[ { "task_name": "STP", "problem_type": "STP", "instruction": "Someone on the infrastructure team laid out a list of potential cable runs and their prices; the decision to make is which runs to actually install so every listed community center is tied into the same network. What makes one decision better than another is simple: the plan that costs less in total (just add up the prices of the selected runs) is preferred. It’s okay to use intermediate junctions as connectors, but every marked center has to be part of the network and segments aren’t to be duplicated. The specific map and costs are provided below.\n\n# total_locations=22\n# potential_segments_count=29\n# community_centers=7 10 15 18\nendpoint_node_a,endpoint_node_b,installation_cost\n19,12,20591.0\n19,2,8015.0\n19,17,20492.0\n10,3,2045.0\n10,9,7747.0\n10,16,11617.0\n7,20,12943.0\n7,15,9193.0\n11,2,28247.0\n11,12,587.0\n11,4,7687.0\n12,15,28663.0\n18,17,4563.0\n18,22,903.0\n18,21,1176.0\n13,5,1594.0\n13,17,1266.0\n13,14,4559.0\n14,20,10215.0\n14,6,5002.0\n2,3,606.0\n2,8,9687.0\n21,15,5168.0\n21,22,1646.0\n1,16,15656.0\n1,9,633.0\n5,6,611.0\n6,22,4621.0\n8,9,1026.0\n\nAlso, when you send back the chosen set of cable runs, please put them in this simple JSON shape so it's easy to check automatically:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nThink of \"solution\" as just a list of segments to install — each inner pair [X, Y] means \"connect node X to node Y\". This is only a sketch of the shape I need, not the actual plan.\n\nPlease use the exact 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”.", "instance": { "problem_type": "STP", "num_nodes": 22, "num_edges": 29, "edges": [ { "u": 19, "v": 12, "w": 20591.0 }, { "u": 19, "v": 2, "w": 8015.0 }, { "u": 19, "v": 17, "w": 20492.0 }, { "u": 10, "v": 3, "w": 2045.0 }, { "u": 10, "v": 9, "w": 7747.0 }, { "u": 10, "v": 16, "w": 11617.0 }, { "u": 7, "v": 20, "w": 12943.0 }, { "u": 7, "v": 15, "w": 9193.0 }, { "u": 11, "v": 2, "w": 28247.0 }, { "u": 11, "v": 12, "w": 587.0 }, { "u": 11, "v": 4, "w": 7687.0 }, { "u": 12, "v": 15, "w": 28663.0 }, { "u": 18, "v": 17, "w": 4563.0 }, { "u": 18, "v": 22, "w": 903.0 }, { "u": 18, "v": 21, "w": 1176.0 }, { "u": 13, "v": 5, "w": 1594.0 }, { "u": 13, "v": 17, "w": 1266.0 }, { "u": 13, "v": 14, "w": 4559.0 }, { "u": 14, "v": 20, "w": 10215.0 }, { "u": 14, "v": 6, "w": 5002.0 }, { "u": 2, "v": 3, "w": 606.0 }, { "u": 2, "v": 8, "w": 9687.0 }, { "u": 21, "v": 15, "w": 5168.0 }, { "u": 21, "v": 22, "w": 1646.0 }, { "u": 1, "v": 16, "w": 15656.0 }, { "u": 1, "v": 9, "w": 633.0 }, { "u": 5, "v": 6, "w": 611.0 }, { "u": 6, "v": 22, "w": 4621.0 }, { "u": 8, "v": 9, "w": 1026.0 } ], "terminals": [ 7, 10, 15, 18 ], "source_file": "I076.stp", "density": 0.12554112554112554, "viz_instance": "generated_data/STP/viz/STP_L/instance_0000.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0000.png" }, "solution": [ [ 2, 19 ], [ 17, 19 ], [ 3, 10 ], [ 7, 15 ], [ 17, 18 ], [ 18, 21 ], [ 2, 3 ], [ 15, 21 ] ], "obj": 51258.0, "instance_variant": { "problem_type": "STP", "num_nodes": 22, "num_edges": 29, "edges": [ { "u": 19, "v": 12, "w": 20591.0 }, { "u": 19, "v": 2, "w": 8015.0 }, { "u": 19, "v": 17, "w": 20492.0 }, { "u": 10, "v": 3, "w": 2045.0 }, { "u": 10, "v": 9, "w": 7747.0 }, { "u": 10, "v": 16, "w": 11617.0 }, { "u": 7, "v": 20, "w": 12943.0 }, { "u": 7, "v": 15, "w": 9193.0 }, { "u": 11, "v": 2, "w": 28247.0 }, { "u": 11, "v": 12, "w": 587.0 }, { "u": 11, "v": 4, "w": 7687.0 }, { "u": 12, "v": 15, "w": 