 3, 'var_index': 2}, {'from': 2, 'to': 5, 'var_index': 3}, {'from': 3, 'to': 6, 'var_index': 4}, {'from': 4, 'to': 5, 'var_index': 5}, {'from': 4, 'to': 7, 'var_index': 6}, {'from': 5, 'to': 6, 'var_index': 7}, {'from': 5, 'to': 8, 'var_index': 8}, {'from': 6, 'to': 9, 'var_index': 9}, {'from': 7, 'to': 8, 'var_index': 10}, {'from': 8, 'to': 9, 'var_index': 11}], 'node_id_map': {0: 1, 1: 2, 2: 3, 3: 4, 4: 5, 5: 6, 6: 7, 7: 8, 8: 9}}","[1, 2, 5, 6, 9]",35,markdown_table,1
QSPP,QSPP,"We’re planning a one-way path through a line of machines: from the starting station to the final assembly, following only the allowed connections. Every machine-to-machine move has a base operating cost, and certain combinations of moves add extra combined setup costs whenever both moves are used (and some moves carry an additional standalone setup). The task is to pick one continuous sequence of moves so that, when summing all the individual move costs and all the extra combination costs that apply, the overall expense is as low as it can be. The chosen path must be a single coherent route beginning at the start and ending at the finish, using only valid forward steps. The concrete details are listed below.

{
  ""total_stations"": 9,
  ""total_moves"": 12,
  ""station_ids"": [
    0,
    1,
    2,
    3,
    4,
    5,
    6,
    7,
    8
  ],
  ""start_station"": 0,
  ""final_assembly_station"": 8,
  ""edges"": [
    {
      ""move_from_station"": 0,
      ""move_to_station"": 1,
      ""move_id"": 0
    },
    {
      ""move_from_station"": 0,
      ""move_to_station"": 3,
      ""move_id"": 1
    },
    {
      ""move_from_station"": 1,
      ""move_to_station"": 2,
      ""move_id"": 2
    },
    {
      ""move_from_station"": 1,
      ""move_to_station"": 4,
      ""move_id"": 3
    },
    {
      ""move_from_station"": 2,
      ""move_to_station"": 5,
      ""move_id"": 4
    },
    {
      ""move_from_station"": 3,
      ""move_to_station"": 4,
      ""move_id"": 5
    },
    {
      ""move_from_station"": 3,
      ""move_to_station"": 6,
      ""move_id"": 6
    },
    {
      ""move_from_station"": 4,
      ""move_to_station"": 5,
      ""move_id"": 7
    },
    {
      ""move_from_station"": 4,
      ""move_to_station"": 7,
      ""move_id"": 8
    },
    {
      ""move_from_station"": 5,
      ""move_to_station"": 8,
      ""move_id"": 9
    },
    {
      ""move_from_station"": 6,
      ""move_to_station"": 7,
      ""move_id"": 10
    },
    {
      ""move_from_station"": 7,
      ""move_to_station"": 8,
      ""move_id"": 11
    }
  ],
  ""linear_costs"": [
    {
      ""move_id"": 0,
      ""operating_cost"": 1.0
    },
    {
      ""move_id"": 1,
      ""operating_cost"": 6.0
    },
    {
      ""move_id"": 2,
      ""operating_cost"": 5.0
    },
    {
      ""move_id"": 3,
      ""operating_cost"": 1.0
    },
    {
      ""move_id"": 4,
      ""operating_cost"": 9.0
    },
    {
      ""move_id"": 5,
      ""operating_cost"": 3.0
    },
    {
      ""move_id"": 6,
      ""operating_cost"": 5.0
    },
    {
      ""move_id"": 7,
      ""operating_cost"": 5.0
    },
    {
      ""move_id"": 8,
      ""operating_cost"": 8.0
    },
    {
      ""move_id"": 9,
      ""operating_cost"": 2.0
    },
    {
      ""move_id"": 10,
      ""operating_cost"": 4.0
    },
    {
      ""move_id"": 11,
      ""operating_cost"": 3.0
    }
  ]
}

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (move_i_id, move_j_id). If two moves with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| move_i_id\move_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 8.0 | 8.0 | 5.0 | 9.0 | 10.0 | 9.0 | 8.0 | 1.0 | 2.0 | 6.0 | 6.0 | 6.0 |
| 1 | 8.0 | 10.0 | 10.0 | 3.0 | 1.0 | 2.0 | 3.0 | 2.0 | 8.0 | 6.0 | 6.0 | 9.0 |
| 2 | 5.0 | 10.0 | 3.0 | 4.0 | 6.0 | 2.0 | 2.0 | 3.0 | 9.0 | 7.0 | 5.0 | 1.0 |
| 3 | 9.0 | 3.0 | 4.0 | 4.0 | 4.0 | 9.0 | 3.0 | 3.0 | 2.0 | 1.0 | 3.0 | 1.0 |
| 4 | 10.0 | 1.0 | 6.0 | 4.0 | 7.0 | 8.0 | 9.0 | 3.0 | 9.0 | 1.0 | 6.0 | 1.0 |
| 5 | 9.0 | 2.0 | 2.0 | 9.0 | 8.0 | 3.0 | 3.0 | 1.0 | 10.0 | 6.0 | 8.0 | 5.0 |
| 6 | 8.0 | 3.0 | 2.0 | 3.0 | 9.0 | 3.0 | 3.0 | 10.0 | 7.0 | 6.0 | 3.0 | 5.0 |
| 7 | 1.0 | 2.0 | 3.0 | 3.0 | 3.0 | 1.0 | 10.0 | 8.0 | 1.0 | 9.0 | 1.0 | 8.0 |
| 8 | 2.0 | 8.0 | 9.0 | 2.0 | 9.0 | 10.0 | 7.0 | 1.0 | 1.0 | 8.0 | 2.0 | 2.0 |
| 9 | 6.0 | 6.0 | 7.0 | 1.0 | 1.0 | 6.0 | 6.0 | 9.0 | 8.0 | 6.0 | 9.0 | 7.0 |
| 10 | 6.0 | 6.0 | 5.0 | 3.0 | 6.0 | 8.0 | 3.0 | 1.0 | 2.0 | 9.0 | 8.0 | 3.0 |
| 11 | 6.0 | 9.0 | 1.0 | 1.0 | 1.0 | 5.0 | 5.0 | 8.0 | 2.0 | 7.0 | 3.0 | 10.0 |

Also, when you send back the chosen route, just stick it into a tiny JSON object so it's easy to parse — something like this:

{
  ""solution"": []
}

Think of ""solution"" as the place to list the nodes in order: start node first, finish node last, and every step in between must follow a valid forward connection. This JSON is only a sketch of the shape I expect you to follow — in your final reply replace the empty array with the actual sequence of node identifiers for the path.

Please use the identifiers exactly as they appear in the instance input — no renaming and no new labels.
""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'name': 'Rostami_Grid1_k3_seedNone', 'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8], 'edges': [{'from': 0, 'to': 1, 'var_index': 0}, {'from': 0, 'to': 3, 'var_index': 1}, {'from': 1, 'to': 2, 'var_index': 2}, {'from': 1, 'to': 4, 'var_index': 3}, {'from': 2, 'to': 5, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 3, 'to': 6, 'var_index': 6}, {'from': 4, 'to': 5, 'var_index': 7}, {'from': 4, 'to': 7, 'var_index': 8}, {'from': 5, 'to': 8, 'var_index': 9}, {'from': 6, 'to': 7, 'var_index': 10}, {'from': 7, 'to': 8, 'var_index': 11}], 'objective': {'constant': 0.0, 'linear': [1.0, 6.0, 5.0, 1.0, 9.0, 3.0, 5.0, 5.0, 8.0, 2.0, 4.0, 3.0], 'quadratic': [[8.0, 8.0, 5.0, 9.0, 10.0, 9.0, 8.0, 1.0, 2.0, 6.0, 6.0, 6.0], [8.0, 10.0, 10.0, 3.0, 1.0, 2.0, 3.0, 2.0, 8.0, 6.0, 6.0, 9.0], [5.0, 10.0, 3.0, 4.0, 6.0, 2.0, 2.0, 3.0, 9.0, 7.0, 5.0, 1.0], [9.0, 3.0, 4.0, 4.0, 4.0, 9.0, 3.0, 3.0, 2.0, 1.0, 3.0, 1.0], [10.0, 1.0, 6.0, 4.0, 7.0, 8.0, 9.0, 3.0, 9.0, 1.0, 6.0, 1.0], [9.0, 2.0, 2.0, 9.0, 8.0, 3.0, 3.0, 1.0, 10.0, 6.0, 8.0, 5.0], [8.0, 3.0, 2.0, 3.0, 9.0, 3.0, 3.0, 10.0, 7.0, 6.0, 3.0, 5.0], [1.0, 2.0, 3.0, 3.0, 3.0, 1.0, 10.0, 8.0, 1.0, 9.0, 1.0, 8.0], [2.0, 8.0, 9.0, 2.0, 9.0, 10.0, 7.0, 1.0, 1.0, 8.0, 2.0, 2.0], [6.0, 6.0, 7.0, 1.0, 1.0, 6.0, 6.0, 9.0, 8.0, 6.0, 9.0, 7.0], [6.0, 6.0, 5.0, 3.0, 6.0, 8.0, 3.0, 1.0, 2.0, 9.0, 8.0, 3.0], [6.0, 9.0, 1.0, 1.0, 1.0, 5.0, 5.0, 8.0, 2.0, 7.0, 3.0, 10.0]]}, 'source': 0, 'target': 8}","[0, 1, 4, 7, 8]",80.0,"{'problem_type': 'QSPP', 'num_nodes': 9, 'num_edges': 12, 'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8], 'source': 0, 'target': 8, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 1.0}, {'var_index': 1, 'linear_cost': 6.0}, {'var_index': 2, 'linear_cost': 5.0}, {'var_index': 3, 'linear_cost': 1.0}, {'var_index': 4, 'linear_cost': 9.0}, {'var_index': 5, 'linear_cost': 3.0}, {'var_index': 6, 'linear_cost': 5.0}, {'var_index': 7, 'linear_cost': 5.0}, {'var_index': 8, 'linear_cost': 8.0}, {'var_index': 9, 'linear_cost': 2.0}, {'var_index': 10, 'linear_cost': 4.0}, {'var_index': 11, 'linear_cost': 3.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 7, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 8, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 8, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 8, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 9, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 9, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 9, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 9, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 9, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 9, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 9, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 9, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 9, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 9, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 10, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 10, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 10, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 10, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 10, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 11, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 11, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 11, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 11, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 11, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 11, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 11, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 11, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 11, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 11, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 11, 'var_j': 11, 'quadratic_cost': 10.0}]}, 'edges': [{'from': 0, 'to': 1, 'var_index': 0}, {'from': 0, 'to': 3, 'var_index': 1}, {'from': 1, 'to': 2, 'var_index': 2}, {'from': 1, 'to': 4, 'var_index': 3}, {'from': 2, 'to': 5, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 3, 'to': 6, 'var_index': 6}, {'from': 4, 'to': 5, 'var_index': 7}, {'from': 4, 'to': 7, 'var_index': 8}, {'from': 5, 'to': 8, 'var_index': 9}, {'from': 6, 'to': 7, 'var_index': 10}, {'from': 7, 'to': 8, 'var_index': 11}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7, 8: 8}}","[0, 1, 4, 7, 8]",36,json,0
QSPP,QSPP,"Someone in dispatch needs a single, clean routing: a continuous sequence of controlled corridors from the departure fix to the arrival fix, following the assigned directions on each corridor. Each corridor costs a bit of fuel, and certain combinations of two corridors together rack up additional penalties, so the plan’s score is just the sum of all those per-leg costs plus any pairwise penalties caused by legs flown together. The aim is to pick the one route that ends up with the lowest total cost, and the route must start at the departure fix, end at the arrival fix, and be made up of connected, directionally allowed legs — listed only as the fixes in order. The full details and numbers are shown below.

There are 8 fixes and 17 directed corridors; the fixes are A, B, C, D, E, F, G, H; the routing must start at G and end at H.
Corridor 0: from G to A.
Corridor 1: from G to B.
Corridor 2: from G to C.
Corridor 3: from G to D.
Corridor 4: from G to E.
Corridor 5: from G to F.
Corridor 6: from A to H.
Corridor 7: from B to H.
Corridor 8: from C to H.
Corridor 9: from D to H.
Corridor 10: from E to H.
Corridor 11: from F to H.
Corridor 12: from A to B.
Corridor 13: from B to C.
Corridor 14: from C to D.
Corridor 15: from D to E.
Corridor 16: from E to F.
Leg 0 incurs fuel penalty 9.0.
Leg 1 incurs fuel penalty 4.0.
Leg 2 incurs fuel penalty 3.0.
Leg 3 incurs fuel penalty 6.0.
Leg 4 incurs fuel penalty 9.0.
Leg 5 incurs fuel penalty 1.0.
Leg 6 incurs fuel penalty 6.0.
Leg 7 incurs fuel penalty 3.0.
Leg 8 incurs fuel penalty 6.0.
Leg 9 incurs fuel penalty 4.0.
Leg 10 incurs fuel penalty 9.0.
Leg 11 incurs fuel penalty 5.0.
Leg 12 incurs fuel penalty 6.0.
Leg 13 incurs fuel penalty 4.0.
Leg 14 incurs fuel penalty 7.0.
Leg 15 incurs fuel penalty 2.0.
Leg 16 incurs fuel penalty 8.0.
Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (corridor_leg_i_id, corridor_leg_j_id). If two corridor_legs with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
quadratic_costs:
| corridor_leg_i_id\corridor_leg_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 6.0 | 2.0 | 5.0 | 5.0 | 6.0 | 8.0 | 3.0 | 10.0 | 2.0 | 6.0 | 8.0 | 2.0 | 8.0 | 5.0 | 3.0 | 8.0 | 2.0 |
| 1 | 2.0 | 7.0 | 8.0 | 1.0 | 7.0 | 4.0 | 2.0 | 4.0 | 2.0 | 10.0 | 3.0 | 2.0 | 2.0 | 8.0 | 6.0 | 1.0 | 7.0 |
| 2 | 5.0 | 8.0 | 1.0 | 4.0 | 9.0 | 10.0 | 2.0 | 9.0 | 10.0 | 5.0 | 2.0 | 5.0 | 1.0 | 5.0 | 2.0 | 4.0 | 9.0 |
| 3 | 5.0 | 1.0 | 4.0 | 9.0 | 5.0 | 6.0 | 5.0 | 9.0 | 9.0 | 10.0 | 1.0 | 6.0 | 4.0 | 2.0 | 7.0 | 8.0 | 3.0 |
| 4 | 6.0 | 7.0 | 9.0 | 5.0 | 3.0 | 2.0 | 5.0 | 1.0 | 6.0 | 10.0 | 5.0 | 3.0 | 4.0 | 3.0 | 5.0 | 1.0 | 10.0 |
| 5 | 8.0 | 4.0 | 10.0 | 6.0 | 2.0 | 6.0 | 3.0 | 5.0 | 7.0 | 3.0 | 7.0 | 3.0 | 8.0 | 10.0 | 8.0 | 2.0 | 1.0 |
| 6 | 3.0 | 2.0 | 2.0 | 5.0 | 5.0 | 3.0 | 5.0 | 4.0 | 4.0 | 6.0 | 7.0 | 10.0 | 9.0 | 10.0 | 6.0 | 5.0 | 4.0 |
| 7 | 10.0 | 4.0 | 9.0 | 9.0 | 1.0 | 5.0 | 4.0 | 5.0 | 5.0 | 3.0 | 3.0 | 6.0 | 7.0 | 9.0 | 7.0 | 9.0 | 1.0 |
| 8 | 2.0 | 2.0 | 10.0 | 9.0 | 6.0 | 7.0 | 4.0 | 5.0 | 7.0 | 3.0 | 6.0 | 6.0 | 7.0 | 6.0 | 8.0 | 10.0 | 6.0 |
| 9 | 6.0 | 10.0 | 5.0 | 10.0 | 10.0 | 3.0 | 6.0 | 3.0 | 3.0 | 2.0 | 9.0 | 4.0 | 6.0 | 10.0 | 1.0 | 2.0 | 2.0 |
| 10 | 8.0 | 3.0 | 2.0 | 1.0 | 5.0 | 7.0 | 7.0 | 3.0 | 6.0 | 9.0 | 2.0 | 4.0 | 7.0 | 6.0 | 8.0 | 1.0 | 10.0 |
| 11 | 2.0 | 2.0 | 5.0 | 6.0 | 3.0 | 3.0 | 10.0 | 6.0 | 6.0 | 4.0 | 4.0 | 1.0 | 7.0 | 3.0 | 1.0 | 7.0 | 9.0 |
| 12 | 8.0 | 2.0 | 1.0 | 4.0 | 4.0 | 8.0 | 9.0 | 7.0 | 7.0 | 6.0 | 7.0 | 7.0 | 8.0 | 5.0 | 9.0 | 5.0 | 7.0 |
| 13 | 5.0 | 8.0 | 5.0 | 2.0 | 3.0 | 10.0 | 10.0 | 9.0 | 6.0 | 10.0 | 6.0 | 3.0 | 5.0 | 5.0 | 6.0 | 3.0 | 4.0 |
| 14 | 3.0 | 6.0 | 2.0 | 7.0 | 5.0 | 8.0 | 6.0 | 7.0 | 8.0 | 1.0 | 8.0 | 1.0 | 9.0 | 6.0 | 3.0 | 6.0 | 6.0 |
| 15 | 8.0 | 1.0 | 4.0 | 8.0 | 1.0 | 2.0 | 5.0 | 9.0 | 10.0 | 2.0 | 1.0 | 7.0 | 5.0 | 3.0 | 6.0 | 8.0 | 5.0 |
| 16 | 2.0 | 7.0 | 9.0 | 3.0 | 10.0 | 1.0 | 4.0 | 1.0 | 6.0 | 2.0 | 10.0 | 9.0 | 7.0 | 4.0 | 6.0 | 5.0 | 4.0 |
Select the single connected route from G to H that minimizes the total of leg penalties and any combined penalties.

You can just drop the final route into a tiny JSON snippet like this when you're ready — it keeps things simple and easy to parse.

{
  ""solution"": []
}

This ""solution"" array is where the chosen route goes: list the fixes (node identifiers) in order from the departure fix to the arrival fix, nothing else. Think of it like filling in a short form — first stop, next stop, …, last stop. The JSON above is just a sketch of the shape we expect, not the actual route.