28663.0 }, { "u": 18, "v": 17, "w": 4563.0 }, { "u": 18, "v": 22, "w": 903.0 }, { "u": 18, "v": 21, "w": 1176.0 }, { "u": 13, "v": 5, "w": 1594.0 }, { "u": 13, "v": 17, "w": 1266.0 }, { "u": 13, "v": 14, "w": 4559.0 }, { "u": 14, "v": 20, "w": 10215.0 }, { "u": 14, "v": 6, "w": 5002.0 }, { "u": 2, "v": 3, "w": 606.0 }, { "u": 2, "v": 8, "w": 9687.0 }, { "u": 21, "v": 15, "w": 5168.0 }, { "u": 21, "v": 22, "w": 1646.0 }, { "u": 1, "v": 16, "w": 15656.0 }, { "u": 1, "v": 9, "w": 633.0 }, { "u": 5, "v": 6, "w": 611.0 }, { "u": 6, "v": 22, "w": 4621.0 }, { "u": 8, "v": 9, "w": 1026.0 } ], "density": 0.12554112554112554, "source_file": "I076.stp", "terminals": [ 7, 10, 15, 18 ] }, "solution_variant": [ [ 2, 19 ], [ 17, 19 ], [ 3, 10 ], [ 7, 15 ], [ 17, 18 ], [ 18, 21 ], [ 2, 3 ], [ 15, 21 ] ], "context_index": 1, "input_format": "csv", "input_index_base": 1 }, { "task_name": "STP", "problem_type": "STP", "instruction": "We’ve got a small courtyard with marked seating spots and a network of existing stepping stones. The decision is which of the possible paths between those stones to actually lay down so that all the flagged seats are connected by the finished network, using other stones as stepping points if needed. One plan beats another if the total amount of path laid (calculated by adding up the lengths of every chosen link) is smaller, and every flagged seat ends up included once in the connected layout without repeating the same segment. The concrete layout and distances follow below.\n\nThere are 25 existing stepping stones, 32 candidate paths, and the flagged seating stones are 8 20.\nBetween stone 25 and stone 17 we could lay a path of length 41.0.\nBetween stone 12 and stone 21 we could lay a path of length 207.0.\nBetween stone 12 and stone 20 we could lay a path of length 102.0.\nBetween stone 13 and stone 14 we could lay a path of length 298.0.\nBetween stone 13 and stone 21 we could lay a path of length 219.0.\nBetween stone 13 and stone 1 we could lay a path of length 562.0.\nBetween stone 14 and stone 1 we could lay a path of length 278.0.\nBetween stone 14 and stone 20 we could lay a path of length 234.0.\nBetween stone 15 and stone 6 we could lay a path of length 414.0.\nBetween stone 15 and stone 23 we could lay a path of length 472.0.\nBetween stone 16 and stone 17 we could lay a path of length 1103.0.\nBetween stone 17 and stone 18 we could lay a path of length 1581.0.\nBetween stone 18 and stone 3 we could lay a path of length 818.0.\nBetween stone 18 and stone 1 we could lay a path of length 871.0.\nBetween stone 19 and stone 3 we could lay a path of length 370.0.\nBetween stone 19 and stone 7 we could lay a path of length 417.0.\nBetween stone 19 and stone 4 we could lay a path of length 737.0.\nBetween stone 20 and stone 5 we could lay a path of length 815.0.\nBetween stone 2 and stone 3 we could lay a path of length 741.0.\nBetween stone 2 and stone 4 we could lay a path of length 377.0.\nBetween stone 2 and stone 5 we could lay a path of length 631.0.\nBetween stone 4 and stone 22 we could lay a path of length 629.0.\nBetween stone 5 and stone 22 we could lay a path of length 373.0.\nBetween stone 6 and stone 7 we could lay a path of length 475.0.\nBetween stone 6 and stone 11 we could lay a path of length 285871.0.\nBetween stone 7 and stone 23 we could lay a path of length 414.0.\nBetween stone 8 and stone 9 we could lay a path of length 718.0.\nBetween stone 8 and stone 10 we could lay a path of length 311.0.\nBetween stone 8 and stone 11 we could lay a path of length 285338.0.\nBetween stone 22 and stone 10 we could lay a path of length 385.0.\nBetween stone 10 and stone 24 we could lay a path of length 752.0.\nBetween stone 9 and stone 24 we could lay a path of length 383.0.\nBelow we list each candidate path so we can choose the shortest set that connects all 8 20.\n\nJust drop your chosen links into this little JSON form so I know which stone-to-stone segments you're proposing:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nThink of \"solution\" as the list of path segments to lay down. Each inner pair like [u1, v1] is one connection between two stones (use the exact labels from the courtyard map). This block is just a sketch of the shape I expect, not the actual answer.\n\nPlease make sure to use the exact identifiers from the instance input — don't rename them or invent new ones. \n- 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”. \"", "instance": { "problem_type": "STP", "num_nodes": 25, "num_edges": 32, "edges": [ { "u": 25, "v": 17, "w": 41.0 }, { "u": 12, "v": 21, "w": 207.0 }, { "u": 12, "v": 20, "w": 102.0 }, { "u": 13, "v": 14, "w": 298.0 }, { "u": 13, "v": 21, "w": 219.0 }, { "u": 13, "v": 1, "w": 562.0 }, { "u": 14, "v": 1, "w": 278.0 }, { "u": 14, "v": 20, "w": 234.0 }, { "u": 15, "v": 6, "w": 414.0 }, { "u": 15, "v": 23, "w": 472.0 }, { "u": 16, "v": 17, "w": 1103.0 }, { "u": 17, "v": 18, "w": 1581.0 }, { "u": 18, "v": 3, "w": 818.0 }, { "u": 18, "v": 1, "w": 871.0 }, { "u": 19, "v": 3, "w": 370.0 }, { "u": 19, "v": 7, "w": 417.0 }, { "u": 19, "v": 4, "w": 737.0 }, { "u": 20, "v": 5, "w": 815.0 }, { "u": 2, "v": 3, "w": 741.0 }, { "u": 2, "v": 4, "w": 377.0 }, { "u": 2, "v": 5, "w": 631.0 }, { "u": 4, "v": 22, "w": 629.0 }, { "u": 5, "v": 22, "w": 373.0 }, { "u": 6, "v": 7, "w": 475.0 }, { "u": 6, "v": 11, "w": 285871.0 }, { "u": 7, "v": 23, "w": 414.0 }, { "u": 8, "v": 9, "w": 718.0 }, { "u": 8, "v": 10, "w": 311.0 }, { "u": 8, "v": 11, "w": 285338.0 }, { "u": 22, "v": 10, "w": 385.0 }, { "u": 10, "v": 24, "w": 752.0 }, { "u": 9, "v": 24, "w": 383.0 } ], "terminals": [ 8, 20 ], "source_file": "I055.stp", "density": 0.10666666666666667, "viz_instance": "generated_data/STP/viz/STP_L/instance_0001.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0001.png" }, "solution": [ [ 5, 20 ], [ 5, 22 ], [ 8, 10 ], [ 10, 22 ] ], "obj": 1884.0, "instance_variant": { "problem_type": "STP", "num_nodes": 25, "num_edges": 32, "edges": [ { "u": 25, "v": 17, "w": 41.0 }, { "u": 12, "v": 21, "w": 207.0 }, { "u": 12, "v": 20, "w": 102.0 }, { "u": 13, "v": 14, "w": 298.0 }, { "u": 13, "v": 21, "w": 219.0 }, { "u": 13, "v": 1, "w": 562.0 }, { "u": 14, "v": 1, "w": 278.0 }, { "u": 14, "v": 20, "w": 234.0 }, { "u": 15, "v": 6, "w": 414.0 }, { "u": 15, "v": 23, "w": 472.0 }, { "u": 16, "v": 17, "w": 1103.0 }, { "u": 17, "v": 18, "w": 1581.0 }, { "u": 18, "v": 3, "w": 818.0 }, { "u": 18, "v": 1, "w": 871.0 }, { "u": 19, "v": 3, "w": 370.0 }, { "u": 19, "v": 7, "w": 417.0 }, { "u": 19, "v": 4, "w": 737.0 }, { "u": 20, "v": 5, "w": 815.0 }, { "u": 2, "v": 3, "w": 741.0 }, { "u": 2, "v": 4, "w": 377.0 }, { "u": 2, "v": 5, "w": 631.0 }, { "u": 4, "v": 22, "w": 629.0 }, { "u": 5, "v": 22, "w": 373.0 }, { "u": 6, "v": 7, "w": 475.0 }, { "u": 6, "v": 11, "w": 285871.0 }, { "u": 7, "v": 23, "w": 414.0 }, { "u": 8, "v": 9, "w": 718.0 }, { "u": 8, "v": 10, "w": 311.0 }, { "u": 8, "v": 11, "w": 285338.0 }, { "u": 22, "v": 10, "w": 385.0 }, { "u": 10, "v": 24, "w": 752.0 }, { "u": 