Please make sure to use the node identifiers exactly as they appear in the instance input — do not rename them or invent new labels. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7], 'edges': [{'from': 6, 'to': 0, 'var_index': 0}, {'from': 6, 'to': 1, 'var_index': 1}, {'from': 6, 'to': 2, 'var_index': 2}, {'from': 6, 'to': 3, 'var_index': 3}, {'from': 6, 'to': 4, 'var_index': 4}, {'from': 6, 'to': 5, 'var_index': 5}, {'from': 0, 'to': 7, 'var_index': 6}, {'from': 1, 'to': 7, 'var_index': 7}, {'from': 2, 'to': 7, 'var_index': 8}, {'from': 3, 'to': 7, 'var_index': 9}, {'from': 4, 'to': 7, 'var_index': 10}, {'from': 5, 'to': 7, 'var_index': 11}, {'from': 0, 'to': 1, 'var_index': 12}, {'from': 1, 'to': 2, 'var_index': 13}, {'from': 2, 'to': 3, 'var_index': 14}, {'from': 3, 'to': 4, 'var_index': 15}, {'from': 4, 'to': 5, 'var_index': 16}], 'objective': {'constant': 0.0, 'linear': [9.0, 4.0, 3.0, 6.0, 9.0, 1.0, 6.0, 3.0, 6.0, 4.0, 9.0, 5.0, 6.0, 4.0, 7.0, 2.0, 8.0], 'quadratic': [[6.0, 2.0, 5.0, 5.0, 6.0, 8.0, 3.0, 10.0, 2.0, 6.0, 8.0, 2.0, 8.0, 5.0, 3.0, 8.0, 2.0], [2.0, 7.0, 8.0, 1.0, 7.0, 4.0, 2.0, 4.0, 2.0, 10.0, 3.0, 2.0, 2.0, 8.0, 6.0, 1.0, 7.0], [5.0, 8.0, 1.0, 4.0, 9.0, 10.0, 2.0, 9.0, 10.0, 5.0, 2.0, 5.0, 1.0, 5.0, 2.0, 4.0, 9.0], [5.0, 1.0, 4.0, 9.0, 5.0, 6.0, 5.0, 9.0, 9.0, 10.0, 1.0, 6.0, 4.0, 2.0, 7.0, 8.0, 3.0], [6.0, 7.0, 9.0, 5.0, 3.0, 2.0, 5.0, 1.0, 6.0, 10.0, 5.0, 3.0, 4.0, 3.0, 5.0, 1.0, 10.0], [8.0, 4.0, 10.0, 6.0, 2.0, 6.0, 3.0, 5.0, 7.0, 3.0, 7.0, 3.0, 8.0, 10.0, 8.0, 2.0, 1.0], [3.0, 2.0, 2.0, 5.0, 5.0, 3.0, 5.0, 4.0, 4.0, 6.0, 7.0, 10.0, 9.0, 10.0, 6.0, 5.0, 4.0], [10.0, 4.0, 9.0, 9.0, 1.0, 5.0, 4.0, 5.0, 5.0, 3.0, 3.0, 6.0, 7.0, 9.0, 7.0, 9.0, 1.0], [2.0, 2.0, 10.0, 9.0, 6.0, 7.0, 4.0, 5.0, 7.0, 3.0, 6.0, 6.0, 7.0, 6.0, 8.0, 10.0, 6.0], [6.0, 10.0, 5.0, 10.0, 10.0, 3.0, 6.0, 3.0, 3.0, 2.0, 9.0, 4.0, 6.0, 10.0, 1.0, 2.0, 2.0], [8.0, 3.0, 2.0, 1.0, 5.0, 7.0, 7.0, 3.0, 6.0, 9.0, 2.0, 4.0, 7.0, 6.0, 8.0, 1.0, 10.0], [2.0, 2.0, 5.0, 6.0, 3.0, 3.0, 10.0, 6.0, 6.0, 4.0, 4.0, 1.0, 7.0, 3.0, 1.0, 7.0, 9.0], [8.0, 2.0, 1.0, 4.0, 4.0, 8.0, 9.0, 7.0, 7.0, 6.0, 7.0, 7.0, 8.0, 5.0, 9.0, 5.0, 7.0], [5.0, 8.0, 5.0, 2.0, 3.0, 10.0, 10.0, 9.0, 6.0, 10.0, 6.0, 3.0, 5.0, 5.0, 6.0, 3.0, 4.0], [3.0, 6.0, 2.0, 7.0, 5.0, 8.0, 6.0, 7.0, 8.0, 1.0, 8.0, 1.0, 9.0, 6.0, 3.0, 6.0, 6.0], [8.0, 1.0, 4.0, 8.0, 1.0, 2.0, 5.0, 9.0, 10.0, 2.0, 1.0, 7.0, 5.0, 3.0, 6.0, 8.0, 5.0], [2.0, 7.0, 9.0, 3.0, 10.0, 1.0, 4.0, 1.0, 6.0, 2.0, 10.0, 9.0, 7.0, 4.0, 6.0, 5.0, 4.0]]}, 'source': 6, 'target': 7}","[6, 5, 7]",19.0,"{'problem_type': 'QSPP', 'num_nodes': 8, 'num_edges': 17, 'nodes': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H'], 'source': 'G', 'target': 'H', 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 9.0}, {'var_index': 1, 'linear_cost': 4.0}, {'var_index': 2, 'linear_cost': 3.0}, {'var_index': 3, 'linear_cost': 6.0}, {'var_index': 4, 'linear_cost': 9.0}, {'var_index': 5, 'linear_cost': 1.0}, {'var_index': 6, 'linear_cost': 6.0}, {'var_index': 7, 'linear_cost': 3.0}, {'var_index': 8, 'linear_cost': 6.0}, {'var_index': 9, 'linear_cost': 4.0}, {'var_index': 10, 'linear_cost': 9.0}, {'var_index': 11, 'linear_cost': 5.0}, {'var_index': 12, 'linear_cost': 6.0}, {'var_index': 13, 'linear_cost': 4.0}, {'var_index': 14, 'linear_cost': 7.0}, {'var_index': 15, 'linear_cost': 2.0}, {'var_index': 16, 'linear_cost': 8.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 13, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 15, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 12, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 15, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 16, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 13, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 14, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 15, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 12, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 15, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 12, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 14, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 15, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 16, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 14, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 16, 'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 15, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 16, 'quadratic_cost': 4.0}, {'var_i': 7, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 7, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 7, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 7, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 7, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 7, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 15, 'quadratic_cost': 9.0}, {'var_i': 7, 'var_j': 16, 'quadratic_cost': 1.0}, {'var_i': 8, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 8, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 8, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 8, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 14, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 15, 'quadratic_cost': 10.0}, {'var_i': 8, 'var_j': 16, 'quadratic_cost': 6.0}, {'var_i': 9, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 9, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 9, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 9, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 9, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 9, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 9, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 9, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 9, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 9, 'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 9, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 9, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 9, 'var_j': 14, 'quadratic_cost': 1.0}, {'var_i': 9, 'var_j': 15, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 10, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 10, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 10, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 10, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 10, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 10, 'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 10, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 14, 'quadratic_cost': 8.0}, {'var_i': 10, 'var_j': 15, 'quadratic_cost': 1.0}, {'var_i': 10, 'var_j': 16, 'quadratic_cost': 10.0}, {'var_i': 11, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 11, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 11, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 11, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 11, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 11, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 11, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 11, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 11, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 11, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 11, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 11, 'var_j': 14, 'quadratic_cost': 1.0}, {'var_i': 11, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 11, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 12, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 12, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 12, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 12, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 12, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 12, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 12, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 12, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 12, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 12, 'var_j': 13, 'quadratic_cost': 5.0}, {'var_i': 12, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 12, 'var_j': 15, 'quadratic_cost': 5.0}, {'var_i': 12, 'var_j': 16, 'quadratic_cost': 7.0}, {'var_i': 13, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 13, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 13, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 13, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 13, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 13, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 13, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 13, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 13, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 13, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 13, 'var_j': 13, 'quadratic_cost': 5.0}, {'var_i': 13, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 13, 'var_j': 15, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 16, 'quadratic_cost': 4.0}, {'var_i': 14, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 14, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 14, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 14, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 14, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 14, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 14, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 14, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 14, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 14, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 14, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 14, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 14, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 14, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 14, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 14, 'var_j': 15, 'quadratic_cost': 6.0}, {'var_i': 14, 'var_j': 16, 'quadratic_cost': 6.0}, {'var_i': 15, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 15, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 15, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 15, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 15, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 15, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 15, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 15, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 15, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 15, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 15, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 15, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 15, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 15, 'var_j': 15, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 16, 'quadratic_cost': 5.0}, {'var_i': 16, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 16, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 16, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 16, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 16, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 16, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 16, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 16, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 16, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 16, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 16, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 16, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 16, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 16, 'var_j': 13, 'quadratic_cost': 4.0}, {'var_i': 16, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 16, 'var_j': 15, 'quadratic_cost': 5.0}, {'var_i': 16, 'var_j': 16, 'quadratic_cost': 4.0}]}, 'edges': [{'from': 'G', 'to': 'A', 'var_index': 0}, {'from': 'G', 'to': 'B', 'var_index': 1}, {'from': 'G', 'to': 'C', 'var_index': 2}, {'from': 'G', 'to': 'D', 'var_index': 3}, {'from': 'G', 'to': 'E', 'var_index': 4}, {'from': 'G', 'to': 'F', 'var_index': 5}, {'from': 'A', 'to': 'H', 'var_index': 6}, {'from': 'B', 'to': 'H', 'var_index': 7}, {'from': 'C', 'to': 'H', 'var_index': 8}, {'from': 'D', 'to': 'H', 'var_index': 9}, {'from': 'E', 'to': 'H', 'var_index': 10}, {'from': 'F', 'to': 'H', 'var_index': 11}, {'from': 'A', 'to': 'B', 'var_index': 12}, {'from': 'B', 'to': 'C', 'var_index': 13}, {'from': 'C', 'to': 'D', 'var_index': 14}, {'from': 'D', 'to': 'E', 'var_index': 15}, {'from': 'E', 'to': 'F', 'var_index': 16}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E', 5: 'F', 6: 'G', 7: 'H'}}","['G', 'F', 'H']",37,nl,names
QSPP,QSPP,"Many people treat a grocery run as a little puzzle: start at the entrance, follow the arrows through one continuous path, and finish at checkout. Each bit of aisle walked brings its own cost, and some pairs of bits interact badly and add extra cost when both are part of the same trip. The aim is to choose one valid, arrow-abiding route and total its cost by summing every segment’s cost and any pairwise penalties for segments that appear together. Don’t skip segments or hop between disconnected aisles; the full layout and the detailed costs are listed below.

# num_locations=7
# num_aisle_segments=6
# location_ids=0, 1, 2, 3, 4, 5, 6
# entrance_location=5
# checkout_location=6

segment_start_location,segment_end_location,segment_id
5,0,0
4,6,1
0,1,2
1,2,3
2,3,4
3,4,5

segment_id,segment_cost
0,1.0
1,2.0
2,6.0
3,4.0
4,10.0
5,7.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (segment_i_id, segment_j_id). If two segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| segment_i_id\segment_j_id | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| 0 | 5.0 | 10.0 | 5.0 | 2.0 | 6.0 | 10.0 |
| 1 | 10.0 | 1.0 | 2.0 | 6.0 | 2.0 | 9.0 |
| 2 | 5.0 | 2.0 | 2.0 | 4.0 | 4.0 | 6.0 |
| 3 | 2.0 | 6.0 | 4.0 | 8.0 | 6.0 | 2.0 |
| 4 | 6.0 | 2.0 | 4.0 | 6.0 | 8.0 | 6.0 |
| 5 | 10.0 | 9.0 | 6.0 | 2.0 | 6.0 | 2.0 |

Oh, and when you send back the chosen route, please tuck it into this tiny JSON shape so it's easy to read:

{
  ""solution"": []
}

Think of that ""solution"" list as the single continuous route: put the node names in order from the entrance to checkout (first entry is the source, last is the target), and only list node identifiers — no edge IDs, no costs. This block is just a sketch of the shape we want, not the actual answer.

Please use the exact node identifiers from the instance input — do not rename or invent labels. Valid identifiers look like plain numbers such as ""1"" or ""23"", single capital letters like ""A"" or ""B"", or a capital letter followed by digits like ""A1"" or ""X7"".","{'nodes': [0, 1, 2, 3, 4, 5, 6], 'edges': [{'from': 5, 'to': 0, 'var_index': 0}, {'from': 4, 'to': 6, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}], 'objective': {'constant': 0.0, 'linear': [1.0, 2.0, 6.0, 4.0, 10.0, 7.0], 'quadratic': [[5.0, 10.0, 5.0, 2.0, 6.0, 10.0], [10.0, 1.0, 2.0, 6.0, 2.0, 9.0], [5.0, 2.0, 2.0, 4.0, 4.0, 6.0], [2.0, 6.0, 4.0, 8.0, 6.0, 2.0], [6.0, 2.0, 4.0, 6.0, 8.0, 6.0], [10.0, 9.0, 6.0, 2.0, 6.0, 2.0]]}, 'source': 5, 'target': 6}","[5, 0, 1, 2, 3, 4, 6]",216.0,"{'problem_type': 'QSPP', 'num_nodes': 7, 'num_edges': 6, 'nodes': [0, 1, 2, 3, 4, 5, 6], 'source': 5, 'target': 6, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 1.0}, {'var_index': 1, 'linear_cost': 2.0}, {'var_index': 2, 'linear_cost': 6.0}, {'var_index': 3, 'linear_cost': 4.0}, {'var_index': 4, 'linear_cost': 10.0}, {'var_index': 5, 'linear_cost': 7.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 2.0}]}, 'edges': [{'from': 5, 'to': 0, 'var_index': 0}, {'from': 4, 'to': 6, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6}}","[5, 0, 1, 2, 3, 4, 6]",38,csv,0
QSPP,QSPP,"We had a pile of parcels and a single conveyor belt system to move each package from intake to the sorting chute, and the tricky bit was picking which continuous belt path to use. Every belt costs something to run, and certain combinations of belts cause extra wear when both are used; that added wear can even be different depending on the order the belts are hit. A belt can also have its own extra wear if it’s used at all. What makes one choice better than another is the total tally: total running costs plus every extra wear charge for every pair of belts that appear on the chosen path. The package must follow one uninterrupted route that respects the belt directions and lists the locations in order — nothing left out or patched together. The exact map and cost details appear below.

It shows 5 locations and 4 directed belt segments: A, B, C, D, E. We load packages at D and expect them to exit at E.
We have belt 0 running from D to A.
We have belt 1 running from C to E.
We have belt 2 running from A to B.
We have belt 3 running from B to C.
If we use belt 0 we pay operating cost 8.0.
If we use belt 1 we pay operating cost 6.0.
If we use belt 2 we pay operating cost 2.0.
If we use belt 3 we pay operating cost 6.0.
Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (belt_i_id, belt_j_id). If two belt_segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
quadratic_costs:
| belt_i_id\belt_j_id | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| 0 | 9.0 | 2.0 | 8.0 | 1.0 |
| 1 | 2.0 | 5.0 | 9.0 | 10.0 |
| 2 | 8.0 | 9.0 | 8.0 | 8.0 |
| 3 | 1.0 | 10.0 | 8.0 | 8.0 |
We must pick one uninterrupted route from D to E that minimizes total running and wear costs.

Oh, and when you send the chosen route back, please stick to a tiny JSON shape so whatever reads it later knows what to expect. Here’s the layout to use:

{
  ""solution"": []
}

Think of this as a little form: put the path you picked into the solution array as an ordered list of node names, starting with the intake (source) and ending with the sorting chute (target). Keep it simple — just the node identifiers in order, nothing else — and this block is only a sketch of the shape, not the actual answer.

Please make sure you use the exact node identifiers from the instance input — don’t rename them or invent new labels. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4], 'edges': [{'from': 3, 'to': 0, 'var_index': 0}, {'from': 2, 'to': 4, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}], 'objective': {'constant': 0.0, 'linear': [8.0, 6.0, 2.0, 6.0], 'quadratic': [[9.0, 2.0, 8.0, 1.0], [2.0, 5.0, 9.0, 10.0], [8.0, 9.0, 8.0, 8.0], [1.0, 10.0, 8.0, 8.0]]}, 'source': 3, 'target': 4}","[3, 0, 1, 2, 4]",128.0,"{'problem_type': 'QSPP', 'num_nodes': 5, 'num_edges': 4, 'nodes': ['A', 'B', 'C', 'D', 'E'], 'source': 'D', 'target': 'E', 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 8.0}, {'var_index': 1, 'linear_cost': 6.0}, {'var_index': 2, 'linear_cost': 2.0}, {'var_index': 3, 'linear_cost': 6.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 8.0}]}, 'edges': [{'from': 'D', 'to': 'A', 'var_index': 0}, {'from': 'C', 'to': 'E', 'var_index': 1}, {'from': 'A', 'to': 'B', 'var_index': 2}, {'from': 'B', 'to': 'C', 'var_index': 3}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E'}}","['D', 'A', 'B', 'C', 'E']",39,nl,names
QSPP,QSPP,"We need to pick one straight patrol from the guard room to the checkpoint, following the one-way flow of halls and doors. Every hallway has a base cost to patrol, and some pairs of hallways create extra added effort if both are on the same route. Even an individual hallway can have its own extra overhead. The task is simple in words: choose a single legal route (start at the guard room, end at the checkpoint, follow only the allowed directions) and make sure the sum of all hallway costs plus any pairwise extra costs is as small as possible. The concrete map and cost details come next below.

The map has 10 locations and 14 directed corridors; the location IDs are A, B, C, D, E, F, G, H, I, J. We must start at I and end at J.
Corridor 0 runs one-way from I to A.
Corridor 1 runs one-way from I to E.
Corridor 2 runs one-way from D to J.
Corridor 3 runs one-way from H to J.
Corridor 4 runs one-way from A to B.
Corridor 5 runs one-way from A to E.
Corridor 6 runs one-way from B to C.
Corridor 7 runs one-way from B to F.
Corridor 8 runs one-way from C to D.
Corridor 9 runs one-way from C to G.
Corridor 10 runs one-way from D to H.
Corridor 11 runs one-way from E to F.
Corridor 12 runs one-way from F to G.
Corridor 13 runs one-way from G to H.
If we use corridor 0 we incur base patrol cost 1.0.
If we use corridor 1 we incur base patrol cost 6.0.
If we use corridor 2 we incur base patrol cost 1.0.
If we use corridor 3 we incur base patrol cost 6.0.
If we use corridor 4 we incur base patrol cost 10.0.
If we use corridor 5 we incur base patrol cost 3.0.
If we use corridor 6 we incur base patrol cost 8.0.
If we use corridor 7 we incur base patrol cost 3.0.
If we use corridor 8 we incur base patrol cost 1.0.
If we use corridor 9 we incur base patrol cost 3.0.
If we use corridor 10 we incur base patrol cost 1.0.
If we use corridor 11 we incur base patrol cost 8.0.
If we use corridor 12 we incur base patrol cost 3.0.
If we use corridor 13 we incur base patrol cost 5.0.
Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (corridor_i_id, corridor_j_id). If two corridors with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
quadratic_costs:
| corridor_i_id\corridor_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 6.0 | 1.0 | 1.0 | 4.0 | 2.0 | 4.0 | 7.0 | 8.0 | 5.0 | 1.0 | 1.0 | 3.0 | 4.0 | 1.0 |
| 1 | 1.0 | 6.0 | 7.0 | 9.0 | 9.0 | 1.0 | 3.0 | 1.0 | 6.0 | 7.0 | 10.0 | 1.0 | 8.0 | 4.0 |
| 2 | 1.0 | 7.0 | 5.0 | 7.0 | 8.0 | 6.0 | 9.0 | 7.0 | 10.0 | 8.0 | 5.0 | 7.0 | 2.0 | 2.0 |
| 3 | 4.0 | 9.0 | 7.0 | 10.0 | 10.0 | 9.0 | 3.0 | 8.0 | 7.0 | 2.0 | 10.0 | 1.0 | 2.0 | 8.0 |
| 4 | 2.0 | 9.0 | 8.0 | 10.0 | 2.0 | 4.0 | 7.0 | 2.0 | 9.0 | 3.0 | 9.0 | 3.0 | 6.0 | 2.0 |
| 5 | 4.0 | 1.0 | 6.0 | 9.0 | 4.0 | 2.0 | 3.0 | 4.0 | 2.0 | 5.0 | 1.0 | 2.0 | 5.0 | 5.0 |
| 6 | 7.0 | 3.0 | 9.0 | 3.0 | 7.0 | 3.0 | 8.0 | 8.0 | 1.0 | 1.0 | 3.0 | 6.0 | 2.0 | 7.0 |
| 7 | 8.0 | 1.0 | 7.0 | 8.0 | 2.0 | 4.0 | 8.0 | 4.0 | 1.0 | 8.0 | 3.0 | 8.0 | 6.0 | 9.0 |
| 8 | 5.0 | 6.0 | 10.0 | 7.0 | 9.0 | 2.0 | 1.0 | 1.0 | 7.0 | 10.0 | 7.0 | 5.0 | 7.0 | 5.0 |
| 9 | 1.0 | 7.0 | 8.0 | 2.0 | 3.0 | 5.0 | 1.0 | 8.0 | 10.0 | 10.0 | 9.0 | 9.0 | 1.0 | 9.0 |
| 10 | 1.0 | 10.0 | 5.0 | 10.0 | 9.0 | 1.0 | 3.0 | 3.0 | 7.0 | 9.0 | 7.0 | 1.0 | 3.0 | 5.0 |
| 11 | 3.0 | 1.0 | 7.0 | 1.0 | 3.0 | 2.0 | 6.0 | 8.0 | 5.0 | 9.0 | 1.0 | 5.0 | 4.0 | 3.0 |
| 12 | 4.0 | 8.0 | 2.0 | 2.0 | 6.0 | 5.0 | 2.0 | 6.0 | 7.0 | 1.0 | 3.0 | 4.0 | 1.0 | 3.0 |
| 13 | 1.0 | 4.0 | 2.0 | 8.0 | 2.0 | 5.0 | 7.0 | 9.0 | 5.0 | 9.0 | 5.0 | 3.0 | 3.0 | 10.0 |
List the corridors, base costs, and pairwise overheads so we can evaluate each legal one-way route and choose the minimum-cost patrol.