9, "v": 24, "w": 383.0 } ], "density": 0.10666666666666667, "source_file": "I055.stp", "terminals": [ 8, 20 ] }, "solution_variant": [ [ 5, 20 ], [ 5, 22 ], [ 8, 10 ], [ 10, 22 ] ], "context_index": 2, "input_format": "markdown_table", "input_index_base": 1 }, { "task_name": "STP", "problem_type": "STP", "instruction": "We have a map of poles and possible spans between them, and a few fixed distribution boxes that all need to be connected into a single overhead line. The decision is which spans to actually string from the list of feasible options, using intermediate poles where it’s handy to hop between runs. The winning plan is the one with the smallest total cable length — total length equals the sum of every chosen span — and every box must be included in the connected chain with no repeats. The specific instance details follow below.\n\nThere are 24 nodes, 31 feasible spans, and the required distribution boxes are 6 9 11 12 17 22 24.\nCandidate span connecting node 9 and node 21, length 1986.0.\nCandidate span connecting node 19 and node 13, length 979.0.\nCandidate span connecting node 19 and node 20, length 8.0.\nCandidate span connecting node 19 and node 21, length 201.0.\nCandidate span connecting node 20 and node 6, length 514.0.\nCandidate span connecting node 21 and node 14, length 626.0.\nCandidate span connecting node 22 and node 18, length 2007.0.\nCandidate span connecting node 24 and node 23, length 3233.0.\nCandidate span connecting node 24 and node 17, length 4805.0.\nCandidate span connecting node 11 and node 1, length 423.0.\nCandidate span connecting node 11 and node 12, length 972.0.\nCandidate span connecting node 11 and node 16, length 1215.0.\nCandidate span connecting node 11 and node 7, length 396.0.\nCandidate span connecting node 12 and node 17, length 866.0.\nCandidate span connecting node 12 and node 8, length 1090.0.\nCandidate span connecting node 13 and node 5, length 502.0.\nCandidate span connecting node 13 and node 14, length 779.0.\nCandidate span connecting node 13 and node 7, length 501.0.\nCandidate span connecting node 14 and node 8, length 386.0.\nCandidate span connecting node 10 and node 5, length 264504.0.\nCandidate span connecting node 10 and node 1, length 265605.0.\nCandidate span connecting node 1 and node 2, length 1408.0.\nCandidate span connecting node 2 and node 16, length 376.0.\nCandidate span connecting node 2 and node 15, length 3423.0.\nCandidate span connecting node 3 and node 18, length 287.0.\nCandidate span connecting node 3 and node 4, length 4327.0.\nCandidate span connecting node 4 and node 15, length 13.0.\nCandidate span connecting node 5 and node 6, length 1162.0.\nCandidate span connecting node 6 and node 18, length 867.0.\nCandidate span connecting node 7 and node 8, length 1098.0.\nCandidate span connecting node 16 and node 17, length 470.0.\nWe must select a subset of these spans so the 6 9 11 12 17 22 24 form a single continuous overhead line with minimal total cable length.\n\nYou can just give the chosen spans in this simple JSON shape — a list of edge pairs inside the \"solution\" array.\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nThis is just a sketch of the shape I want: each inner pair is a span (an edge) between two poles/points you picked. Fill that array with the actual pairs from the instance when you submit the final plan.\n\nPlease use the exact identifiers that appear in the instance input — no renaming and no new labels. \nFor 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”.", "instance": { "problem_type": "STP", "num_nodes": 24, "num_edges": 31, "edges": [ { "u": 9, "v": 21, "w": 1986.0 }, { "u": 19, "v": 13, "w": 979.0 }, { "u": 19, "v": 20, "w": 8.0 }, { "u": 19, "v": 21, "w": 201.0 }, { "u": 20, "v": 6, "w": 514.0 }, { "u": 21, "v": 14, "w": 626.0 }, { "u": 22, "v": 18, "w": 2007.0 }, { "u": 24, "v": 23, "w": 3233.0 }, { "u": 24, "v": 17, "w": 4805.0 }, { "u": 11, "v": 1, "w": 423.0 }, { "u": 11, "v": 12, "w": 972.0 }, { "u": 11, "v": 16, "w": 1215.0 }, { "u": 11, "v": 7, "w": 396.0 }, { "u": 12, "v": 17, "w": 866.0 }, { "u": 12, "v": 8, "w": 1090.0 }, { "u": 13, "v": 5, "w": 502.0 }, { "u": 13, "v": 14, "w": 779.0 }, { "u": 13, "v": 7, "w": 501.0 }, { "u": 14, "v": 8, "w": 386.0 }, { "u": 10, "v": 5, "w": 264504.0 }, { "u": 10, "v": 1, "w": 265605.0 }, { "u": 1, "v": 2, "w": 1408.0 }, { "u": 2, "v": 16, "w": 376.0 }, { "u": 2, "v": 15, "w": 3423.0 }, { "u": 3, "v": 18, "w": 287.0 }, { "u": 3, "v": 4, "w": 4327.0 }, { "u": 4, "v": 15, "w": 13.0 }, { "u": 5, "v": 6, "w": 1162.0 }, { "u": 6, "v": 18, "w": 867.0 }, { "u": 7, "v": 8, "w": 1098.0 }, { "u": 16, "v": 17, "w": 470.0 } ], "terminals": [ 6, 9, 11, 12, 17, 22, 24 ], "source_file": "I011.stp", "density": 0.11231884057971014, "viz_instance": "generated_data/STP/viz/STP_L/instance_0002.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0002.png" }, "solution": [ [ 9, 21 ], [ 13, 19 ], [ 19, 20 ], [ 19, 21 ], [ 6, 20 ], [ 18, 22 ], [ 17, 24 ], [ 11, 12 ], [ 7, 11 ], [ 12, 17 ], [ 7, 13 ], [ 6, 18 ] ], "obj": 14102.0, "instance_variant": { "problem_type": "STP", "num_nodes": 24, "num_edges": 31, "edges": [ { "u": 9, "v": 21, "w": 1986.0 }, { "u": 19, "v": 13, "w": 979.0 }, { "u": 19, "v": 20, "w": 8.0 }, { "u": 19, "v": 21, "w": 201.0 }, { "u": 20, "v": 6, "w": 514.0 }, { "u": 21, "v": 14, "w": 626.0 }, { "u": 22, "v": 18, "w": 2007.0 }, { "u": 24, "v": 23, "w": 3233.0 }, { "u": 24, "v": 17, "w": 4805.0 }, { "u": 11, "v": 1, "w": 423.0 }, { "u": 11, "v": 12, "w": 972.0 }, { "u": 11, "v": 16, "w": 1215.0 }, { "u": 11, "v": 7, "w": 396.0 }, { "u": 12, "v": 17, "w": 866.0 }, { "u": 12, "v": 8, "w": 1090.0 }, { "u": 13, "v": 5, "w": 502.0 }, { "u": 13, "v": 14, "w": 779.0 }, { "u": 13, "v": 7, "w": 501.0 }, { "u": 14, "v": 8, "w": 386.0 }, { "u": 10, "v": 5, "w": 264504.0 }, { "u": 10, "v": 1, "w": 265605.0 }, { "u": 1, "v": 2, "w": 1408.0 }, { "u": 2, "v": 16, "w": 376.0 }, { "u": 2, "v": 15, "w": 3423.0 }, { "u": 3, "v": 18, "w": 287.0 }, { "u": 3, "v": 4, "w": 4327.0 }, { "u": 4, "v": 15, "w": 13.0 }, { "u": 5, "v": 6, "w": 1162.0 }, { "u": 6, "v": 18, "w": 867.0 }, { "u": 7, "v": 8, "w": 1098.0 }, { "u": 16, "v": 17, "w": 470.0 } ], "density": 0.11231884057971014, "source_file": "I011.stp", "terminals": [ 6, 9, 11, 12, 17, 22, 24 ] }, "solution_variant": [ [ 9, 21 ], [ 13, 19 ], [ 19, 20 ], [ 19, 21 ], [ 6, 20 ], [ 18, 22 ], [ 17, 24 ], [ 11, 12 ], [ 7, 11 ], [ 12, 17 ], [ 7, 13 ], [ 6, 18 ] ], "context_index": 3, "input_format": "nl", "input_index_base": 1 }, { "task_name": "STP", "problem_type": "STP", "instruction": "We’re planning a walkable route through a museum by deciding which hallways to unlock so all of the flagged exhibit rooms are connected without any breaks. The route can pass through extra galleries to make connections easier, but every highlighted room must be on that single continuous route. To compare plans, just sum the lengths of every corridor section opened — the plan with the lowest total length wins. Every highlighted room has to be included, and corridor pieces are counted once when opened. The specific layout and measurements are listed below.