Also, when you send back the chosen route, please use this simple JSON layout so it's easy to read and check:

{
  ""solution"": []
}

Here, ""solution"" should be an array containing the sequence of NODE identifiers from the guard room (source) to the checkpoint (target), in order. Keep it light — just the node names, nothing about hallway IDs or costs. This JSON is just a sketch of the expected shape, not the actual answer.

Please use the exact node identifiers as they appear in the instance input — do not rename or invent new labels. Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 'edges': [{'from': 8, 'to': 0, 'var_index': 0}, {'from': 8, 'to': 4, 'var_index': 1}, {'from': 3, 'to': 9, 'var_index': 2}, {'from': 7, 'to': 9, 'var_index': 3}, {'from': 0, 'to': 1, 'var_index': 4}, {'from': 0, 'to': 4, 'var_index': 5}, {'from': 1, 'to': 2, 'var_index': 6}, {'from': 1, 'to': 5, 'var_index': 7}, {'from': 2, 'to': 3, 'var_index': 8}, {'from': 2, 'to': 6, 'var_index': 9}, {'from': 3, 'to': 7, 'var_index': 10}, {'from': 4, 'to': 5, 'var_index': 11}, {'from': 5, 'to': 6, 'var_index': 12}, {'from': 6, 'to': 7, 'var_index': 13}], 'objective': {'constant': 0.0, 'linear': [1.0, 6.0, 1.0, 6.0, 10.0, 3.0, 8.0, 3.0, 1.0, 3.0, 1.0, 8.0, 3.0, 5.0], 'quadratic': [[6.0, 1.0, 1.0, 4.0, 2.0, 4.0, 7.0, 8.0, 5.0, 1.0, 1.0, 3.0, 4.0, 1.0], [1.0, 6.0, 7.0, 9.0, 9.0, 1.0, 3.0, 1.0, 6.0, 7.0, 10.0, 1.0, 8.0, 4.0], [1.0, 7.0, 5.0, 7.0, 8.0, 6.0, 9.0, 7.0, 10.0, 8.0, 5.0, 7.0, 2.0, 2.0], [4.0, 9.0, 7.0, 10.0, 10.0, 9.0, 3.0, 8.0, 7.0, 2.0, 10.0, 1.0, 2.0, 8.0], [2.0, 9.0, 8.0, 10.0, 2.0, 4.0, 7.0, 2.0, 9.0, 3.0, 9.0, 3.0, 6.0, 2.0], [4.0, 1.0, 6.0, 9.0, 4.0, 2.0, 3.0, 4.0, 2.0, 5.0, 1.0, 2.0, 5.0, 5.0], [7.0, 3.0, 9.0, 3.0, 7.0, 3.0, 8.0, 8.0, 1.0, 1.0, 3.0, 6.0, 2.0, 7.0], [8.0, 1.0, 7.0, 8.0, 2.0, 4.0, 8.0, 4.0, 1.0, 8.0, 3.0, 8.0, 6.0, 9.0], [5.0, 6.0, 10.0, 7.0, 9.0, 2.0, 1.0, 1.0, 7.0, 10.0, 7.0, 5.0, 7.0, 5.0], [1.0, 7.0, 8.0, 2.0, 3.0, 5.0, 1.0, 8.0, 10.0, 10.0, 9.0, 9.0, 1.0, 9.0], [1.0, 10.0, 5.0, 10.0, 9.0, 1.0, 3.0, 3.0, 7.0, 9.0, 7.0, 1.0, 3.0, 5.0], [3.0, 1.0, 7.0, 1.0, 3.0, 2.0, 6.0, 8.0, 5.0, 9.0, 1.0, 5.0, 4.0, 3.0], [4.0, 8.0, 2.0, 2.0, 6.0, 5.0, 2.0, 6.0, 7.0, 1.0, 3.0, 4.0, 1.0, 3.0], [1.0, 4.0, 2.0, 8.0, 2.0, 5.0, 7.0, 9.0, 5.0, 9.0, 5.0, 3.0, 3.0, 10.0]]}, 'source': 8, 'target': 9}","[8, 4, 5, 6, 7, 9]",146.0,"{'problem_type': 'QSPP', 'num_nodes': 10, 'num_edges': 14, 'nodes': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J'], 'source': 'I', 'target': 'J', 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 1.0}, {'var_index': 1, 'linear_cost': 6.0}, {'var_index': 2, 'linear_cost': 1.0}, {'var_index': 3, 'linear_cost': 6.0}, {'var_index': 4, 'linear_cost': 10.0}, {'var_index': 5, 'linear_cost': 3.0}, {'var_index': 6, 'linear_cost': 8.0}, {'var_index': 7, 'linear_cost': 3.0}, {'var_index': 8, 'linear_cost': 1.0}, {'var_index': 9, 'linear_cost': 3.0}, {'var_index': 10, 'linear_cost': 1.0}, {'var_index': 11, 'linear_cost': 8.0}, {'var_index': 12, 'linear_cost': 3.0}, {'var_index': 13, 'linear_cost': 5.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 12, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 13, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 13, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 12, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 12, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 13, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 12, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 13, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 7, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 7, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 8, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 8, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 8, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 8, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 8, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 8, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 13, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 9, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 9, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 9, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 9, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 9, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 9, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 9, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 9, 'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 9, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 10, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 10, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 10, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 10, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 10, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 10, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 10, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 10, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 13, 'quadratic_cost': 5.0}, {'var_i': 11, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 11, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 11, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 11, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 11, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 11, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 11, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 11, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 11, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 11, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 11, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 11, 'var_j': 12, 'quadratic_cost': 4.0}, {'var_i': 11, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 12, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 12, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 12, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 12, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 12, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 12, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 12, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 12, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 12, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 12, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 12, 'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 12, 'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 12, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 13, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 13, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 13, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 13, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 13, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 13, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 13, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 13, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 13, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 13, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 13, 'quadratic_cost': 10.0}]}, 'edges': [{'from': 'I', 'to': 'A', 'var_index': 0}, {'from': 'I', 'to': 'E', 'var_index': 1}, {'from': 'D', 'to': 'J', 'var_index': 2}, {'from': 'H', 'to': 'J', 'var_index': 3}, {'from': 'A', 'to': 'B', 'var_index': 4}, {'from': 'A', 'to': 'E', 'var_index': 5}, {'from': 'B', 'to': 'C', 'var_index': 6}, {'from': 'B', 'to': 'F', 'var_index': 7}, {'from': 'C', 'to': 'D', 'var_index': 8}, {'from': 'C', 'to': 'G', 'var_index': 9}, {'from': 'D', 'to': 'H', 'var_index': 10}, {'from': 'E', 'to': 'F', 'var_index': 11}, {'from': 'F', 'to': 'G', 'var_index': 12}, {'from': 'G', 'to': 'H', 'var_index': 13}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E', 5: 'F', 6: 'G', 7: 'H', 8: 'I', 9: 'J'}}","['I', 'E', 'F', 'G', 'H', 'J']",40,nl,names
QSPP,QSPP,"Someone on the team described it like planning a courier route through a set of conveyor belts: each belt moves the package forward but charges a fee, and certain belt combinations create extra handling fees if they’re used together — some belts also have a small handling surcharge by themselves. The task is to pick exactly one conveyor route from the pickup point to the delivery point so the total handling bill (every belt’s fee plus any extra pair fees) is as low as it can be. The route has to follow the arrows on the belts so every step is valid, and the final report should only list the sequence of locations visited — keep the internal belt codes and pricing out of that list. The full map and fee table are shown below.

# location_count=9
# links_count=12
# locations=0, 1, 2, 3, 4, 5, 6, 7, 8
# pickup_location=0
# delivery_location=8

link_from_location,link_to_location,link_code
0,1,0
0,3,1
1,2,2
1,4,3
2,5,4
3,4,5
3,6,6
4,5,7
4,7,8
5,8,9
6,7,10
7,8,11

link_code,link_fee
0,6.0
1,5.0
2,3.0
3,7.0
4,4.0
5,10.0
6,10.0
7,8.0
8,10.0
9,6.0
10,8.0
11,1.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (link_i_code, link_j_code). If two link_codes with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| link_i_code\link_j_code | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 2.0 | 4.0 | 2.0 | 7.0 | 8.0 | 8.0 | 9.0 | 2.0 | 6.0 | 4.0 | 4.0 | 3.0 |
| 1 | 4.0 | 10.0 | 5.0 | 2.0 | 10.0 | 3.0 | 5.0 | 6.0 | 5.0 | 7.0 | 5.0 | 5.0 |
| 2 | 2.0 | 5.0 | 2.0 | 10.0 | 5.0 | 1.0 | 5.0 | 3.0 | 5.0 | 7.0 | 3.0 | 4.0 |
| 3 | 7.0 | 2.0 | 10.0 | 3.0 | 10.0 | 5.0 | 7.0 | 5.0 | 8.0 | 5.0 | 6.0 | 7.0 |
| 4 | 8.0 | 10.0 | 5.0 | 10.0 | 7.0 | 3.0 | 9.0 | 3.0 | 3.0 | 1.0 | 7.0 | 5.0 |
| 5 | 8.0 | 3.0 | 1.0 | 5.0 | 3.0 | 1.0 | 6.0 | 8.0 | 3.0 | 9.0 | 4.0 | 1.0 |
| 6 | 9.0 | 5.0 | 5.0 | 7.0 | 9.0 | 6.0 | 3.0 | 7.0 | 10.0 | 5.0 | 2.0 | 9.0 |
| 7 | 2.0 | 6.0 | 3.0 | 5.0 | 3.0 | 8.0 | 7.0 | 3.0 | 3.0 | 2.0 | 5.0 | 8.0 |
| 8 | 6.0 | 5.0 | 5.0 | 8.0 | 3.0 | 3.0 | 10.0 | 3.0 | 9.0 | 7.0 | 1.0 | 8.0 |
| 9 | 4.0 | 7.0 | 7.0 | 5.0 | 1.0 | 9.0 | 5.0 | 2.0 | 7.0 | 6.0 | 7.0 | 4.0 |
| 10 | 4.0 | 5.0 | 3.0 | 6.0 | 7.0 | 4.0 | 2.0 | 5.0 | 1.0 | 7.0 | 8.0 | 3.0 |
| 11 | 3.0 | 5.0 | 4.0 | 7.0 | 5.0 | 1.0 | 9.0 | 8.0 | 8.0 | 4.0 | 3.0 | 7.0 |

Also, when you send the route back, it'd be great if you pop it into a tiny JSON snippet so it's easy to read and machine-friendly — nothing fancy, just the shape below.

{
  ""solution"": []
}

Think of that as a little form: ""solution"" should be the ordered list of locations (nodes) you travel through from pickup to delivery, first entry the source and last the target. Keep it simple and human: just the location names in order, no belt codes or cost bits. This block is just the expected shape — it’s a sketch, not the actual answer.

One more thing: use the node identifiers exactly as they appear in the instance input — do not rename or invent labels.  

Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'name': 'Rostami_Grid1_k3_seedNone', 'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8], 'edges': [{'from': 0, 'to': 1, 'var_index': 0}, {'from': 0, 'to': 3, 'var_index': 1}, {'from': 1, 'to': 2, 'var_index': 2}, {'from': 1, 'to': 4, 'var_index': 3}, {'from': 2, 'to': 5, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 3, 'to': 6, 'var_index': 6}, {'from': 4, 'to': 5, 'var_index': 7}, {'from': 4, 'to': 7, 'var_index': 8}, {'from': 5, 'to': 8, 'var_index': 9}, {'from': 6, 'to': 7, 'var_index': 10}, {'from': 7, 'to': 8, 'var_index': 11}], 'objective': {'constant': 0.0, 'linear': [6.0, 5.0, 3.0, 7.0, 4.0, 10.0, 10.0, 8.0, 10.0, 6.0, 8.0, 1.0], 'quadratic': [[2.0, 4.0, 2.0, 7.0, 8.0, 8.0, 9.0, 2.0, 6.0, 4.0, 4.0, 3.0], [4.0, 10.0, 5.0, 2.0, 10.0, 3.0, 5.0, 6.0, 5.0, 7.0, 5.0, 5.0], [2.0, 5.0, 2.0, 10.0, 5.0, 1.0, 5.0, 3.0, 5.0, 7.0, 3.0, 4.0], [7.0, 2.0, 10.0, 3.0, 10.0, 5.0, 7.0, 5.0, 8.0, 5.0, 6.0, 7.0], [8.0, 10.0, 5.0, 10.0, 7.0, 3.0, 9.0, 3.0, 3.0, 1.0, 7.0, 5.0], [8.0, 3.0, 1.0, 5.0, 3.0, 1.0, 6.0, 8.0, 3.0, 9.0, 4.0, 1.0], [9.0, 5.0, 5.0, 7.0, 9.0, 6.0, 3.0, 7.0, 10.0, 5.0, 2.0, 9.0], [2.0, 6.0, 3.0, 5.0, 3.0, 8.0, 7.0, 3.0, 3.0, 2.0, 5.0, 8.0], [6.0, 5.0, 5.0, 8.0, 3.0, 3.0, 10.0, 3.0, 9.0, 7.0, 1.0, 8.0], [4.0, 7.0, 7.0, 5.0, 1.0, 9.0, 5.0, 2.0, 7.0, 6.0, 7.0, 4.0], [4.0, 5.0, 3.0, 6.0, 7.0, 4.0, 2.0, 5.0, 1.0, 7.0, 8.0, 3.0], [3.0, 5.0, 4.0, 7.0, 5.0, 1.0, 9.0, 8.0, 8.0, 4.0, 3.0, 7.0]]}, 'source': 0, 'target': 8}","[0, 1, 2, 5, 8]",90.0,"{'problem_type': 'QSPP', 'num_nodes': 9, 'num_edges': 12, 'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8], 'source': 0, 'target': 8, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 6.0}, {'var_index': 1, 'linear_cost': 5.0}, {'var_index': 2, 'linear_cost': 3.0}, {'var_index': 3, 'linear_cost': 7.0}, {'var_index': 4, 'linear_cost': 4.0}, {'var_index': 5, 'linear_cost': 10.0}, {'var_index': 6, 'linear_cost': 10.0}, {'var_index': 7, 'linear_cost': 8.0}, {'var_index': 8, 'linear_cost': 10.0}, {'var_index': 9, 'linear_cost': 6.0}, {'var_index': 10, 'linear_cost': 8.0}, {'var_index': 11, 'linear_cost': 1.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 11, 'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 7, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 8, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 8, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 8, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 8, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 9, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 9, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 9, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 9, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 9, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 9, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 9, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 9, 'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 10, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 10, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 10, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 10, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 10, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 10, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 10, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 11, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 11, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 11, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 11, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 11, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 11, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 11, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 11, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 11, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 11, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 11, 'var_j': 10, 'quadratic_cost': 3.0}, {'var_i': 11, 'var_j': 11, 'quadratic_cost': 7.0}]}, 'edges': [{'from': 0, 'to': 1, 'var_index': 0}, {'from': 0, 'to': 3, 'var_index': 1}, {'from': 1, 'to': 2, 'var_index': 2}, {'from': 1, 'to': 4, 'var_index': 3}, {'from': 2, 'to': 5, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 3, 'to': 6, 'var_index': 6}, {'from': 4, 'to': 5, 'var_index': 7}, {'from': 4, 'to': 7, 'var_index': 8}, {'from': 5, 'to': 8, 'var_index': 9}, {'from': 6, 'to': 7, 'var_index': 10}, {'from': 7, 'to': 8, 'var_index': 11}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7, 8: 8}}","[0, 1, 2, 5, 8]",41,csv,0
QSPP,QSPP,"I was imagining a day out on the mountain: start at the trailhead and follow the one-way, signposted routes up to the summit. The job is to pick one continuous trail that goes from the start to the top without jumping around or breaking the route, and that respects the uphill/downhill directions posted along the way. Each trail segment has its usual level of effort, and some combinations of segments add extra annoyances when taken together — the total toll of a route is just the sum of every segment’s effort plus any extra trouble that pops up between particular pairs of segments. The goal is to pick the single route with the smallest total toll, and the exact map, segment efforts, and interaction details are shown below.

# total_locations=6
# total_trail_segments=8
# location_ids=0, 1, 2, 3, 4, 5
# trailhead=4
# summit=5

segment_start_location,segment_end_location,segment_id
4,0,0
4,2,1
1,5,2
3,5,3
0,1,4
0,2,5
1,3,6
2,3,7

segment_ref_id,segment_effort
0,2.0
1,10.0
2,5.0
3,1.0
4,1.0
5,6.0
6,8.0
7,3.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (segment_i_id, segment_j_id). If two segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| segment_i_id\segment_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|---|
| 0 | 2.0 | 8.0 | 8.0 | 3.0 | 8.0 | 10.0 | 4.0 | 4.0 |
| 1 | 8.0 | 2.0 | 8.0 | 3.0 | 2.0 | 5.0 | 5.0 | 4.0 |
| 2 | 8.0 | 8.0 | 4.0 | 5.0 | 10.0 | 4.0 | 9.0 | 2.0 |
| 3 | 3.0 | 3.0 | 5.0 | 9.0 | 3.0 | 9.0 | 7.0 | 6.0 |
| 4 | 8.0 | 2.0 | 10.0 | 3.0 | 3.0 | 5.0 | 3.0 | 6.0 |
| 5 | 10.0 | 5.0 | 4.0 | 9.0 | 5.0 | 1.0 | 2.0 | 6.0 |
| 6 | 4.0 | 5.0 | 9.0 | 7.0 | 3.0 | 2.0 | 6.0 | 10.0 |
| 7 | 4.0 | 4.0 | 2.0 | 6.0 | 6.0 | 6.0 | 10.0 | 3.0 |

When you send back your chosen trail, just drop it into this little JSON layout so it's easy to parse:

{
  ""solution"": []
}

Think of ""solution"" as the place to list the trail from the trailhead to the summit — just the node names in order (start, any intermediate waypoints, then the top). Keep it simple and human: the array holds the path nodes only. This JSON is just a sketch of the shape I want, not the actual answer — you'll fill the array with the node IDs from the map when you reply.

Please make sure to use the exact identifiers exactly as they appear in the instance input — no renaming and no new labels.
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5], 'edges': [{'from': 4, 'to': 0, 'var_index': 0}, {'from': 4, 'to': 2, 'var_index': 1}, {'from': 1, 'to': 5, 'var_index': 2}, {'from': 3, 'to': 5, 'var_index': 3}, {'from': 0, 'to': 1, 'var_index': 4}, {'from': 0, 'to': 2, 'var_index': 5}, {'from': 1, 'to': 3, 'var_index': 6}, {'from': 2, 'to': 3, 'var_index': 7}], 'objective': {'constant': 0.0, 'linear': [2.0, 10.0, 5.0, 1.0, 1.0, 6.0, 8.0, 3.0], 'quadratic': [[2.0, 8.0, 8.0, 3.0, 8.0, 10.0, 4.0, 4.0], [8.0, 2.0, 8.0, 3.0, 2.0, 5.0, 5.0, 4.0], [8.0, 8.0, 4.0, 5.0, 10.0, 4.0, 9.0, 2.0], [3.0, 3.0, 5.0, 9.0, 3.0, 9.0, 7.0, 6.0], [8.0, 2.0, 10.0, 3.0, 3.0, 5.0, 3.0, 6.0], [10.0, 5.0, 4.0, 9.0, 5.0, 1.0, 2.0, 6.0], [4.0, 5.0, 9.0, 7.0, 3.0, 2.0, 6.0, 10.0], [4.0, 4.0, 2.0, 6.0, 6.0, 6.0, 10.0, 3.0]]}, 'source': 4, 'target': 5}","[4, 2, 3, 5]",54.0,"{'problem_type': 'QSPP', 'num_nodes': 6, 'num_edges': 8, 'nodes': [0, 1, 2, 3, 4, 5], 'source': 4, 'target': 5, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 2.0}, {'var_index': 1, 'linear_cost': 10.0}, {'var_index': 2, 'linear_cost': 5.0}, {'var_index': 3, 'linear_cost': 1.0}, {'var_index': 4, 'linear_cost': 1.0}, {'var_index': 5, 'linear_cost': 6.0}, {'var_index': 6, 'linear_cost': 8.0}, {'var_index': 7, 'linear_cost': 3.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 7, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 7, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 7, 'quadratic_cost': 3.0}]}, 'edges': [{'from': 4, 'to': 0, 'var_index': 0}, {'from': 4, 'to': 2, 'var_index': 1}, {'from': 1, 'to': 5, 'var_index': 2}, {'from': 3, 'to': 5, 'var_index': 3}, {'from': 0, 'to': 1, 'var_index': 4}, {'from': 0, 'to': 2, 'var_index': 5}, {'from': 1, 'to': 3, 'var_index': 6}, {'from': 2, 'to': 3, 'var_index': 7}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5}}","[4, 2, 3, 5]",42,csv,0
QSPP,QSPP,"I’m picturing the shift where a robot has to roll from the charging dock over the conveyor network to the assembly area, and the job is to pick one clear route that follows the arrows. Each conveyor segment has its own running cost, and some segments carry extra charges all by themselves; plus certain pairs of segments together can trigger extra penalties — and if two different segments show up in the route, any penalties that apply between them are added in both directions. The aim is to end up with the cheapest possible route once every segment cost and all those pair penalties are added up. The route must be a single continuous trip from dock to assembly along the conveyors, listing every location in order and nothing else, and the exact layout and costs will be shown below.

{
  ""total_locations"": 6,
  ""total_conveyor_segments"": 5,
  ""location_ids"": [
    0,
    1,
    2,
    3,
    4,
    5
  ],
  ""charging_dock_location"": 4,
  ""assembly_zone_location"": 5,
  ""edges"": [
    {
      ""conveyor_from_node"": 4,
      ""conveyor_to_node"": 0,
      ""conveyor_segment_id"": 0
    },
    {
      ""conveyor_from_node"": 3,
      ""conveyor_to_node"": 5,
      ""conveyor_segment_id"": 1
    },
    {
      ""conveyor_from_node"": 0,
      ""conveyor_to_node"": 1,
      ""conveyor_segment_id"": 2
    },
    {
      ""conveyor_from_node"": 1,
      ""conveyor_to_node"": 2,
      ""conveyor_segment_id"": 3
    },
    {
      ""conveyor_from_node"": 2,
      ""conveyor_to_node"": 3,
      ""conveyor_segment_id"": 4
    }
  ],
  ""linear_costs"": [
    {
      ""conveyor_segment_id"": 0,
      ""segment_operating_cost"": 4.0
    },
    {
      ""conveyor_segment_id"": 1,
      ""segment_operating_cost"": 5.0
    },
    {
      ""conveyor_segment_id"": 2,
      ""segment_operating_cost"": 2.0
    },
    {
      ""conveyor_segment_id"": 3,
      ""segment_operating_cost"": 7.0
    },
    {
      ""conveyor_segment_id"": 4,
      ""segment_operating_cost"": 4.0
    }
  ]
}

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (segment_i_id, segment_j_id). If two conveyor_segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| segment_i_id\segment_j_id | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| 0 | 5.0 | 3.0 | 4.0 | 6.0 | 6.0 |
| 1 | 3.0 | 7.0 | 3.0 | 3.0 | 5.0 |
| 2 | 4.0 | 3.0 | 10.0 | 2.0 | 10.0 |
| 3 | 6.0 | 3.0 | 2.0 | 6.0 | 4.0 |
| 4 | 6.0 | 5.0 | 10.0 | 4.0 | 9.0 |

Also, when you give the final route, tuck it into a tiny JSON sketch like this so it's easy to read and parse:

{
  ""solution"": []
}

Here ""solution"" is meant to be an ordered list of the location names (the nodes) the robot will travel through, starting at the dock and ending at the assembly area. Think of it like writing down each stop in order — this block just shows the shape I want, not the actual filled-in route.

Please use the exact identifiers from the instance input — don’t rename or invent labels. 
""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5], 'edges': [{'from': 4, 'to': 0, 'var_index': 0}, {'from': 3, 'to': 5, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}], 'objective': {'constant': 0.0, 'linear': [4.0, 5.0, 2.0, 7.0, 4.0], 'quadratic': [[5.0, 3.0, 4.0, 6.0, 6.0], [3.0, 7.0, 3.0, 3.0, 5.0], [4.0, 3.0, 10.0, 2.0, 10.0], [6.0, 3.0, 2.0, 6.0, 4.0], [6.0, 5.0, 10.0, 4.0, 9.0]]}, 'source': 4, 'target': 5}","[4, 0, 1, 2, 3, 5]",151.0,"{'problem_type': 'QSPP', 'num_nodes': 6, 'num_edges': 5, 'nodes': [0, 1, 2, 3, 4, 5], 'source': 4, 'target': 5, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 4.0}, {'var_index': 1, 'linear_cost': 5.0}, {'var_index': 2, 'linear_cost': 2.0}, {'var_index': 3, 'linear_cost': 7.0}, {'var_index': 4, 'linear_cost': 4.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 9.0}]}, 'edges': [{'from': 4, 'to': 0, 'var_index': 0}, {'from': 3, 'to': 5, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5}}","[4, 0, 1, 2, 3, 5]",43,json,0
QSPP,QSPP,"There's a little puzzle in planning connecting flights: pick one uninterrupted itinerary from the first airport to the last, using only the flights that actually go from one stop to the next. Each flight carries its own cost, and some combinations of flights trigger extra fees or slowdowns when they appear together — those extras are counted only if both flights are on the same itinerary. So the aim is to choose the route whose sum of base fares plus any pairwise extras is smallest. Everything must be included in that one route — no splitting into separate trips or inventing connections. The concrete schedule and cost details follow below.

# total_airports_count=10
# total_flights_count=23
# airport_codes=A, B, C, D, E, F, G, H, I, J
# origin_airport=I
# destination_airport=J

flight_departure_airport,flight_arrival_airport,flight_id
I,A,0
I,B,1
I,C,2
I,D,3
I,E,4
I,F,5
I,G,6
I,H,7
A,J,8
B,J,9
C,J,10
D,J,11
E,J,12
F,J,13
G,J,14
H,J,15
A,B,16
B,C,17
C,D,18
D,E,19
E,F,20
F,G,21
G,H,22

flight_id_ref,base_fare
0,2.0
1,6.0
2,8.0
3,1.0
4,9.0
5,2.0
6,6.0
7,1.0
8,1.0
9,4.0
10,3.0
11,2.0
12,6.0
13,7.0
14,5.0
15,4.0
16,6.0
17,3.0
18,9.0
19,8.0
20,9.0
21,6.0
22,1.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (flight_i_id, flight_j_id). If two flights with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| flight_i_id\flight_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 9.0 | 4.0 | 7.0 | 1.0 | 10.0 | 1.0 | 5.0 | 8.0 | 3.0 | 10.0 | 2.0 | 6.0 | 6.0 | 10.0 | 6.0 | 1.0 | 1.0 | 3.0 | 8.0 | 5.0 | 2.0 | 5.0 | 2.0 |
| 1 | 4.0 | 4.0 | 3.0 | 5.0 | 10.0 | 5.0 | 8.0 | 8.0 | 3.0 | 8.0 | 4.0 | 9.0 | 1.0 | 9.0 | 5.0 | 6.0 | 9.0 | 8.0 | 2.0 | 2.0 | 7.0 | 1.0 | 10.0 |
| 2 | 7.0 | 3.0 | 9.0 | 7.0 | 2.0 | 1.0 | 3.0 | 4.0 | 10.0 | 4.0 | 6.0 | 7.0 | 9.0 | 6.0 | 1.0 | 1.0 | 8.0 | 6.0 | 6.0 | 1.0 | 2.0 | 1.0 | 1.0 |
| 3 | 1.0 | 5.0 | 7.0 | 1.0 | 3.0 | 6.0 | 10.0 | 3.0 | 8.0 | 3.0 | 6.0 | 6.0 | 5.0 | 5.0 | 8.0 | 9.0 | 1.0 | 6.0 | 6.0 | 3.0 | 2.0 | 1.0 | 4.0 |
| 4 | 10.0 | 10.0 | 2.0 | 3.0 | 4.0 | 4.0 | 7.0 | 8.0 | 5.0 | 8.0 | 4.0 | 6.0 | 8.0 | 1.0 | 5.0 | 4.0 | 6.0 | 7.0 | 1.0 | 2.0 | 2.0 | 4.0 | 7.0 |
| 5 | 1.0 | 5.0 | 1.0 | 6.0 | 4.0 | 10.0 | 8.0 | 5.0 | 5.0 | 1.0 | 3.0 | 6.0 | 6.0 | 7.0 | 5.0 | 8.0 | 3.0 | 9.0 | 3.0 | 6.0 | 4.0 | 7.0 | 9.0 |
| 6 | 5.0 | 8.0 | 3.0 | 10.0 | 7.0 | 8.0 | 6.0 | 2.0 | 5.0 | 10.0 | 8.0 | 8.0 | 3.0 | 7.0 | 9.0 | 7.0 | 8.0 | 8.0 | 6.0 | 4.0 | 6.0 | 7.0 | 6.0 |
| 7 | 8.0 | 8.0 | 4.0 | 3.0 | 8.0 | 5.0 | 2.0 | 6.0 | 3.0 | 4.0 | 3.0 | 4.0 | 3.0 | 7.0 | 8.0 | 2.0 | 9.0 | 4.0 | 7.0 | 7.0 | 4.0 | 6.0 | 5.0 |
| 8 | 3.0 | 3.0 | 10.0 | 8.0 | 5.0 | 5.0 | 5.0 | 3.0 | 10.0 | 3.0 | 8.0 | 3.0 | 1.0 | 3.0 | 2.0 | 1.0 | 7.0 | 8.0 | 4.0 | 5.0 | 8.0 | 4.0 | 9.0 |
| 9 | 10.0 | 8.0 | 4.0 | 3.0 | 8.0 | 1.0 | 10.0 | 4.0 | 3.0 | 7.0 | 4.0 | 9.0 | 9.0 | 8.0 | 10.0 | 6.0 | 3.0 | 5.0 | 9.0 | 5.0 | 6.0 | 10.0 | 3.0 |
| 10 | 2.0 | 4.0 | 6.0 | 6.0 | 4.0 | 3.0 | 8.0 | 3.0 | 8.0 | 4.0 | 10.0 | 9.0 | 7.0 | 3.0 | 9.0 | 5.0 | 3.0 | 4.0 | 4.0 | 3.0 | 8.0 | 6.0 | 10.0 |
| 11 | 6.0 | 9.0 | 7.0 | 6.0 | 6.0 | 6.0 | 8.0 | 4.0 | 3.0 | 9.0 | 9.0 | 3.0 | 2.0 | 4.0 | 6.0 | 4.0 | 2.0 | 8.0 | 9.0 | 1.0 | 6.0 | 8.0 | 5.0 |
| 12 | 6.0 | 1.0 | 9.0 | 5.0 | 8.0 | 6.0 | 3.0 | 3.0 | 1.0 | 9.0 | 7.0 | 2.0 | 8.0 | 2.0 | 8.0 | 5.0 | 3.0 | 4.0 | 2.0 | 6.0 | 10.0 | 3.0 | 2.0 |
| 13 | 10.0 | 9.0 | 6.0 | 5.0 | 1.0 | 7.0 | 7.0 | 7.0 | 3.0 | 8.0 | 3.0 | 4.0 | 2.0 | 1.0 | 2.0 | 3.0 | 10.0 | 3.0 | 1.0 | 3.0 | 6.0 | 9.0 | 5.0 |
| 14 | 6.0 | 5.0 | 1.0 | 8.0 | 5.0 | 5.0 | 9.0 | 8.0 | 2.0 | 10.0 | 9.0 | 6.0 | 8.0 | 2.0 | 1.0 | 9.0 | 10.0 | 2.0 | 1.0 | 3.0 | 2.0 | 9.0 | 10.0 |
| 15 | 1.0 | 6.0 | 1.0 | 9.0 | 4.0 | 8.0 | 7.0 | 2.0 | 1.0 | 6.0 | 5.0 | 4.0 | 5.0 | 3.0 | 9.0 | 7.0 | 7.0 | 5.0 | 6.0 | 2.0 | 6.0 | 3.0 | 10.0 |
| 16 | 1.0 | 9.0 | 8.0 | 1.0 | 6.0 | 3.0 | 8.0 | 9.0 | 7.0 | 3.0 | 3.0 | 2.0 | 3.0 | 10.0 | 10.0 | 7.0 | 9.0 | 3.0 | 4.0 | 1.0 | 6.0 | 3.0 | 3.0 |
| 17 | 3.0 | 8.0 | 6.0 | 6.0 | 7.0 | 9.0 | 8.0 | 4.0 | 8.0 | 5.0 | 4.0 | 8.0 | 4.0 | 3.0 | 2.0 | 5.0 | 3.0 | 4.0 | 4.0 | 2.0 | 5.0 | 5.0 | 2.0 |
| 18 | 8.0 | 2.0 | 6.0 | 6.0 | 1.0 | 3.0 | 6.0 | 7.0 | 4.0 | 9.0 | 4.0 | 9.0 | 2.0 | 1.0 | 1.0 | 6.0 | 4.0 | 4.0 | 1.0 | 3.0 | 6.0 | 10.0 | 7.0 |
| 19 | 5.0 | 2.0 | 1.0 | 3.0 | 2.0 | 6.0 | 4.0 | 7.0 | 5.0 | 5.0 | 3.0 | 1.0 | 6.0 | 3.0 | 3.0 | 2.0 | 1.0 | 2.0 | 3.0 | 9.0 | 5.0 | 7.0 | 5.0 |
| 20 | 2.0 | 7.0 | 2.0 | 2.0 | 2.0 | 4.0 | 6.0 | 4.0 | 8.0 | 6.0 | 8.0 | 6.0 | 10.0 | 6.0 | 2.0 | 6.0 | 6.0 | 5.0 | 6.0 | 5.0 | 10.0 | 9.0 | 8.0 |
| 21 | 5.0 | 1.0 | 1.0 | 1.0 | 4.0 | 7.0 | 7.0 | 6.0 | 4.0 | 10.0 | 6.0 | 8.0 | 3.0 | 9.0 | 9.0 | 3.0 | 3.0 | 5.0 | 10.0 | 7.0 | 9.0 | 8.0 | 10.0 |
| 22 | 2.0 | 10.0 | 1.0 | 4.0 | 7.0 | 9.0 | 6.0 | 5.0 | 9.0 | 3.0 | 10.0 | 5.0 | 2.0 | 5.0 | 10.0 | 10.0 | 3.0 | 2.0 | 7.0 | 5.0 | 8.0 | 10.0 | 2.0 |

Also, when you send back the chosen itinerary, please put it in a tiny JSON object like this:

{
  ""solution"": []
}

Here ""solution"" should be an array listing the node identifiers in order from the starting airport to the final one — just the node names, nothing else. Think of it like filling in a short form: the array is the stops along the route (first is the source, last is the target). This JSON is just a sketch of the shape I expect, not the actual answer itself.

Please make sure to use the node identifiers exactly as they appear in the instance input — do not rename them or invent new labels.

- For example: ""Valid identifiers look like plain numbers such as ""1"" or ""23"", single capital letters like ""A"" or ""B"", or a capital letter followed by digits like ""A1"" or ""X7"".