\n\nThere are 22 total locations, 27 corridor segments, and the highlighted exhibit rooms are 1 2 3 4 8 9 12 15 18 19 22.\nWe can open the corridor between 10 and 13 with length 440.0.\nWe can open the corridor between 10 and 18 with length 1409.0.\nWe can open the corridor between 21 and 8 with length 368.0.\nWe can open the corridor between 21 and 2 with length 315451.0.\nWe can open the corridor between 21 and 9 with length 840.0.\nWe can open the corridor between 22 and 19 with length 542.0.\nWe can open the corridor between 22 and 20 with length 221.0.\nWe can open the corridor between 22 and 4 with length 786.0.\nWe can open the corridor between 11 and 15 with length 527.0.\nWe can open the corridor between 6 and 7 with length 1878.0.\nWe can open the corridor between 6 and 3 with length 2177.0.\nWe can open the corridor between 7 and 9 with length 614.0.\nWe can open the corridor between 7 and 5 with length 1711.0.\nWe can open the corridor between 12 and 13 with length 514.0.\nWe can open the corridor between 12 and 16 with length 221.0.\nWe can open the corridor between 13 and 17 with length 449.0.\nWe can open the corridor between 14 and 15 with length 462.0.\nWe can open the corridor between 14 and 8 with length 893.0.\nWe can open the corridor between 14 and 19 with length 291.0.\nWe can open the corridor between 15 and 16 with length 1613.0.\nWe can open the corridor between 17 and 19 with length 1219.0.\nWe can open the corridor between 17 and 18 with length 530.0.\nWe can open the corridor between 3 and 4 with length 1691.0.\nWe can open the corridor between 4 and 1 with length 696.0.\nWe can open the corridor between 18 and 20 with length 1012.0.\nWe can open the corridor between 1 and 9 with length 1125.0.\nWe can open the corridor between 8 and 2 with length 315483.0.\nWe’ll use these measurements to choose the shortest set of corridors that connects all highlighted rooms.\n\nWhen you send back the plan, just use a tiny JSON snippet that lists which corridor segments to open. Something casual like this works fine:\n\n{\n \"solution\": [[\"room1\", \"room2\"], [\"room3\", \"room4\"]]\n}\n\nEach pair in the solution array is one corridor to unlock — the two entries are the room labels at the ends of that corridor. Think of it like filling out a short checklist of hallway connections: one pair per opened passage. This is just a sketch of the shape I want, not the actual answer.\n\nPlease make sure to use the exact identifiers from the instance input — don't rename them or invent new ones. \n- 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 22, "num_edges": 27, "edges": [ { "u": 10, "v": 13, "w": 440.0 }, { "u": 10, "v": 18, "w": 1409.0 }, { "u": 21, "v": 8, "w": 368.0 }, { "u": 21, "v": 2, "w": 315451.0 }, { "u": 21, "v": 9, "w": 840.0 }, { "u": 22, "v": 19, "w": 542.0 }, { "u": 22, "v": 20, "w": 221.0 }, { "u": 22, "v": 4, "w": 786.0 }, { "u": 11, "v": 15, "w": 527.0 }, { "u": 6, "v": 7, "w": 1878.0 }, { "u": 6, "v": 3, "w": 2177.0 }, { "u": 7, "v": 9, "w": 614.0 }, { "u": 7, "v": 5, "w": 1711.0 }, { "u": 12, "v": 13, "w": 514.0 }, { "u": 12, "v": 16, "w": 221.0 }, { "u": 13, "v": 17, "w": 449.0 }, { "u": 14, "v": 15, "w": 462.0 }, { "u": 14, "v": 8, "w": 893.0 }, { "u": 14, "v": 19, "w": 291.0 }, { "u": 15, "v": 16, "w": 1613.0 }, { "u": 17, "v": 19, "w": 1219.0 }, { "u": 17, "v": 18, "w": 530.0 }, { "u": 3, "v": 4, "w": 1691.0 }, { "u": 4, "v": 1, "w": 696.0 }, { "u": 18, "v": 20, "w": 1012.0 }, { "u": 1, "v": 9, "w": 1125.0 }, { "u": 8, "v": 2, "w": 315483.0 } ], "terminals": [ 1, 2, 3, 4, 8, 9, 12, 15, 18, 19, 22 ], "source_file": "I024.stp", "density": 0.11688311688311688, "viz_instance": "generated_data/STP/viz/STP_L/instance_0003.