Alright — pick the best uninterrupted route and return it in that JSON shape.","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 'edges': [{'from': 8, 'to': 0, 'var_index': 0}, {'from': 8, 'to': 1, 'var_index': 1}, {'from': 8, 'to': 2, 'var_index': 2}, {'from': 8, 'to': 3, 'var_index': 3}, {'from': 8, 'to': 4, 'var_index': 4}, {'from': 8, 'to': 5, 'var_index': 5}, {'from': 8, 'to': 6, 'var_index': 6}, {'from': 8, 'to': 7, 'var_index': 7}, {'from': 0, 'to': 9, 'var_index': 8}, {'from': 1, 'to': 9, 'var_index': 9}, {'from': 2, 'to': 9, 'var_index': 10}, {'from': 3, 'to': 9, 'var_index': 11}, {'from': 4, 'to': 9, 'var_index': 12}, {'from': 5, 'to': 9, 'var_index': 13}, {'from': 6, 'to': 9, 'var_index': 14}, {'from': 7, 'to': 9, 'var_index': 15}, {'from': 0, 'to': 1, 'var_index': 16}, {'from': 1, 'to': 2, 'var_index': 17}, {'from': 2, 'to': 3, 'var_index': 18}, {'from': 3, 'to': 4, 'var_index': 19}, {'from': 4, 'to': 5, 'var_index': 20}, {'from': 5, 'to': 6, 'var_index': 21}, {'from': 6, 'to': 7, 'var_index': 22}], 'objective': {'constant': 0.0, 'linear': [2.0, 6.0, 8.0, 1.0, 9.0, 2.0, 6.0, 1.0, 1.0, 4.0, 3.0, 2.0, 6.0, 7.0, 5.0, 4.0, 6.0, 3.0, 9.0, 8.0, 9.0, 6.0, 1.0], 'quadratic': [[9.0, 4.0, 7.0, 1.0, 10.0, 1.0, 5.0, 8.0, 3.0, 10.0, 2.0, 6.0, 6.0, 10.0, 6.0, 1.0, 1.0, 3.0, 8.0, 5.0, 2.0, 5.0, 2.0], [4.0, 4.0, 3.0, 5.0, 10.0, 5.0, 8.0, 8.0, 3.0, 8.0, 4.0, 9.0, 1.0, 9.0, 5.0, 6.0, 9.0, 8.0, 2.0, 2.0, 7.0, 1.0, 10.0], [7.0, 3.0, 9.0, 7.0, 2.0, 1.0, 3.0, 4.0, 10.0, 4.0, 6.0, 7.0, 9.0, 6.0, 1.0, 1.0, 8.0, 6.0, 6.0, 1.0, 2.0, 1.0, 1.0], [1.0, 5.0, 7.0, 1.0, 3.0, 6.0, 10.0, 3.0, 8.0, 3.0, 6.0, 6.0, 5.0, 5.0, 8.0, 9.0, 1.0, 6.0, 6.0, 3.0, 2.0, 1.0, 4.0], [10.0, 10.0, 2.0, 3.0, 4.0, 4.0, 7.0, 8.0, 5.0, 8.0, 4.0, 6.0, 8.0, 1.0, 5.0, 4.0, 6.0, 7.0, 1.0, 2.0, 2.0, 4.0, 7.0], [1.0, 5.0, 1.0, 6.0, 4.0, 10.0, 8.0, 5.0, 5.0, 1.0, 3.0, 6.0, 6.0, 7.0, 5.0, 8.0, 3.0, 9.0, 3.0, 6.0, 4.0, 7.0, 9.0], [5.0, 8.0, 3.0, 10.0, 7.0, 8.0, 6.0, 2.0, 5.0, 10.0, 8.0, 8.0, 3.0, 7.0, 9.0, 7.0, 8.0, 8.0, 6.0, 4.0, 6.0, 7.0, 6.0], [8.0, 8.0, 4.0, 3.0, 8.0, 5.0, 2.0, 6.0, 3.0, 4.0, 3.0, 4.0, 3.0, 7.0, 8.0, 2.0, 9.0, 4.0, 7.0, 7.0, 4.0, 6.0, 5.0], [3.0, 3.0, 10.0, 8.0, 5.0, 5.0, 5.0, 3.0, 10.0, 3.0, 8.0, 3.0, 1.0, 3.0, 2.0, 1.0, 7.0, 8.0, 4.0, 5.0, 8.0, 4.0, 9.0], [10.0, 8.0, 4.0, 3.0, 8.0, 1.0, 10.0, 4.0, 3.0, 7.0, 4.0, 9.0, 9.0, 8.0, 10.0, 6.0, 3.0, 5.0, 9.0, 5.0, 6.0, 10.0, 3.0], [2.0, 4.0, 6.0, 6.0, 4.0, 3.0, 8.0, 3.0, 8.0, 4.0, 10.0, 9.0, 7.0, 3.0, 9.0, 5.0, 3.0, 4.0, 4.0, 3.0, 8.0, 6.0, 10.0], [6.0, 9.0, 7.0, 6.0, 6.0, 6.0, 8.0, 4.0, 3.0, 9.0, 9.0, 3.0, 2.0, 4.0, 6.0, 4.0, 2.0, 8.0, 9.0, 1.0, 6.0, 8.0, 5.0], [6.0, 1.0, 9.0, 5.0, 8.0, 6.0, 3.0, 3.0, 1.0, 9.0, 7.0, 2.0, 8.0, 2.0, 8.0, 5.0, 3.0, 4.0, 2.0, 6.0, 10.0, 3.0, 2.0], [10.0, 9.0, 6.0, 5.0, 1.0, 7.0, 7.0, 7.0, 3.0, 8.0, 3.0, 4.0, 2.0, 1.0, 2.0, 3.0, 10.0, 3.0, 1.0, 3.0, 6.0, 9.0, 5.0], [6.0, 5.0, 1.0, 8.0, 5.0, 5.0, 9.0, 8.0, 2.0, 10.0, 9.0, 6.0, 8.0, 2.0, 1.0, 9.0, 10.0, 2.0, 1.0, 3.0, 2.0, 9.0, 10.0], [1.0, 6.0, 1.0, 9.0, 4.0, 8.0, 7.0, 2.0, 1.0, 6.0, 5.0, 4.0, 5.0, 3.0, 9.0, 7.0, 7.0, 5.0, 6.0, 2.0, 6.0, 3.0, 10.0], [1.0, 9.0, 8.0, 1.0, 6.0, 3.0, 8.0, 9.0, 7.0, 3.0, 3.0, 2.0, 3.0, 10.0, 10.0, 7.0, 9.0, 3.0, 4.0, 1.0, 6.0, 3.0, 3.0], [3.0, 8.0, 6.0, 6.0, 7.0, 9.0, 8.0, 4.0, 8.0, 5.0, 4.0, 8.0, 4.0, 3.0, 2.0, 5.0, 3.0, 4.0, 4.0, 2.0, 5.0, 5.0, 2.0], [8.0, 2.0, 6.0, 6.0, 1.0, 3.0, 6.0, 7.0, 4.0, 9.0, 4.0, 9.0, 2.0, 1.0, 1.0, 6.0, 4.0, 4.0, 1.0, 3.0, 6.0, 10.0, 7.0], [5.0, 2.0, 1.0, 3.0, 2.0, 6.0, 4.0, 7.0, 5.0, 5.0, 3.0, 1.0, 6.0, 3.0, 3.0, 2.0, 1.0, 2.0, 3.0, 9.0, 5.0, 7.0, 5.0], [2.0, 7.0, 2.0, 2.0, 2.0, 4.0, 6.0, 4.0, 8.0, 6.0, 8.0, 6.0, 10.0, 6.0, 2.0, 6.0, 6.0, 5.0, 6.0, 5.0, 10.0, 9.0, 8.0], [5.0, 1.0, 1.0, 1.0, 4.0, 7.0, 7.0, 6.0, 4.0, 10.0, 6.0, 8.0, 3.0, 9.0, 9.0, 3.0, 3.0, 5.0, 10.0, 7.0, 9.0, 8.0, 10.0], [2.0, 10.0, 1.0, 4.0, 7.0, 9.0, 6.0, 5.0, 9.0, 3.0, 10.0, 5.0, 2.0, 5.0, 10.0, 10.0, 3.0, 2.0, 7.0, 5.0, 8.0, 10.0, 2.0]]}, 'source': 8, 'target': 9}","[8, 3, 9]",19.0,"{'problem_type': 'QSPP', 'num_nodes': 10, 'num_edges': 23, 'nodes': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J'], 'source': 'I', 'target': 'J', 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 2.0}, {'var_index': 1, 'linear_cost': 6.0}, {'var_index': 2, 'linear_cost': 8.0}, {'var_index': 3, 'linear_cost': 1.0}, {'var_index': 4, 'linear_cost': 9.0}, {'var_index': 5, 'linear_cost': 2.0}, {'var_index': 6, 'linear_cost': 6.0}, {'var_index': 7, 'linear_cost': 1.0}, {'var_index': 8, 'linear_cost': 1.0}, {'var_index': 9, 'linear_cost': 4.0}, {'var_index': 10, 'linear_cost': 3.0}, {'var_index': 11, 'linear_cost': 2.0}, {'var_index': 12, 'linear_cost': 6.0}, {'var_index': 13, 'linear_cost': 7.0}, {'var_index': 14, 'linear_cost': 5.0}, {'var_index': 15, 'linear_cost': 4.0}, {'var_index': 16, 'linear_cost': 6.0}, {'var_index': 17, 'linear_cost': 3.0}, {'var_index': 18, 'linear_cost': 9.0}, {'var_index': 19, 'linear_cost': 8.0}, {'var_index': 20, 'linear_cost': 9.0}, {'var_index': 21, 'linear_cost': 6.0}, {'var_index': 22, 'linear_cost': 1.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 14, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 15, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 16, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 17, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 18, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 19, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 20, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 21, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 22, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 12, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 14, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 15, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 17, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 18, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 19, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 20, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 21, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 22, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 12, 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{'var_i': 21, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 21, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 21, 'var_j': 13, 'quadratic_cost': 9.0}, {'var_i': 21, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 21, 'var_j': 15, 'quadratic_cost': 3.0}, {'var_i': 21, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 21, 'var_j': 17, 'quadratic_cost': 5.0}, {'var_i': 21, 'var_j': 18, 'quadratic_cost': 10.0}, {'var_i': 21, 'var_j': 19, 'quadratic_cost': 7.0}, {'var_i': 21, 'var_j': 20, 'quadratic_cost': 9.0}, {'var_i': 21, 'var_j': 21, 'quadratic_cost': 8.0}, {'var_i': 21, 'var_j': 22, 'quadratic_cost': 10.0}, {'var_i': 22, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 22, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 22, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 22, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 22, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 22, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 22, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 22, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 22, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 22, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 22, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 22, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 22, 'var_j': 12, 'quadratic_cost': 2.0}, {'var_i': 22, 'var_j': 13, 'quadratic_cost': 5.0}, {'var_i': 22, 'var_j': 14, 'quadratic_cost': 10.0}, {'var_i': 22, 'var_j': 15, 'quadratic_cost': 10.0}, {'var_i': 22, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 22, 'var_j': 17, 'quadratic_cost': 2.0}, {'var_i': 22, 'var_j': 18, 'quadratic_cost': 7.0}, {'var_i': 22, 'var_j': 19, 'quadratic_cost': 5.0}, {'var_i': 22, 'var_j': 20, 'quadratic_cost': 8.0}, {'var_i': 22, 'var_j': 21, 'quadratic_cost': 10.0}, {'var_i': 22, 'var_j': 22, 'quadratic_cost': 2.0}]}, 'edges': [{'from': 'I', 'to': 'A', 'var_index': 0}, {'from': 'I', 'to': 'B', 'var_index': 1}, {'from': 'I', 'to': 'C', 'var_index': 2}, {'from': 'I', 'to': 'D', 'var_index': 3}, {'from': 'I', 'to': 'E', 'var_index': 4}, {'from': 'I', 'to': 'F', 'var_index': 5}, {'from': 'I', 'to': 'G', 'var_index': 6}, {'from': 'I', 'to': 'H', 'var_index': 7}, {'from': 'A', 'to': 'J', 'var_index': 8}, {'from': 'B', 'to': 'J', 'var_index': 9}, {'from': 'C', 'to': 'J', 'var_index': 10}, {'from': 'D', 'to': 'J', 'var_index': 11}, {'from': 'E', 'to': 'J', 'var_index': 12}, {'from': 'F', 'to': 'J', 'var_index': 13}, {'from': 'G', 'to': 'J', 'var_index': 14}, {'from': 'H', 'to': 'J', 'var_index': 15}, {'from': 'A', 'to': 'B', 'var_index': 16}, {'from': 'B', 'to': 'C', 'var_index': 17}, {'from': 'C', 'to': 'D', 'var_index': 18}, {'from': 'D', 'to': 'E', 'var_index': 19}, {'from': 'E', 'to': 'F', 'var_index': 20}, {'from': 'F', 'to': 'G', 'var_index': 21}, {'from': 'G', 'to': 'H', 'var_index': 22}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E', 5: 'F', 6: 'G', 7: 'H', 8: 'I', 9: 'J'}}","['I', 'D', 'J']",44,csv,names
QSPP,QSPP,"Many people on campus follow one-way pedestrian arrows, and for this task a messenger must pick a single such route from the administration building to the research block. Each segment has a baseline effort, some segments also carry an extra standalone penalty, and certain pairs of segments generate additional penalties only if both are included in the same path. To compare routes, add up all baseline efforts plus any standalone penalties and any pair penalties that apply, and take the single continuous, one-way route with the lowest combined score. The specific walkway details and penalty values are provided below.

There are 9 locations and 12 directed walkways; valid location IDs are A, B, C, D, E, F, G, H, I. The messenger starts at A and must end at I.

| walkway_from_node | walkway_to_node | walkway_segment_id |
|---|---|---|
| A | B | 0 |
| A | D | 1 |
| B | C | 2 |
| B | E | 3 |
| C | F | 4 |
| D | E | 5 |
| D | G | 6 |
| E | F | 7 |
| E | H | 8 |
| F | I | 9 |
| G | H | 10 |
| H | I | 11 |

| walkway_segment_ref | baseline_effort |
|---|---|
| 0 | 9.0 |
| 1 | 4.0 |
| 2 | 7.0 |
| 3 | 7.0 |
| 4 | 7.0 |
| 5 | 8.0 |
| 6 | 8.0 |
| 7 | 5.0 |
| 8 | 7.0 |
| 9 | 3.0 |
| 10 | 8.0 |
| 11 | 2.0 |

*Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (segment_i_ref, segment_j_ref). If two walkway_segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).*

**quadratic_costs**

| segment_i_ref\segment_j_ref | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 6.0 | 9.0 | 6.0 | 8.0 | 6.0 | 10.0 | 7.0 | 5.0 | 6.0 | 4.0 | 7.0 | 2.0 |
| 1 | 9.0 | 2.0 | 3.0 | 3.0 | 2.0 | 6.0 | 6.0 | 3.0 | 3.0 | 1.0 | 8.0 | 2.0 |
| 2 | 6.0 | 3.0 | 4.0 | 8.0 | 10.0 | 5.0 | 2.0 | 1.0 | 1.0 | 6.0 | 1.0 | 8.0 |
| 3 | 8.0 | 3.0 | 8.0 | 4.0 | 7.0 | 1.0 | 2.0 | 1.0 | 4.0 | 6.0 | 2.0 | 9.0 |
| 4 | 6.0 | 2.0 | 10.0 | 7.0 | 1.0 | 3.0 | 6.0 | 5.0 | 5.0 | 7.0 | 5.0 | 6.0 |
| 5 | 10.0 | 6.0 | 5.0 | 1.0 | 3.0 | 6.0 | 1.0 | 1.0 | 9.0 | 5.0 | 5.0 | 2.0 |
| 6 | 7.0 | 6.0 | 2.0 | 2.0 | 6.0 | 1.0 | 10.0 | 3.0 | 2.0 | 4.0 | 5.0 | 5.0 |
| 7 | 5.0 | 3.0 | 1.0 | 1.0 | 5.0 | 1.0 | 3.0 | 10.0 | 9.0 | 10.0 | 7.0 | 9.0 |
| 8 | 6.0 | 3.0 | 1.0 | 4.0 | 5.0 | 9.0 | 2.0 | 9.0 | 8.0 | 8.0 | 4.0 | 2.0 |
| 9 | 4.0 | 1.0 | 6.0 | 6.0 | 7.0 | 5.0 | 4.0 | 10.0 | 8.0 | 5.0 | 9.0 | 2.0 |
| 10 | 7.0 | 8.0 | 1.0 | 2.0 | 5.0 | 5.0 | 5.0 | 7.0 | 4.0 | 9.0 | 7.0 | 7.0 |
| 11 | 2.0 | 2.0 | 8.0 | 9.0 | 6.0 | 2.0 | 5.0 | 9.0 | 2.0 | 2.0 | 7.0 | 3.0 |

Compare routes by summing baseline efforts and any standalone or pair penalties, then select the single continuous one-way route with the lowest total from A to I.

When you send back the chosen route, just drop it into a tiny JSON snippet so it's easy to read and check. Here's the shape to use:

{
  ""solution"": []
}

Think of that ""solution"" array as the little form field where you list the path: the nodes in order from the administration building (source) to the research block (target). Keep it simple — it's just a sketch of the shape we expect, not the actual route itself.

Please use the exact identifiers as they appear in the instance input; don't rename them or make up new labels.
- for example: ""Valid identifiers look like plain numbers such as ""1"" or ""23"", single capital letters like ""A"" or ""B"", or a capital letter followed by digits like ""A1"" or ""X7"".""","{'name': 'Rostami_Grid1_k3_seedNone', 'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8], 'edges': [{'from': 0, 'to': 1, 'var_index': 0}, {'from': 0, 'to': 3, 'var_index': 1}, {'from': 1, 'to': 2, 'var_index': 2}, {'from': 1, 'to': 4, 'var_index': 3}, {'from': 2, 'to': 5, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 3, 'to': 6, 'var_index': 6}, {'from': 4, 'to': 5, 'var_index': 7}, {'from': 4, 'to': 7, 'var_index': 8}, {'from': 5, 'to': 8, 'var_index': 9}, {'from': 6, 'to': 7, 'var_index': 10}, {'from': 7, 'to': 8, 'var_index': 11}], 'objective': {'constant': 0.0, 'linear': [9.0, 4.0, 7.0, 7.0, 7.0, 8.0, 8.0, 5.0, 7.0, 3.0, 8.0, 2.0], 'quadratic': [[6.0, 9.0, 6.0, 8.0, 6.0, 10.0, 7.0, 5.0, 6.0, 4.0, 7.0, 2.0], [9.0, 2.0, 3.0, 3.0, 2.0, 6.0, 6.0, 3.0, 3.0, 1.0, 8.0, 2.0], [6.0, 3.0, 4.0, 8.0, 10.0, 5.0, 2.0, 1.0, 1.0, 6.0, 1.0, 8.0], [8.0, 3.0, 8.0, 4.0, 7.0, 1.0, 2.0, 1.0, 4.0, 6.0, 2.0, 9.0], [6.0, 2.0, 10.0, 7.0, 1.0, 3.0, 6.0, 5.0, 5.0, 7.0, 5.0, 6.0], [10.0, 6.0, 5.0, 1.0, 3.0, 6.0, 1.0, 1.0, 9.0, 5.0, 5.0, 2.0], [7.0, 6.0, 2.0, 2.0, 6.0, 1.0, 10.0, 3.0, 2.0, 4.0, 5.0, 5.0], [5.0, 3.0, 1.0, 1.0, 5.0, 1.0, 3.0, 10.0, 9.0, 10.0, 7.0, 9.0], [6.0, 3.0, 1.0, 4.0, 5.0, 9.0, 2.0, 9.0, 8.0, 8.0, 4.0, 2.0], [4.0, 1.0, 6.0, 6.0, 7.0, 5.0, 4.0, 10.0, 8.0, 5.0, 9.0, 2.0], [7.0, 8.0, 1.0, 2.0, 5.0, 5.0, 5.0, 7.0, 4.0, 9.0, 7.0, 7.0], [2.0, 2.0, 8.0, 9.0, 6.0, 2.0, 5.0, 9.0, 2.0, 2.0, 7.0, 3.0]]}, 'source': 0, 'target': 8}","[0, 3, 4, 7, 8]",88.0,"{'problem_type': 'QSPP', 'num_nodes': 9, 'num_edges': 12, 'nodes': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I'], 'source': 'A', 'target': 'I', 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 9.0}, {'var_index': 1, 'linear_cost': 4.0}, {'var_index': 2, 'linear_cost': 7.0}, {'var_index': 3, 'linear_cost': 7.0}, {'var_index': 4, 'linear_cost': 7.0}, {'var_index': 5, 'linear_cost': 8.0}, {'var_index': 6, 'linear_cost': 8.0}, {'var_index': 7, 'linear_cost': 5.0}, {'var_index': 8, 'linear_cost': 7.0}, {'var_index': 9, 'linear_cost': 3.0}, {'var_index': 10, 'linear_cost': 8.0}, {'var_index': 11, 'linear_cost': 2.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 9, 'quadratic_cost': 1.0}, {'var_i': 1, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 6, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 7, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 8, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 8, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 8, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 8, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 9, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 9, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 9, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 9, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 9, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 9, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 9, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 10, 'quadratic_cost': 9.0}, {'var_i': 9, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 10, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 10, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 10, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 10, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 10, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 10, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 10, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 11, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 11, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 11, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 11, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 11, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 11, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 11, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 11, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 11, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 11, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 11, 'var_j': 11, 'quadratic_cost': 3.0}]}, 'edges': [{'from': 'A', 'to': 'B', 'var_index': 0}, {'from': 'A', 'to': 'D', 'var_index': 1}, {'from': 'B', 'to': 'C', 'var_index': 2}, {'from': 'B', 'to': 'E', 'var_index': 3}, {'from': 'C', 'to': 'F', 'var_index': 4}, {'from': 'D', 'to': 'E', 'var_index': 5}, {'from': 'D', 'to': 'G', 'var_index': 6}, {'from': 'E', 'to': 'F', 'var_index': 7}, {'from': 'E', 'to': 'H', 'var_index': 8}, {'from': 'F', 'to': 'I', 'var_index': 9}, {'from': 'G', 'to': 'H', 'var_index': 10}, {'from': 'H', 'to': 'I', 'var_index': 11}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E', 5: 'F', 6: 'G', 7: 'H', 8: 'I'}}","['A', 'D', 'E', 'H', 'I']",45,markdown_table,names
QSPP,QSPP,"Someone suggested a walking route challenge: start at the square, finish at the viewpoint, obey all one-way signs, and try to make the whole walk as easy as possible. The task is to select exactly one legal route from start to finish and list the sequence of places visited in order. The way to tell which route is better is simple in practice — add up the base tiredness for every leg of the trip, and then add any extra discomfort that comes from particular pairs of legs being combined (certain legs even add a tiny extra cost by themselves). The full map and the specific costs are shown below.

# total_places=9
# total_directed_legs=8
# place_ids=1, 2, 3, 4, 5, 6, 7, 8, 9
# start_square=8
# end_viewpoint=9

leg_from_place,leg_to_place,leg_identifier
8,1,0
7,9,1
1,2,2
2,3,3
3,4,4
4,5,5
5,6,6
6,7,7

leg_id_ref,base_fatigue
0,2.0
1,4.0
2,4.0
3,5.0
4,2.0
5,4.0
6,10.0
7,5.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (first_leg_id_ref, second_leg_id_ref). If two leg_identifiers with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| first_leg_id_ref\second_leg_id_ref | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|---|
| 0 | 5.0 | 6.0 | 7.0 | 10.0 | 2.0 | 4.0 | 6.0 | 7.0 |
| 1 | 6.0 | 3.0 | 3.0 | 6.0 | 2.0 | 3.0 | 8.0 | 6.0 |
| 2 | 7.0 | 3.0 | 8.0 | 8.0 | 10.0 | 6.0 | 7.0 | 2.0 |
| 3 | 10.0 | 6.0 | 8.0 | 9.0 | 6.0 | 8.0 | 9.0 | 5.0 |
| 4 | 2.0 | 2.0 | 10.0 | 6.0 | 10.0 | 10.0 | 6.0 | 5.0 |
| 5 | 4.0 | 3.0 | 6.0 | 8.0 | 10.0 | 1.0 | 7.0 | 4.0 |
| 6 | 6.0 | 8.0 | 7.0 | 9.0 | 6.0 | 7.0 | 9.0 | 9.0 |
| 7 | 7.0 | 6.0 | 2.0 | 5.0 | 5.0 | 4.0 | 9.0 | 7.0 |

If you're ready to give the route, just drop the sequence of places into this tiny JSON snippet and send it back — nice and simple:

{
  ""solution"": []
}

Think of ""solution"" as the field where you list the walk: a straight sequence of node names from the square (start) to the viewpoint (finish). Keep it informal — it's just a little form to fill in, not a technical report. This JSON is only a sketch of the shape I expect, so replace the empty list with the actual ordered nodes you choose.

Please make sure you use the node identifiers exactly as they appear in the instance input — don't rename them or invent new ones. 
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8], 'edges': [{'from': 7, 'to': 0, 'var_index': 0}, {'from': 6, 'to': 8, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 4, 'to': 5, 'var_index': 6}, {'from': 5, 'to': 6, 'var_index': 7}], 'objective': {'constant': 0.0, 'linear': [2.0, 4.0, 4.0, 5.0, 2.0, 4.0, 10.0, 5.0], 'quadratic': [[5.0, 6.0, 7.0, 10.0, 2.0, 4.0, 6.0, 7.0], [6.0, 3.0, 3.0, 6.0, 2.0, 3.0, 8.0, 6.0], [7.0, 3.0, 8.0, 8.0, 10.0, 6.0, 7.0, 2.0], [10.0, 6.0, 8.0, 9.0, 6.0, 8.0, 9.0, 5.0], [2.0, 2.0, 10.0, 6.0, 10.0, 10.0, 6.0, 5.0], [4.0, 3.0, 6.0, 8.0, 10.0, 1.0, 7.0, 4.0], [6.0, 8.0, 7.0, 9.0, 6.0, 7.0, 9.0, 9.0], [7.0, 6.0, 2.0, 5.0, 5.0, 4.0, 9.0, 7.0]]}, 'source': 7, 'target': 8}","[7, 0, 1, 2, 3, 4, 5, 6, 8]",432.0,"{'problem_type': 'QSPP', 'num_nodes': 9, 'num_edges': 8, 'nodes': [1, 2, 3, 4, 5, 6, 7, 8, 9], 'source': 8, 'target': 9, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 2.0}, {'var_index': 1, 'linear_cost': 4.0}, {'var_index': 2, 'linear_cost': 4.0}, {'var_index': 3, 'linear_cost': 5.0}, {'var_index': 4, 'linear_cost': 2.0}, {'var_index': 5, 'linear_cost': 4.0}, {'var_index': 6, 'linear_cost': 10.0}, {'var_index': 7, 'linear_cost': 5.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 7, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 7, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 7, 'var_j': 7, 'quadratic_cost': 7.0}]}, 'edges': [{'from': 8, 'to': 1, 'var_index': 0}, {'from': 7, 'to': 9, 'var_index': 1}, {'from': 1, 'to': 2, 'var_index': 2}, {'from': 2, 'to': 3, 'var_index': 3}, {'from': 3, 'to': 4, 'var_index': 4}, {'from': 4, 'to': 5, 'var_index': 5}, {'from': 5, 'to': 6, 'var_index': 6}, {'from': 6, 'to': 7, 'var_index': 7}], 'node_id_map': {0: 1, 1: 2, 2: 3, 3: 4, 4: 5, 5: 6, 6: 7, 7: 8, 8: 9}}","[8, 1, 2, 3, 4, 5, 6, 7, 9]",46,csv,1
QSPP,QSPP,"Many people on a busy set know the drill: choose one path to move the equipment from the storage area to the shooting area, and make sure it follows the one-way corridors. Each corridor has its own handling charge, a few have a built-in extra cost, and some corridor combinations create additional trouble if both are used — sometimes that trouble is different depending on the order. The practical rule is to pick a single continuous route, start at storage and finish at the set without splitting the move, and keep the total expense (the sum of all corridor charges and any pairwise extras) as low as you can. The exact diagram and price list are shown below.

# num_locations=8
# num_corridors=7
# location_ids=0, 1, 2, 3, 4, 5, 6, 7
# storage_location=6
# set_location=7

corridor_from,corridor_to,corridor_id
6,0,0
5,7,1
0,1,2
1,2,3
2,3,4
3,4,5
4,5,6

corridor_id,handling_charge
0,3.0
1,3.0
2,3.0
3,10.0
4,6.0
5,4.0
6,3.0

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (corridor_i_id, corridor_j_id). If two corridors with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| corridor_i_id\corridor_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| 0 | 9.0 | 9.0 | 2.0 | 4.0 | 5.0 | 1.0 | 9.0 |
| 1 | 9.0 | 8.0 | 2.0 | 10.0 | 6.0 | 9.0 | 8.0 |
| 2 | 2.0 | 2.0 | 10.0 | 3.0 | 6.0 | 1.0 | 8.0 |
| 3 | 4.0 | 10.0 | 3.0 | 10.0 | 7.0 | 8.0 | 10.0 |
| 4 | 5.0 | 6.0 | 6.0 | 7.0 | 8.0 | 2.0 | 2.0 |
| 5 | 1.0 | 9.0 | 1.0 | 8.0 | 2.0 | 6.0 | 6.0 |
| 6 | 9.0 | 8.0 | 8.0 | 10.0 | 2.0 | 6.0 | 2.0 |

You can just drop the path into a tiny JSON snippet when you're ready — keeps things tidy and easy to check. Here's the little shape I expect:

{
  ""solution"": []
}

Think of ""solution"" as the place where you'll list the chosen route as a simple array of node names, from the storage spot to the shooting area. It's just a sketch for the format — not the actual answer — so fill that array with the nodes in order when you submit the final route.

Please make sure to use the node identifiers exactly as they appear in the instance input — don't rename them or invent new labels.  
Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7], 'edges': [{'from': 6, 'to': 0, 'var_index': 0}, {'from': 5, 'to': 7, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 4, 'to': 5, 'var_index': 6}], 'objective': {'constant': 0.0, 'linear': [3.0, 3.0, 3.0, 10.0, 6.0, 4.0, 3.0], 'quadratic': [[9.0, 9.0, 2.0, 4.0, 5.0, 1.0, 9.0], [9.0, 8.0, 2.0, 10.0, 6.0, 9.0, 8.0], [2.0, 2.0, 10.0, 3.0, 6.0, 1.0, 8.0], [4.0, 10.0, 3.0, 10.0, 7.0, 8.0, 10.0], [5.0, 6.0, 6.0, 7.0, 8.0, 2.0, 2.0], [1.0, 9.0, 1.0, 8.0, 2.0, 6.0, 6.0], [9.0, 8.0, 8.0, 10.0, 2.0, 6.0, 2.0]]}, 'source': 6, 'target': 7}","[6, 0, 1, 2, 3, 4, 5, 7]",321.0,"{'problem_type': 'QSPP', 'num_nodes': 8, 'num_edges': 7, 'nodes': [0, 1, 2, 3, 4, 5, 6, 7], 'source': 6, 'target': 7, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 3.0}, {'var_index': 1, 'linear_cost': 3.0}, {'var_index': 2, 'linear_cost': 3.0}, {'var_index': 3, 'linear_cost': 10.0}, {'var_index': 4, 'linear_cost': 6.0}, {'var_index': 5, 'linear_cost': 4.0}, {'var_index': 6, 'linear_cost': 3.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 2.0}]}, 'edges': [{'from': 6, 'to': 0, 'var_index': 0}, {'from': 5, 'to': 7, 'var_index': 1}, {'from': 0, 'to': 1, 'var_index': 2}, {'from': 1, 'to': 2, 'var_index': 3}, {'from': 2, 'to': 3, 'var_index': 4}, {'from': 3, 'to': 4, 'var_index': 5}, {'from': 4, 'to': 5, 'var_index': 6}], 'node_id_map': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7}}","[6, 0, 1, 2, 3, 4, 5, 7]",47,csv,0
QSPP,QSPP,"We were in charge of picking one routed run from the main tank to the receiving tank, always following the one-way valves. The route had to be a single, uninterrupted chain of tank-to-tank hops that begins at the source and finishes at the destination. Every hop has a base cost, and certain combinations of hops add little extra fees only if both are part of the same run — some hops even add a self-fee when used. To evaluate any candidate run, add up each hop’s base cost and all the extra pairwise (and self) fees that apply; the best run is simply the one with the lowest total. The specific layout and cost figures are listed below.

{
  ""total_tanks"": 9,
  ""total_pipeline_segments"": 20,
  ""tank_ids_list"": [
    ""A"",
    ""B"",
    ""C"",
    ""D"",
    ""E"",
    ""F"",
    ""G"",
    ""H"",
    ""I""
  ],
  ""source_tank"": ""H"",
  ""receiving_tank"": ""I"",
  ""edges"": [
    {
      ""segment_from_tank"": ""H"",
      ""segment_to_tank"": ""A"",
      ""segment_id"": 0
    },
    {
      ""segment_from_tank"": ""H"",
      ""segment_to_tank"": ""B"",
      ""segment_id"": 1
    },
    {
      ""segment_from_tank"": ""H"",
      ""segment_to_tank"": ""C"",
      ""segment_id"": 2
    },
    {
      ""segment_from_tank"": ""H"",
      ""segment_to_tank"": ""D"",
      ""segment_id"": 3
    },
    {
      ""segment_from_tank"": ""H"",
      ""segment_to_tank"": ""E"",
      ""segment_id"": 4
    },
    {
      ""segment_from_tank"": ""H"",
      ""segment_to_tank"": ""F"",
      ""segment_id"": 5
    },
    {
      ""segment_from_tank"": ""H"",
      ""segment_to_tank"": ""G"",
      ""segment_id"": 6
    },
    {
      ""segment_from_tank"": ""A"",
      ""segment_to_tank"": ""I"",
      ""segment_id"": 7
    },
    {
      ""segment_from_tank"": ""B"",
      ""segment_to_tank"": ""I"",
      ""segment_id"": 8
    },
    {
      ""segment_from_tank"": ""C"",
      ""segment_to_tank"": ""I"",
      ""segment_id"": 9
    },
    {
      ""segment_from_tank"": ""D"",
      ""segment_to_tank"": ""I"",
      ""segment_id"": 10
    },
    {
      ""segment_from_tank"": ""E"",
      ""segment_to_tank"": ""I"",
      ""segment_id"": 11
    },
    {
      ""segment_from_tank"": ""F"",
      ""segment_to_tank"": ""I"",
      ""segment_id"": 12
    },
    {
      ""segment_from_tank"": ""G"",
      ""segment_to_tank"": ""I"",
      ""segment_id"": 13
    },
    {
      ""segment_from_tank"": ""A"",
      ""segment_to_tank"": ""B"",
      ""segment_id"": 14
    },
    {
      ""segment_from_tank"": ""B"",
      ""segment_to_tank"": ""C"",
      ""segment_id"": 15
    },
    {
      ""segment_from_tank"": ""C"",
      ""segment_to_tank"": ""D"",
      ""segment_id"": 16
    },
    {
      ""segment_from_tank"": ""D"",
      ""segment_to_tank"": ""E"",
      ""segment_id"": 17
    },
    {
      ""segment_from_tank"": ""E"",
      ""segment_to_tank"": ""F"",
      ""segment_id"": 18
    },
    {
      ""segment_from_tank"": ""F"",
      ""segment_to_tank"": ""G"",
      ""segment_id"": 19
    }
  ],
  ""linear_costs"": [
    {
      ""segment_id"": 0,
      ""base_transfer_cost"": 6.0
    },
    {
      ""segment_id"": 1,
      ""base_transfer_cost"": 6.0
    },
    {
      ""segment_id"": 2,
      ""base_transfer_cost"": 2.0
    },
    {
      ""segment_id"": 3,
      ""base_transfer_cost"": 6.0
    },
    {
      ""segment_id"": 4,
      ""base_transfer_cost"": 8.0
    },
    {
      ""segment_id"": 5,
      ""base_transfer_cost"": 6.0
    },
    {
      ""segment_id"": 6,
      ""base_transfer_cost"": 9.0
    },
    {
      ""segment_id"": 7,
      ""base_transfer_cost"": 6.0
    },
    {
      ""segment_id"": 8,
      ""base_transfer_cost"": 10.0
    },
    {
      ""segment_id"": 9,
      ""base_transfer_cost"": 1.0
    },
    {
      ""segment_id"": 10,
      ""base_transfer_cost"": 5.0
    },
    {
      ""segment_id"": 11,
      ""base_transfer_cost"": 4.0
    },
    {
      ""segment_id"": 12,
      ""base_transfer_cost"": 7.0
    },
    {
      ""segment_id"": 13,
      ""base_transfer_cost"": 3.0
    },
    {
      ""segment_id"": 14,
      ""base_transfer_cost"": 1.0
    },
    {
      ""segment_id"": 15,
      ""base_transfer_cost"": 7.0
    },
    {
      ""segment_id"": 16,
      ""base_transfer_cost"": 5.0
    },
    {
      ""segment_id"": 17,
      ""base_transfer_cost"": 3.0
    },
    {
      ""segment_id"": 18,
      ""base_transfer_cost"": 9.0
    },
    {
      ""segment_id"": 19,
      ""base_transfer_cost"": 8.0
    }
  ]
}

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (segment_i_id, segment_j_id). If two segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| segment_i_id\segment_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 6.0 | 2.0 | 7.0 | 1.0 | 8.0 | 7.0 | 2.0 | 7.0 | 10.0 | 5.0 | 6.0 | 5.0 | 2.0 | 6.0 | 5.0 | 8.0 | 2.0 | 10.0 | 1.0 | 5.0 |
| 1 | 2.0 | 8.0 | 1.0 | 6.0 | 7.0 | 8.0 | 6.0 | 3.0 | 10.0 | 3.0 | 2.0 | 6.0 | 2.0 | 9.0 | 5.0 | 10.0 | 9.0 | 3.0 | 1.0 | 1.0 |
| 2 | 7.0 | 1.0 | 1.0 | 3.0 | 2.0 | 10.0 | 9.0 | 5.0 | 9.0 | 2.0 | 8.0 | 9.0 | 6.0 | 10.0 | 1.0 | 1.0 | 10.0 | 3.0 | 1.0 | 6.0 |
| 3 | 1.0 | 6.0 | 3.0 | 10.0 | 4.0 | 4.0 | 8.0 | 1.0 | 5.0 | 9.0 | 10.0 | 2.0 | 9.0 | 4.0 | 6.0 | 2.0 | 10.0 | 8.0 | 9.0 | 6.0 |
| 4 | 8.0 | 7.0 | 2.0 | 4.0 | 8.0 | 6.0 | 5.0 | 7.0 | 1.0 | 10.0 | 9.0 | 7.0 | 4.0 | 2.0 | 7.0 | 3.0 | 1.0 | 2.0 | 1.0 | 1.0 |
| 5 | 7.0 | 8.0 | 10.0 | 4.0 | 6.0 | 1.0 | 1.0 | 1.0 | 8.0 | 6.0 | 10.0 | 5.0 | 2.0 | 2.0 | 10.0 | 5.0 | 4.0 | 5.0 | 1.0 | 10.0 |
| 6 | 2.0 | 6.0 | 9.0 | 8.0 | 5.0 | 1.0 | 4.0 | 7.0 | 7.0 | 3.0 | 9.0 | 1.0 | 3.0 | 1.0 | 4.0 | 9.0 | 1.0 | 6.0 | 7.0 | 1.0 |
| 7 | 7.0 | 3.0 | 5.0 | 1.0 | 7.0 | 1.0 | 7.0 | 8.0 | 8.0 | 3.0 | 7.0 | 10.0 | 10.0 | 6.0 | 4.0 | 1.0 | 10.0 | 6.0 | 1.0 | 2.0 |
| 8 | 10.0 | 10.0 | 9.0 | 5.0 | 1.0 | 8.0 | 7.0 | 8.0 | 1.0 | 4.0 | 6.0 | 8.0 | 8.0 | 6.0 | 6.0 | 8.0 | 1.0 | 6.0 | 6.0 | 5.0 |
| 9 | 5.0 | 3.0 | 2.0 | 9.0 | 10.0 | 6.0 | 3.0 | 3.0 | 4.0 | 10.0 | 8.0 | 4.0 | 9.0 | 7.0 | 5.0 | 7.0 | 5.0 | 9.0 | 8.0 | 3.0 |
| 10 | 6.0 | 2.0 | 8.0 | 10.0 | 9.0 | 10.0 | 9.0 | 7.0 | 6.0 | 8.0 | 1.0 | 8.0 | 5.0 | 5.0 | 6.0 | 8.0 | 10.0 | 1.0 | 8.0 | 2.0 |
| 11 | 5.0 | 6.0 | 9.0 | 2.0 | 7.0 | 5.0 | 1.0 | 10.0 | 8.0 | 4.0 | 8.0 | 5.0 | 8.0 | 7.0 | 5.0 | 9.0 | 3.0 | 3.0 | 6.0 | 10.0 |
| 12 | 2.0 | 2.0 | 6.0 | 9.0 | 4.0 | 2.0 | 3.0 | 10.0 | 8.0 | 9.0 | 5.0 | 8.0 | 9.0 | 3.0 | 3.0 | 9.0 | 6.0 | 7.0 | 2.0 | 3.0 |
| 13 | 6.0 | 9.0 | 10.0 | 4.0 | 2.0 | 2.0 | 1.0 | 6.0 | 6.0 | 7.0 | 5.0 | 7.0 | 3.0 | 5.0 | 7.0 | 3.0 | 5.0 | 10.0 | 7.0 | 4.0 |
| 14 | 5.0 | 5.0 | 1.0 | 6.0 | 7.0 | 10.0 | 4.0 | 4.0 | 6.0 | 5.0 | 6.0 | 5.0 | 3.0 | 7.0 | 4.0 | 7.0 | 8.0 | 10.0 | 9.0 | 9.0 |
| 15 | 8.0 | 10.0 | 1.0 | 2.0 | 3.0 | 5.0 | 9.0 | 1.0 | 8.0 | 7.0 | 8.0 | 9.0 | 9.0 | 3.0 | 7.0 | 3.0 | 7.0 | 4.0 | 8.0 | 8.0 |
| 16 | 2.0 | 9.0 | 10.0 | 10.0 | 1.0 | 4.0 | 1.0 | 10.0 | 1.0 | 5.0 | 10.0 | 3.0 | 6.0 | 5.0 | 8.0 | 7.0 | 4.0 | 10.0 | 9.0 | 2.0 |
| 17 | 10.0 | 3.0 | 3.0 | 8.0 | 2.0 | 5.0 | 6.0 | 6.0 | 6.0 | 9.0 | 1.0 | 3.0 | 7.0 | 10.0 | 10.0 | 4.0 | 10.0 | 7.0 | 2.0 | 9.0 |
| 18 | 1.0 | 1.0 | 1.0 | 9.0 | 1.0 | 1.0 | 7.0 | 1.0 | 6.0 | 8.0 | 8.0 | 6.0 | 2.0 | 7.0 | 9.0 | 8.0 | 9.0 | 2.0 | 8.0 | 5.0 |
| 19 | 5.0 | 1.0 | 6.0 | 6.0 | 1.0 | 10.0 | 1.0 | 2.0 | 5.0 | 3.0 | 2.0 | 10.0 | 3.0 | 4.0 | 9.0 | 8.0 | 2.0 | 9.0 | 5.0 | 1.0 |

Oh, and when you send back the chosen route, please put it in a tiny JSON snippet so it's easy to parse. Something casual like this will do:

{
  ""solution"": []
}

Think of ""solution"" as the place where you list the tanks (node names) in order from the starting tank to the receiving tank — just the node identifiers, nothing else (no hop/edge IDs, no costs). This JSON is just a sketch of the shape I expect, not the actual run.