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0003.png" }, "solution": [ [ 19, 22 ], [ 4, 22 ], [ 12, 13 ], [ 13, 17 ], [ 14, 15 ], [ 8, 14 ], [ 14, 19 ], [ 17, 19 ], [ 17, 18 ], [ 3, 4 ], [ 1, 4 ], [ 1, 9 ], [ 2, 8 ] ], "obj": 324681.0, "instance_variant": { "problem_type": "STP", "num_nodes": 22, "num_edges": 27, "edges": [ { "u": 10, "v": 13, "w": 440.0 }, { "u": 10, "v": 18, "w": 1409.0 }, { "u": 21, "v": 8, "w": 368.0 }, { "u": 21, "v": 2, "w": 315451.0 }, { "u": 21, "v": 9, "w": 840.0 }, { "u": 22, "v": 19, "w": 542.0 }, { "u": 22, "v": 20, "w": 221.0 }, { "u": 22, "v": 4, "w": 786.0 }, { "u": 11, "v": 15, "w": 527.0 }, { "u": 6, "v": 7, "w": 1878.0 }, { "u": 6, "v": 3, "w": 2177.0 }, { "u": 7, "v": 9, "w": 614.0 }, { "u": 7, "v": 5, "w": 1711.0 }, { "u": 12, "v": 13, "w": 514.0 }, { "u": 12, "v": 16, "w": 221.0 }, { "u": 13, "v": 17, "w": 449.0 }, { "u": 14, "v": 15, "w": 462.0 }, { "u": 14, "v": 8, "w": 893.0 }, { "u": 14, "v": 19, "w": 291.0 }, { "u": 15, "v": 16, "w": 1613.0 }, { "u": 17, "v": 19, "w": 1219.0 }, { "u": 17, "v": 18, "w": 530.0 }, { "u": 3, "v": 4, "w": 1691.0 }, { "u": 4, "v": 1, "w": 696.0 }, { "u": 18, "v": 20, "w": 1012.0 }, { "u": 1, "v": 9, "w": 1125.0 }, { "u": 8, "v": 2, "w": 315483.0 } ], "density": 0.11688311688311688, "source_file": "I024.stp", "terminals": [ 1, 2, 3, 4, 8, 9, 12, 15, 18, 19, 22 ] }, "solution_variant": [ [ 19, 22 ], [ 4, 22 ], [ 12, 13 ], [ 13, 17 ], [ 14, 15 ], [ 8, 14 ], [ 14, 19 ], [ 17, 19 ], [ 17, 18 ], [ 3, 4 ], [ 1, 4 ], [ 1, 9 ], [ 2, 8 ] ], "context_index": 4, "input_format": "markdown_table", "input_index_base": 1 }, { "task_name": "STP", "problem_type": "STP", "instruction": "There’s a straightforward but picky task on the table: pick which irrigation ditches to build across a farm grid so that every highlighted crop plot is part of one continuous watering system, using corner junctions when useful. The smarter choices are the ones that keep the total digging short — just add up the lengths of all the built sections to see how much work they require. Every flagged plot must be connected to that single network, and each section is either built or not, counted only once. The concrete layout and which plots need water are listed below.\n\n# total_junctions=22\n# total_channel_sections=26\n# required_plot_nodes=F G O R\njunction_u,junction_v,section_length\nP,Q,807.0\nP,M,809.0\nP,N,971.0\nQ,I,2549.0\nV,R,639.0\nV,T,175.0\nK,U,850.0\nK,C,2124.0\nL,G,144.0\nL,T,1692.0\nM,H,375.0\nM,G,773.0\nN,R,1642.0\nN,O,974.0\nO,I,150.0\nJ,G,271796.0\nJ,H,271129.0\nC,A,185.0\nC,E,392.0\nD,A,421.0\nE,F,189.0\nF,H,822.0\nF,A,390.0\nS,U,1806.0\nB,A,1297.0\nT,U,744.0\n\nAlso, when you hand back the chosen ditch segments, please use this simple JSON shape so I (and any tools) can read it easily:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nThink of \"solution\" as just a list of built ditch sections — each item is a pair giving the two corner junctions that the section runs between. This example is just the shape I expect, not the actual plan — fill it with the actual pairs from the instance.\n\nAll identifiers must be used exactly as they appear in the instance input — no renaming and no new labels.