Please use the exact node identifiers from the instance input — don't rename them or invent new labels. 
for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8], 'edges': [{'from': 7, 'to': 0, 'var_index': 0}, {'from': 7, 'to': 1, 'var_index': 1}, {'from': 7, 'to': 2, 'var_index': 2}, {'from': 7, 'to': 3, 'var_index': 3}, {'from': 7, 'to': 4, 'var_index': 4}, {'from': 7, 'to': 5, 'var_index': 5}, {'from': 7, 'to': 6, 'var_index': 6}, {'from': 0, 'to': 8, 'var_index': 7}, {'from': 1, 'to': 8, 'var_index': 8}, {'from': 2, 'to': 8, 'var_index': 9}, {'from': 3, 'to': 8, 'var_index': 10}, {'from': 4, 'to': 8, 'var_index': 11}, {'from': 5, 'to': 8, 'var_index': 12}, {'from': 6, 'to': 8, 'var_index': 13}, {'from': 0, 'to': 1, 'var_index': 14}, {'from': 1, 'to': 2, 'var_index': 15}, {'from': 2, 'to': 3, 'var_index': 16}, {'from': 3, 'to': 4, 'var_index': 17}, {'from': 4, 'to': 5, 'var_index': 18}, {'from': 5, 'to': 6, 'var_index': 19}], 'objective': {'constant': 0.0, 'linear': [6.0, 6.0, 2.0, 6.0, 8.0, 6.0, 9.0, 6.0, 10.0, 1.0, 5.0, 4.0, 7.0, 3.0, 1.0, 7.0, 5.0, 3.0, 9.0, 8.0], 'quadratic': [[6.0, 2.0, 7.0, 1.0, 8.0, 7.0, 2.0, 7.0, 10.0, 5.0, 6.0, 5.0, 2.0, 6.0, 5.0, 8.0, 2.0, 10.0, 1.0, 5.0], [2.0, 8.0, 1.0, 6.0, 7.0, 8.0, 6.0, 3.0, 10.0, 3.0, 2.0, 6.0, 2.0, 9.0, 5.0, 10.0, 9.0, 3.0, 1.0, 1.0], [7.0, 1.0, 1.0, 3.0, 2.0, 10.0, 9.0, 5.0, 9.0, 2.0, 8.0, 9.0, 6.0, 10.0, 1.0, 1.0, 10.0, 3.0, 1.0, 6.0], [1.0, 6.0, 3.0, 10.0, 4.0, 4.0, 8.0, 1.0, 5.0, 9.0, 10.0, 2.0, 9.0, 4.0, 6.0, 2.0, 10.0, 8.0, 9.0, 6.0], [8.0, 7.0, 2.0, 4.0, 8.0, 6.0, 5.0, 7.0, 1.0, 10.0, 9.0, 7.0, 4.0, 2.0, 7.0, 3.0, 1.0, 2.0, 1.0, 1.0], [7.0, 8.0, 10.0, 4.0, 6.0, 1.0, 1.0, 1.0, 8.0, 6.0, 10.0, 5.0, 2.0, 2.0, 10.0, 5.0, 4.0, 5.0, 1.0, 10.0], [2.0, 6.0, 9.0, 8.0, 5.0, 1.0, 4.0, 7.0, 7.0, 3.0, 9.0, 1.0, 3.0, 1.0, 4.0, 9.0, 1.0, 6.0, 7.0, 1.0], [7.0, 3.0, 5.0, 1.0, 7.0, 1.0, 7.0, 8.0, 8.0, 3.0, 7.0, 10.0, 10.0, 6.0, 4.0, 1.0, 10.0, 6.0, 1.0, 2.0], [10.0, 10.0, 9.0, 5.0, 1.0, 8.0, 7.0, 8.0, 1.0, 4.0, 6.0, 8.0, 8.0, 6.0, 6.0, 8.0, 1.0, 6.0, 6.0, 5.0], [5.0, 3.0, 2.0, 9.0, 10.0, 6.0, 3.0, 3.0, 4.0, 10.0, 8.0, 4.0, 9.0, 7.0, 5.0, 7.0, 5.0, 9.0, 8.0, 3.0], [6.0, 2.0, 8.0, 10.0, 9.0, 10.0, 9.0, 7.0, 6.0, 8.0, 1.0, 8.0, 5.0, 5.0, 6.0, 8.0, 10.0, 1.0, 8.0, 2.0], [5.0, 6.0, 9.0, 2.0, 7.0, 5.0, 1.0, 10.0, 8.0, 4.0, 8.0, 5.0, 8.0, 7.0, 5.0, 9.0, 3.0, 3.0, 6.0, 10.0], [2.0, 2.0, 6.0, 9.0, 4.0, 2.0, 3.0, 10.0, 8.0, 9.0, 5.0, 8.0, 9.0, 3.0, 3.0, 9.0, 6.0, 7.0, 2.0, 3.0], [6.0, 9.0, 10.0, 4.0, 2.0, 2.0, 1.0, 6.0, 6.0, 7.0, 5.0, 7.0, 3.0, 5.0, 7.0, 3.0, 5.0, 10.0, 7.0, 4.0], [5.0, 5.0, 1.0, 6.0, 7.0, 10.0, 4.0, 4.0, 6.0, 5.0, 6.0, 5.0, 3.0, 7.0, 4.0, 7.0, 8.0, 10.0, 9.0, 9.0], [8.0, 10.0, 1.0, 2.0, 3.0, 5.0, 9.0, 1.0, 8.0, 7.0, 8.0, 9.0, 9.0, 3.0, 7.0, 3.0, 7.0, 4.0, 8.0, 8.0], [2.0, 9.0, 10.0, 10.0, 1.0, 4.0, 1.0, 10.0, 1.0, 5.0, 10.0, 3.0, 6.0, 5.0, 8.0, 7.0, 4.0, 10.0, 9.0, 2.0], [10.0, 3.0, 3.0, 8.0, 2.0, 5.0, 6.0, 6.0, 6.0, 9.0, 1.0, 3.0, 7.0, 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{'var_i': 11, 'var_j': 14, 'quadratic_cost': 5.0}, {'var_i': 11, 'var_j': 15, 'quadratic_cost': 9.0}, {'var_i': 11, 'var_j': 16, 'quadratic_cost': 3.0}, {'var_i': 11, 'var_j': 17, 'quadratic_cost': 3.0}, {'var_i': 11, 'var_j': 18, 'quadratic_cost': 6.0}, {'var_i': 11, 'var_j': 19, 'quadratic_cost': 10.0}, {'var_i': 12, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 12, 'var_j': 1, 'quadratic_cost': 2.0}, {'var_i': 12, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 12, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 12, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 12, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 12, 'var_j': 6, 'quadratic_cost': 3.0}, {'var_i': 12, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 12, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 12, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 12, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 12, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 12, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 12, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 12, 'var_j': 14, 'quadratic_cost': 3.0}, {'var_i': 12, 'var_j': 15, 'quadratic_cost': 9.0}, {'var_i': 12, 'var_j': 16, 'quadratic_cost': 6.0}, {'var_i': 12, 'var_j': 17, 'quadratic_cost': 7.0}, {'var_i': 12, 'var_j': 18, 'quadratic_cost': 2.0}, {'var_i': 12, 'var_j': 19, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 13, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 13, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 13, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 13, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 13, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 13, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 13, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 13, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 13, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 13, 'var_j': 10, 'quadratic_cost': 5.0}, {'var_i': 13, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 13, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 13, 'quadratic_cost': 5.0}, {'var_i': 13, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 13, 'var_j': 15, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 16, 'quadratic_cost': 5.0}, {'var_i': 13, 'var_j': 17, 'quadratic_cost': 10.0}, {'var_i': 13, 'var_j': 18, 'quadratic_cost': 7.0}, {'var_i': 13, 'var_j': 19, 'quadratic_cost': 4.0}, {'var_i': 14, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 14, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 14, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 14, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 14, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 14, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 14, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 14, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 14, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 14, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 14, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 14, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 14, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 14, 'var_j': 13, 'quadratic_cost': 7.0}, {'var_i': 14, 'var_j': 14, 'quadratic_cost': 4.0}, {'var_i': 14, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 14, 'var_j': 16, 'quadratic_cost': 8.0}, {'var_i': 14, 'var_j': 17, 'quadratic_cost': 10.0}, {'var_i': 14, 'var_j': 18, 'quadratic_cost': 9.0}, {'var_i': 14, 'var_j': 19, 'quadratic_cost': 9.0}, {'var_i': 15, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 15, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 15, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 15, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 15, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 15, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 15, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 15, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 9, 'quadratic_cost': 7.0}, {'var_i': 15, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 15, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 15, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 15, 'var_j': 14, 'quadratic_cost': 7.0}, {'var_i': 15, 'var_j': 15, 'quadratic_cost': 3.0}, {'var_i': 15, 'var_j': 16, 'quadratic_cost': 7.0}, {'var_i': 15, 'var_j': 17, 'quadratic_cost': 4.0}, {'var_i': 15, 'var_j': 18, 'quadratic_cost': 8.0}, {'var_i': 15, 'var_j': 19, 'quadratic_cost': 8.0}, {'var_i': 16, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 16, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 16, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 16, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 16, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 16, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 16, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 16, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 16, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 16, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 16, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 16, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 16, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 16, 'var_j': 13, 'quadratic_cost': 5.0}, {'var_i': 16, 'var_j': 14, 'quadratic_cost': 8.0}, {'var_i': 16, 'var_j': 15, 'quadratic_cost': 7.0}, {'var_i': 16, 'var_j': 16, 'quadratic_cost': 4.0}, {'var_i': 16, 'var_j': 17, 'quadratic_cost': 10.0}, {'var_i': 16, 'var_j': 18, 'quadratic_cost': 9.0}, {'var_i': 16, 'var_j': 19, 'quadratic_cost': 2.0}, {'var_i': 17, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 17, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 17, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 17, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 17, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 17, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 17, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 17, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 17, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 17, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 17, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 17, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 17, 'var_j': 12, 'quadratic_cost': 7.0}, {'var_i': 17, 'var_j': 13, 'quadratic_cost': 10.0}, {'var_i': 17, 'var_j': 14, 'quadratic_cost': 10.0}, {'var_i': 17, 'var_j': 15, 'quadratic_cost': 4.0}, {'var_i': 17, 'var_j': 16, 'quadratic_cost': 10.0}, {'var_i': 17, 'var_j': 17, 'quadratic_cost': 7.0}, {'var_i': 17, 'var_j': 18, 'quadratic_cost': 2.0}, {'var_i': 17, 'var_j': 19, 'quadratic_cost': 9.0}, {'var_i': 18, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 18, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 18, 'var_j': 2, 'quadratic_cost': 1.0}, {'var_i': 18, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 18, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 18, 'var_j': 5, 'quadratic_cost': 1.0}, {'var_i': 18, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 18, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 18, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 18, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 18, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 18, 'var_j': 11, 'quadratic_cost': 6.0}, {'var_i': 18, 'var_j': 12, 'quadratic_cost': 2.0}, {'var_i': 18, 'var_j': 13, 'quadratic_cost': 7.0}, {'var_i': 18, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 18, 'var_j': 15, 'quadratic_cost': 8.0}, {'var_i': 18, 'var_j': 16, 'quadratic_cost': 9.0}, {'var_i': 18, 'var_j': 17, 'quadratic_cost': 2.0}, {'var_i': 18, 'var_j': 18, 'quadratic_cost': 8.0}, {'var_i': 18, 'var_j': 19, 'quadratic_cost': 5.0}, {'var_i': 19, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 19, 'var_j': 1, 'quadratic_cost': 1.0}, {'var_i': 19, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 19, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 19, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 19, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 19, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 19, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 19, 'var_j': 8, 'quadratic_cost': 5.0}, {'var_i': 19, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 19, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 19, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 19, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 19, 'var_j': 13, 'quadratic_cost': 4.0}, {'var_i': 19, 'var_j': 14, 'quadratic_cost': 9.0}, {'var_i': 19, 'var_j': 15, 'quadratic_cost': 8.0}, {'var_i': 19, 'var_j': 16, 'quadratic_cost': 2.0}, {'var_i': 19, 'var_j': 17, 'quadratic_cost': 9.0}, {'var_i': 19, 'var_j': 18, 'quadratic_cost': 5.0}, {'var_i': 19, 'var_j': 19, 'quadratic_cost': 1.0}]}, 'edges': [{'from': 'H', 'to': 'A', 'var_index': 0}, {'from': 'H', 'to': 'B', 'var_index': 1}, {'from': 'H', 'to': 'C', 'var_index': 2}, {'from': 'H', 'to': 'D', 'var_index': 3}, {'from': 'H', 'to': 'E', 'var_index': 4}, {'from': 'H', 'to': 'F', 'var_index': 5}, {'from': 'H', 'to': 'G', 'var_index': 6}, {'from': 'A', 'to': 'I', 'var_index': 7}, {'from': 'B', 'to': 'I', 'var_index': 8}, {'from': 'C', 'to': 'I', 'var_index': 9}, {'from': 'D', 'to': 'I', 'var_index': 10}, {'from': 'E', 'to': 'I', 'var_index': 11}, {'from': 'F', 'to': 'I', 'var_index': 12}, {'from': 'G', 'to': 'I', 'var_index': 13}, {'from': 'A', 'to': 'B', 'var_index': 14}, {'from': 'B', 'to': 'C', 'var_index': 15}, {'from': 'C', 'to': 'D', 'var_index': 16}, {'from': 'D', 'to': 'E', 'var_index': 17}, {'from': 'E', 'to': 'F', 'var_index': 18}, {'from': 'F', 'to': 'G', 'var_index': 19}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E', 5: 'F', 6: 'G', 7: 'H', 8: 'I'}}","['H', 'C', 'I']",48,json,names
QSPP,QSPP,"Out in the yard a gardener must pick one single line of hoses and valves from the water source to the flower bed, walking the water along only the allowed one‑way connections. The route needs to be continuous — a clear start at the source and a clear finish at the bed, using existing links and not leaving out or repeating segments. Each link has a basic upkeep cost, and some links also interact: using a particular link might add its own extra cost, and certain pairs of links together trigger additional charges that can depend on which comes first. To choose, total up the upkeep for every used link and then add any extra charges for every pair of links that are both in the route; the route with the lowest overall total is the goal. The exact network and cost details are listed below.

{
  ""total_locations"": 10,
  ""total_segments"": 14,
  ""locations_list"": [
    ""A"",
    ""B"",
    ""C"",
    ""D"",
    ""E"",
    ""F"",
    ""G"",
    ""H"",
    ""I"",
    ""J""
  ],
  ""water_supply_location"": ""I"",
  ""flower_bed_location"": ""J"",
  ""edges"": [
    {
      ""segment_start_location"": ""I"",
      ""segment_end_location"": ""A"",
      ""segment_id"": 0
    },
    {
      ""segment_start_location"": ""I"",
      ""segment_end_location"": ""E"",
      ""segment_id"": 1
    },
    {
      ""segment_start_location"": ""D"",
      ""segment_end_location"": ""J"",
      ""segment_id"": 2
    },
    {
      ""segment_start_location"": ""H"",
      ""segment_end_location"": ""J"",
      ""segment_id"": 3
    },
    {
      ""segment_start_location"": ""A"",
      ""segment_end_location"": ""B"",
      ""segment_id"": 4
    },
    {
      ""segment_start_location"": ""A"",
      ""segment_end_location"": ""E"",
      ""segment_id"": 5
    },
    {
      ""segment_start_location"": ""B"",
      ""segment_end_location"": ""C"",
      ""segment_id"": 6
    },
    {
      ""segment_start_location"": ""B"",
      ""segment_end_location"": ""F"",
      ""segment_id"": 7
    },
    {
      ""segment_start_location"": ""C"",
      ""segment_end_location"": ""D"",
      ""segment_id"": 8
    },
    {
      ""segment_start_location"": ""C"",
      ""segment_end_location"": ""G"",
      ""segment_id"": 9
    },
    {
      ""segment_start_location"": ""D"",
      ""segment_end_location"": ""H"",
      ""segment_id"": 10
    },
    {
      ""segment_start_location"": ""E"",
      ""segment_end_location"": ""F"",
      ""segment_id"": 11
    },
    {
      ""segment_start_location"": ""F"",
      ""segment_end_location"": ""G"",
      ""segment_id"": 12
    },
    {
      ""segment_start_location"": ""G"",
      ""segment_end_location"": ""H"",
      ""segment_id"": 13
    }
  ],
  ""linear_costs"": [
    {
      ""segment_id"": 0,
      ""maintenance_cost"": 9.0
    },
    {
      ""segment_id"": 1,
      ""maintenance_cost"": 1.0
    },
    {
      ""segment_id"": 2,
      ""maintenance_cost"": 3.0
    },
    {
      ""segment_id"": 3,
      ""maintenance_cost"": 9.0
    },
    {
      ""segment_id"": 4,
      ""maintenance_cost"": 6.0
    },
    {
      ""segment_id"": 5,
      ""maintenance_cost"": 6.0
    },
    {
      ""segment_id"": 6,
      ""maintenance_cost"": 6.0
    },
    {
      ""segment_id"": 7,
      ""maintenance_cost"": 9.0
    },
    {
      ""segment_id"": 8,
      ""maintenance_cost"": 7.0
    },
    {
      ""segment_id"": 9,
      ""maintenance_cost"": 4.0
    },
    {
      ""segment_id"": 10,
      ""maintenance_cost"": 5.0
    },
    {
      ""segment_id"": 11,
      ""maintenance_cost"": 2.0
    },
    {
      ""segment_id"": 12,
      ""maintenance_cost"": 6.0
    },
    {
      ""segment_id"": 13,
      ""maintenance_cost"": 10.0
    }
  ]
}

# Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (segment_i_id, segment_j_id). If two segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
# quadratic_costs
| segment_i_id\segment_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 10.0 | 4.0 | 10.0 | 6.0 | 5.0 | 3.0 | 9.0 | 6.0 | 1.0 | 10.0 | 7.0 | 9.0 | 2.0 | 4.0 |
| 1 | 4.0 | 7.0 | 4.0 | 5.0 | 6.0 | 4.0 | 7.0 | 3.0 | 9.0 | 8.0 | 8.0 | 5.0 | 5.0 | 8.0 |
| 2 | 10.0 | 4.0 | 5.0 | 7.0 | 3.0 | 7.0 | 2.0 | 5.0 | 3.0 | 5.0 | 8.0 | 8.0 | 8.0 | 5.0 |
| 3 | 6.0 | 5.0 | 7.0 | 1.0 | 9.0 | 2.0 | 8.0 | 1.0 | 6.0 | 3.0 | 2.0 | 7.0 | 6.0 | 8.0 |
| 4 | 5.0 | 6.0 | 3.0 | 9.0 | 10.0 | 9.0 | 9.0 | 6.0 | 7.0 | 2.0 | 4.0 | 10.0 | 9.0 | 1.0 |
| 5 | 3.0 | 4.0 | 7.0 | 2.0 | 9.0 | 10.0 | 7.0 | 7.0 | 4.0 | 8.0 | 2.0 | 2.0 | 8.0 | 6.0 |
| 6 | 9.0 | 7.0 | 2.0 | 8.0 | 9.0 | 7.0 | 6.0 | 10.0 | 6.0 | 5.0 | 1.0 | 7.0 | 8.0 | 5.0 |
| 7 | 6.0 | 3.0 | 5.0 | 1.0 | 6.0 | 7.0 | 10.0 | 5.0 | 3.0 | 4.0 | 8.0 | 2.0 | 9.0 | 6.0 |
| 8 | 1.0 | 9.0 | 3.0 | 6.0 | 7.0 | 4.0 | 6.0 | 3.0 | 8.0 | 6.0 | 8.0 | 2.0 | 10.0 | 8.0 |
| 9 | 10.0 | 8.0 | 5.0 | 3.0 | 2.0 | 8.0 | 5.0 | 4.0 | 6.0 | 8.0 | 4.0 | 9.0 | 3.0 | 8.0 |
| 10 | 7.0 | 8.0 | 8.0 | 2.0 | 4.0 | 2.0 | 1.0 | 8.0 | 8.0 | 4.0 | 6.0 | 8.0 | 10.0 | 4.0 |
| 11 | 9.0 | 5.0 | 8.0 | 7.0 | 10.0 | 2.0 | 7.0 | 2.0 | 2.0 | 9.0 | 8.0 | 5.0 | 4.0 | 3.0 |
| 12 | 2.0 | 5.0 | 8.0 | 6.0 | 9.0 | 8.0 | 8.0 | 9.0 | 10.0 | 3.0 | 10.0 | 4.0 | 5.0 | 2.0 |
| 13 | 4.0 | 8.0 | 5.0 | 8.0 | 1.0 | 6.0 | 5.0 | 6.0 | 8.0 | 8.0 | 4.0 | 3.0 | 2.0 | 3.0 |

If it helps, when you send back your chosen route just put it into this little JSON layout so it's easy to pick up programmatically — nothing fancy, just the shape below.

{
  ""solution"": []
}

Think of ""solution"" as the spot where you'll drop the sequence of node names that form the path from the water source to the flower bed (a simple list like [""Source"",""X"",""Y"",""Bed""] — just as an example sketch). This JSON is just a template showing the expected shape; it's not the actual answer yet.

Also a quick reminder: use the exact node identifiers given in the instance, do not rename them or invent new labels — they must match character-for-character.  
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.""","{'nodes': [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], 'edges': [{'from': 8, 'to': 0, 'var_index': 0}, {'from': 8, 'to': 4, 'var_index': 1}, {'from': 3, 'to': 9, 'var_index': 2}, {'from': 7, 'to': 9, 'var_index': 3}, {'from': 0, 'to': 1, 'var_index': 4}, {'from': 0, 'to': 4, 'var_index': 5}, {'from': 1, 'to': 2, 'var_index': 6}, {'from': 1, 'to': 5, 'var_index': 7}, {'from': 2, 'to': 3, 'var_index': 8}, {'from': 2, 'to': 6, 'var_index': 9}, {'from': 3, 'to': 7, 'var_index': 10}, {'from': 4, 'to': 5, 'var_index': 11}, {'from': 5, 'to': 6, 'var_index': 12}, {'from': 6, 'to': 7, 'var_index': 13}], 'objective': {'constant': 0.0, 'linear': [9.0, 1.0, 3.0, 9.0, 6.0, 6.0, 6.0, 9.0, 7.0, 4.0, 5.0, 2.0, 6.0, 10.0], 'quadratic': [[10.0, 4.0, 10.0, 6.0, 5.0, 3.0, 9.0, 6.0, 1.0, 10.0, 7.0, 9.0, 2.0, 4.0], [4.0, 7.0, 4.0, 5.0, 6.0, 4.0, 7.0, 3.0, 9.0, 8.0, 8.0, 5.0, 5.0, 8.0], [10.0, 4.0, 5.0, 7.0, 3.0, 7.0, 2.0, 5.0, 3.0, 5.0, 8.0, 8.0, 8.0, 5.0], [6.0, 5.0, 7.0, 1.0, 9.0, 2.0, 8.0, 1.0, 6.0, 3.0, 2.0, 7.0, 6.0, 8.0], [5.0, 6.0, 3.0, 9.0, 10.0, 9.0, 9.0, 6.0, 7.0, 2.0, 4.0, 10.0, 9.0, 1.0], [3.0, 4.0, 7.0, 2.0, 9.0, 10.0, 7.0, 7.0, 4.0, 8.0, 2.0, 2.0, 8.0, 6.0], [9.0, 7.0, 2.0, 8.0, 9.0, 7.0, 6.0, 10.0, 6.0, 5.0, 1.0, 7.0, 8.0, 5.0], [6.0, 3.0, 5.0, 1.0, 6.0, 7.0, 10.0, 5.0, 3.0, 4.0, 8.0, 2.0, 9.0, 6.0], [1.0, 9.0, 3.0, 6.0, 7.0, 4.0, 6.0, 3.0, 8.0, 6.0, 8.0, 2.0, 10.0, 8.0], [10.0, 8.0, 5.0, 3.0, 2.0, 8.0, 5.0, 4.0, 6.0, 8.0, 4.0, 9.0, 3.0, 8.0], [7.0, 8.0, 8.0, 2.0, 4.0, 2.0, 1.0, 8.0, 8.0, 4.0, 6.0, 8.0, 10.0, 4.0], [9.0, 5.0, 8.0, 7.0, 10.0, 2.0, 7.0, 2.0, 2.0, 9.0, 8.0, 5.0, 4.0, 3.0], [2.0, 5.0, 8.0, 6.0, 9.0, 8.0, 8.0, 9.0, 10.0, 3.0, 10.0, 4.0, 5.0, 2.0], [4.0, 8.0, 5.0, 8.0, 1.0, 6.0, 5.0, 6.0, 8.0, 8.0, 4.0, 3.0, 2.0, 3.0]]}, 'source': 8, 'target': 9}","[8, 4, 5, 6, 7, 9]",155.0,"{'problem_type': 'QSPP', 'num_nodes': 10, 'num_edges': 14, 'nodes': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J'], 'source': 'I', 'target': 'J', 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 9.0}, {'var_index': 1, 'linear_cost': 1.0}, {'var_index': 2, 'linear_cost': 3.0}, {'var_index': 3, 'linear_cost': 9.0}, {'var_index': 4, 'linear_cost': 6.0}, {'var_index': 5, 'linear_cost': 6.0}, {'var_index': 6, 'linear_cost': 6.0}, {'var_index': 7, 'linear_cost': 9.0}, {'var_index': 8, 'linear_cost': 7.0}, {'var_index': 9, 'linear_cost': 4.0}, {'var_index': 10, 'linear_cost': 5.0}, {'var_index': 11, 'linear_cost': 2.0}, {'var_index': 12, 'linear_cost': 6.0}, {'var_index': 13, 'linear_cost': 10.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 5.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 0, 'var_j': 8, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 9, 'quadratic_cost': 10.0}, {'var_i': 0, 'var_j': 10, 'quadratic_cost': 7.0}, {'var_i': 0, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 12, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 13, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 8, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 1, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 1, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 2, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 13, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 1.0}, {'var_i': 3, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 3, 'var_j': 12, 'quadratic_cost': 6.0}, {'var_i': 3, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 8, 'quadratic_cost': 7.0}, {'var_i': 4, 'var_j': 9, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 11, 'quadratic_cost': 10.0}, {'var_i': 4, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 4, 'var_j': 13, 'quadratic_cost': 1.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 10.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 7, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 8, 'quadratic_cost': 4.0}, {'var_i': 5, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 10, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 5, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 9, 'quadratic_cost': 5.0}, {'var_i': 6, 'var_j': 10, 'quadratic_cost': 1.0}, {'var_i': 6, 'var_j': 11, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 12, 'quadratic_cost': 8.0}, {'var_i': 6, 'var_j': 13, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 0, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 1, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 3, 'quadratic_cost': 1.0}, {'var_i': 7, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 7, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 8, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 7, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 7, 'var_j': 12, 'quadratic_cost': 9.0}, {'var_i': 7, 'var_j': 13, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 8, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 8, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 4, 'quadratic_cost': 7.0}, {'var_i': 8, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 8, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 8, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 9, 'quadratic_cost': 6.0}, {'var_i': 8, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 8, 'var_j': 11, 'quadratic_cost': 2.0}, {'var_i': 8, 'var_j': 12, 'quadratic_cost': 10.0}, {'var_i': 8, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 0, 'quadratic_cost': 10.0}, {'var_i': 9, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 9, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 9, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 9, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 9, 'var_j': 8, 'quadratic_cost': 6.0}, {'var_i': 9, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 9, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 9, 'var_j': 11, 'quadratic_cost': 9.0}, {'var_i': 9, 'var_j': 12, 'quadratic_cost': 3.0}, {'var_i': 9, 'var_j': 13, 'quadratic_cost': 8.0}, {'var_i': 10, 'var_j': 0, 'quadratic_cost': 7.0}, {'var_i': 10, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 10, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 10, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 10, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 10, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 10, 'var_j': 6, 'quadratic_cost': 1.0}, {'var_i': 10, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 10, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 10, 'var_j': 9, 'quadratic_cost': 4.0}, {'var_i': 10, 'var_j': 10, 'quadratic_cost': 6.0}, {'var_i': 10, 'var_j': 11, 'quadratic_cost': 8.0}, {'var_i': 10, 'var_j': 12, 'quadratic_cost': 10.0}, {'var_i': 10, 'var_j': 13, 'quadratic_cost': 4.0}, {'var_i': 11, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 11, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 11, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 11, 'var_j': 3, 'quadratic_cost': 7.0}, {'var_i': 11, 'var_j': 4, 'quadratic_cost': 10.0}, {'var_i': 11, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 11, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 11, 'var_j': 7, 'quadratic_cost': 2.0}, {'var_i': 11, 'var_j': 8, 'quadratic_cost': 2.0}, {'var_i': 11, 'var_j': 9, 'quadratic_cost': 9.0}, {'var_i': 11, 'var_j': 10, 'quadratic_cost': 8.0}, {'var_i': 11, 'var_j': 11, 'quadratic_cost': 5.0}, {'var_i': 11, 'var_j': 12, 'quadratic_cost': 4.0}, {'var_i': 11, 'var_j': 13, 'quadratic_cost': 3.0}, {'var_i': 12, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 12, 'var_j': 1, 'quadratic_cost': 5.0}, {'var_i': 12, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 12, 'var_j': 3, 'quadratic_cost': 6.0}, {'var_i': 12, 'var_j': 4, 'quadratic_cost': 9.0}, {'var_i': 12, 'var_j': 5, 'quadratic_cost': 8.0}, {'var_i': 12, 'var_j': 6, 'quadratic_cost': 8.0}, {'var_i': 12, 'var_j': 7, 'quadratic_cost': 9.0}, {'var_i': 12, 'var_j': 8, 'quadratic_cost': 10.0}, {'var_i': 12, 'var_j': 9, 'quadratic_cost': 3.0}, {'var_i': 12, 'var_j': 10, 'quadratic_cost': 10.0}, {'var_i': 12, 'var_j': 11, 'quadratic_cost': 4.0}, {'var_i': 12, 'var_j': 12, 'quadratic_cost': 5.0}, {'var_i': 12, 'var_j': 13, 'quadratic_cost': 2.0}, {'var_i': 13, 'var_j': 0, 'quadratic_cost': 4.0}, {'var_i': 13, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 2, 'quadratic_cost': 5.0}, {'var_i': 13, 'var_j': 3, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 13, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 13, 'var_j': 6, 'quadratic_cost': 5.0}, {'var_i': 13, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 13, 'var_j': 8, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 9, 'quadratic_cost': 8.0}, {'var_i': 13, 'var_j': 10, 'quadratic_cost': 4.0}, {'var_i': 13, 'var_j': 11, 'quadratic_cost': 3.0}, {'var_i': 13, 'var_j': 12, 'quadratic_cost': 2.0}, {'var_i': 13, 'var_j': 13, 'quadratic_cost': 3.0}]}, 'edges': [{'from': 'I', 'to': 'A', 'var_index': 0}, {'from': 'I', 'to': 'E', 'var_index': 1}, {'from': 'D', 'to': 'J', 'var_index': 2}, {'from': 'H', 'to': 'J', 'var_index': 3}, {'from': 'A', 'to': 'B', 'var_index': 4}, {'from': 'A', 'to': 'E', 'var_index': 5}, {'from': 'B', 'to': 'C', 'var_index': 6}, {'from': 'B', 'to': 'F', 'var_index': 7}, {'from': 'C', 'to': 'D', 'var_index': 8}, {'from': 'C', 'to': 'G', 'var_index': 9}, {'from': 'D', 'to': 'H', 'var_index': 10}, {'from': 'E', 'to': 'F', 'var_index': 11}, {'from': 'F', 'to': 'G', 'var_index': 12}, {'from': 'G', 'to': 'H', 'var_index': 13}], 'node_id_map': {0: 'A', 1: 'B', 2: 'C', 3: 'D', 4: 'E', 5: 'F', 6: 'G', 7: 'H', 8: 'I', 9: 'J'}}","['I', 'E', 'F', 'G', 'H', 'J']",49,json,names
QSPP,QSPP,"I pictured a small inspection team moving through the water network from the entry valve to the exit gate, following only the pipes that let the water flow the right way. They have to pick one continuous route and list the places they pass in order — starting at the entry and finishing at the exit — with every step following a permitted flow. Each pipe on the route takes some inspection time, and some pipe combinations create extra headaches if both are inspected, plus a few pipes have their own extra penalties. The goal is to pick the single route that makes the total inspection burden as small as possible by adding up each segment’s time and any extra penalties for pairs (including any self-penalties). The concrete map, times, and penalty details are shown below.

I see 5 distinct junctions and 8 directed pipe segments; the valid locations are 1, 2, 3, 4, 5, the entry valve is at 4 and the exit gate at 5.
I pictured a pipe from 4 to 1 labeled 0.
I pictured a pipe from 4 to 2 labeled 1.
I pictured a pipe from 4 to 3 labeled 2.
I pictured a pipe from 1 to 5 labeled 3.
I pictured a pipe from 2 to 5 labeled 4.
I pictured a pipe from 3 to 5 labeled 5.
I pictured a pipe from 1 to 2 labeled 6.
I pictured a pipe from 2 to 3 labeled 7.
I pictured segment 0 taking 7.0 time to inspect.
I pictured segment 1 taking 8.0 time to inspect.
I pictured segment 2 taking 6.0 time to inspect.
I pictured segment 3 taking 2.0 time to inspect.
I pictured segment 4 taking 10.0 time to inspect.
I pictured segment 5 taking 6.0 time to inspect.
I pictured segment 6 taking 6.0 time to inspect.
I pictured segment 7 taking 1.0 time to inspect.
Meaning: the quadratic_costs matrix is assumed symmetric and contributes to the objective as a sum over ALL ordered pairs (pipe_i_id, pipe_j_id). If two pipe_segments with IDs i and j are both used in the chosen path, then quadratic_costs[i][j] is added to the total. This includes diagonal terms (i == j), so selecting edge i also adds quadratic_costs[i][i]. Because the matrix is symmetric, the interaction between two distinct edges i and j is counted twice in the ordered-pair sum: quadratic_costs[i][j] + quadratic_costs[j][i] (= 2 * quadratic_costs[i][j]).
quadratic_costs:
| pipe_i_id\pipe_j_id | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|---|
| 0 | 8.0 | 9.0 | 3.0 | 3.0 | 1.0 | 2.0 | 2.0 | 3.0 |
| 1 | 9.0 | 4.0 | 4.0 | 4.0 | 4.0 | 6.0 | 10.0 | 8.0 |
| 2 | 3.0 | 4.0 | 6.0 | 9.0 | 2.0 | 3.0 | 6.0 | 8.0 |
| 3 | 3.0 | 4.0 | 9.0 | 4.0 | 2.0 | 5.0 | 10.0 | 5.0 |
| 4 | 1.0 | 4.0 | 2.0 | 2.0 | 1.0 | 6.0 | 4.0 | 6.0 |
| 5 | 2.0 | 6.0 | 3.0 | 5.0 | 6.0 | 5.0 | 7.0 | 4.0 |
| 6 | 2.0 | 10.0 | 6.0 | 10.0 | 4.0 | 7.0 | 9.0 | 10.0 |
| 7 | 3.0 | 8.0 | 8.0 | 5.0 | 6.0 | 4.0 | 10.0 | 4.0 |
I will use these details to pick the single route with the smallest total inspection burden.

Oh, and to keep things machine-friendly, please return the chosen route in a tiny JSON wrapper like this:

{
  ""solution"": []
}

Think of ""solution"" as the ordered list of places the team walks through — start node first, end node last — and nothing else. It's just a sketch of the shape I want, not the actual answer; when you fill it in, put only the node identifiers (no edge ids, no times, no penalties).

Please use the exact identifiers from the problem input, with no renaming or invented labels.  
- for example: ""Valid identifiers look like plain numbers such as “1” or “23”, single capital letters like “A” or “B”, or a capital letter followed by digits like “A1” or “X7”.","{'nodes': [0, 1, 2, 3, 4], 'edges': [{'from': 3, 'to': 0, 'var_index': 0}, {'from': 3, 'to': 1, 'var_index': 1}, {'from': 3, 'to': 2, 'var_index': 2}, {'from': 0, 'to': 4, 'var_index': 3}, {'from': 1, 'to': 4, 'var_index': 4}, {'from': 2, 'to': 4, 'var_index': 5}, {'from': 0, 'to': 1, 'var_index': 6}, {'from': 1, 'to': 2, 'var_index': 7}], 'objective': {'constant': 0.0, 'linear': [7.0, 8.0, 6.0, 2.0, 10.0, 6.0, 6.0, 1.0], 'quadratic': [[8.0, 9.0, 3.0, 3.0, 1.0, 2.0, 2.0, 3.0], [9.0, 4.0, 4.0, 4.0, 4.0, 6.0, 10.0, 8.0], [3.0, 4.0, 6.0, 9.0, 2.0, 3.0, 6.0, 8.0], [3.0, 4.0, 9.0, 4.0, 2.0, 5.0, 10.0, 5.0], [1.0, 4.0, 2.0, 2.0, 1.0, 6.0, 4.0, 6.0], [2.0, 6.0, 3.0, 5.0, 6.0, 5.0, 7.0, 4.0], [2.0, 10.0, 6.0, 10.0, 4.0, 7.0, 9.0, 10.0], [3.0, 8.0, 8.0, 5.0, 6.0, 4.0, 10.0, 4.0]]}, 'source': 3, 'target': 4}","[3, 0, 4]",27.0,"{'problem_type': 'QSPP', 'num_nodes': 5, 'num_edges': 8, 'nodes': [1, 2, 3, 4, 5], 'source': 4, 'target': 5, 'objective': {'constant': 0.0, 'linear': [{'var_index': 0, 'linear_cost': 7.0}, {'var_index': 1, 'linear_cost': 8.0}, {'var_index': 2, 'linear_cost': 6.0}, {'var_index': 3, 'linear_cost': 2.0}, {'var_index': 4, 'linear_cost': 10.0}, {'var_index': 5, 'linear_cost': 6.0}, {'var_index': 6, 'linear_cost': 6.0}, {'var_index': 7, 'linear_cost': 1.0}], 'quadratic': [{'var_i': 0, 'var_j': 0, 'quadratic_cost': 8.0}, {'var_i': 0, 'var_j': 1, 'quadratic_cost': 9.0}, {'var_i': 0, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 3, 'quadratic_cost': 3.0}, {'var_i': 0, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 0, 'var_j': 5, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 6, 'quadratic_cost': 2.0}, {'var_i': 0, 'var_j': 7, 'quadratic_cost': 3.0}, {'var_i': 1, 'var_j': 0, 'quadratic_cost': 9.0}, {'var_i': 1, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 2, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 1, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 1, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 1, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 2, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 2, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 3, 'quadratic_cost': 9.0}, {'var_i': 2, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 2, 'var_j': 5, 'quadratic_cost': 3.0}, {'var_i': 2, 'var_j': 6, 'quadratic_cost': 6.0}, {'var_i': 2, 'var_j': 7, 'quadratic_cost': 8.0}, {'var_i': 3, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 3, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 2, 'quadratic_cost': 9.0}, {'var_i': 3, 'var_j': 3, 'quadratic_cost': 4.0}, {'var_i': 3, 'var_j': 4, 'quadratic_cost': 2.0}, {'var_i': 3, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 3, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 3, 'var_j': 7, 'quadratic_cost': 5.0}, {'var_i': 4, 'var_j': 0, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 1, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 2, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 3, 'quadratic_cost': 2.0}, {'var_i': 4, 'var_j': 4, 'quadratic_cost': 1.0}, {'var_i': 4, 'var_j': 5, 'quadratic_cost': 6.0}, {'var_i': 4, 'var_j': 6, 'quadratic_cost': 4.0}, {'var_i': 4, 'var_j': 7, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 5, 'var_j': 1, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 2, 'quadratic_cost': 3.0}, {'var_i': 5, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 5, 'var_j': 5, 'quadratic_cost': 5.0}, {'var_i': 5, 'var_j': 6, 'quadratic_cost': 7.0}, {'var_i': 5, 'var_j': 7, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 0, 'quadratic_cost': 2.0}, {'var_i': 6, 'var_j': 1, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 2, 'quadratic_cost': 6.0}, {'var_i': 6, 'var_j': 3, 'quadratic_cost': 10.0}, {'var_i': 6, 'var_j': 4, 'quadratic_cost': 4.0}, {'var_i': 6, 'var_j': 5, 'quadratic_cost': 7.0}, {'var_i': 6, 'var_j': 6, 'quadratic_cost': 9.0}, {'var_i': 6, 'var_j': 7, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 0, 'quadratic_cost': 3.0}, {'var_i': 7, 'var_j': 1, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 2, 'quadratic_cost': 8.0}, {'var_i': 7, 'var_j': 3, 'quadratic_cost': 5.0}, {'var_i': 7, 'var_j': 4, 'quadratic_cost': 6.0}, {'var_i': 7, 'var_j': 5, 'quadratic_cost': 4.0}, {'var_i': 7, 'var_j': 6, 'quadratic_cost': 10.0}, {'var_i': 7, 'var_j': 7, 'quadratic_cost': 4.0}]}, 'edges': [{'from': 4, 'to': 1, 'var_index': 0}, {'from': 4, 'to': 2, 'var_index': 1}, {'from': 4, 'to': 3, 'var_index': 2}, {'from': 1, 'to': 5, 'var_index': 3}, {'from': 2, 'to': 5, 'var_index': 4}, {'from': 3, 'to': 5, 'var_index': 5}, {'from': 1, 'to': 2, 'var_index': 6}, {'from': 2, 'to': 3, 'var_index': 7}], 'node_id_map': {0: 1, 1: 2, 2: 3, 3: 4, 4: 5}}","[4, 1, 5]",50,nl,1