\n- 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 22, "num_edges": 26, "edges": [ { "u": 16, "v": 17, "w": 807.0 }, { "u": 16, "v": 13, "w": 809.0 }, { "u": 16, "v": 14, "w": 971.0 }, { "u": 17, "v": 9, "w": 2549.0 }, { "u": 22, "v": 18, "w": 639.0 }, { "u": 22, "v": 20, "w": 175.0 }, { "u": 11, "v": 21, "w": 850.0 }, { "u": 11, "v": 3, "w": 2124.0 }, { "u": 12, "v": 7, "w": 144.0 }, { "u": 12, "v": 20, "w": 1692.0 }, { "u": 13, "v": 8, "w": 375.0 }, { "u": 13, "v": 7, "w": 773.0 }, { "u": 14, "v": 18, "w": 1642.0 }, { "u": 14, "v": 15, "w": 974.0 }, { "u": 15, "v": 9, "w": 150.0 }, { "u": 10, "v": 7, "w": 271796.0 }, { "u": 10, "v": 8, "w": 271129.0 }, { "u": 3, "v": 1, "w": 185.0 }, { "u": 3, "v": 5, "w": 392.0 }, { "u": 4, "v": 1, "w": 421.0 }, { "u": 5, "v": 6, "w": 189.0 }, { "u": 6, "v": 8, "w": 822.0 }, { "u": 6, "v": 1, "w": 390.0 }, { "u": 19, "v": 21, "w": 1806.0 }, { "u": 2, "v": 1, "w": 1297.0 }, { "u": 20, "v": 21, "w": 744.0 } ], "terminals": [ 6, 7, 15, 18 ], "source_file": "I007.stp", "density": 0.11255411255411256, "viz_instance": "generated_data/STP/viz/STP_L/instance_0004.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0004.png" }, "solution": [ [ 13, 16 ], [ 14, 16 ], [ 8, 13 ], [ 7, 13 ], [ 14, 18 ], [ 14, 15 ], [ 6, 8 ] ], "obj": 6366.0, "instance_variant": { "problem_type": "STP", "num_nodes": 22, "num_edges": 26, "edges": [ { "u": "P", "v": "Q", "w": 807.0 }, { "u": "P", "v": "M", "w": 809.0 }, { "u": "P", "v": "N", "w": 971.0 }, { "u": "Q", "v": "I", "w": 2549.0 }, { "u": "V", "v": "R", "w": 639.0 }, { "u": "V", "v": "T", "w": 175.0 }, { "u": "K", "v": "U", "w": 850.0 }, { "u": "K", "v": "C", "w": 2124.0 }, { "u": "L", "v": "G", "w": 144.0 }, { "u": "L", "v": "T", "w": 1692.0 }, { "u": "M", "v": "H", "w": 375.0 }, { "u": "M", "v": "G", "w": 773.0 }, { "u": "N", "v": "R", "w": 1642.0 }, { "u": "N", "v": "O", "w": 974.0 }, { "u": "O", "v": "I", "w": 150.0 }, { "u": "J", "v": "G", "w": 271796.0 }, { "u": "J", "v": "H", "w": 271129.0 }, { "u": "C", "v": "A", "w": 185.0 }, { "u": "C", "v": "E", "w": 392.0 }, { "u": "D", "v": "A", "w": 421.0 }, { "u": "E", "v": "F", "w": 189.0 }, { "u": "F", "v": "H", "w": 822.0 }, { "u": "F", "v": "A", "w": 390.0 }, { "u": "S", "v": "U", "w": 1806.0 }, { "u": "B", "v": "A", "w": 1297.0 }, { "u": "T", "v": "U", "w": 744.0 } ], "density": 0.11255411255411256, "source_file": "I007.stp", "terminals": [ "F", "G", "O", "R" ] }, "solution_variant": [ [ "M", "P" ], [ "N", "P" ], [ "H", "M" ], [ "G", "M" ], [ "N", "R" ], [ "N", "O" ], [ "F", "H" ] ], "context_index": 5, "input_format": "csv", "input_index_base": "names" }, { "task_name": "STP", "problem_type": "STP", "instruction": "There’s a festival coming, and the organizers need to figure out which temporary walkways to lay across the lawns so the marked vendor booths form one connected network; existing plazas can be used as crossroads to make connections shorter. A good plan links every booth (nothing left disconnected), avoids needless duplicate stretches, and minimizes the total length of walkway installed — simply total the lengths of all chosen pieces. The plan and exact distances are shown below.\n\n{\n \"total_locations_count\": 27,\n \"potential_walkway_count\": 35,\n \"edges\": [\n {\n \"endpoint_a\": \"R\",\n \"endpoint_b\": \"I\",\n \"segment_length\": 200281.0\n },\n {\n \"endpoint_a\": \"R\",\n \"endpoint_b\": \"L\",\n \"segment_length\": 201621.0\n },\n {\n \"endpoint_a\": \"S\",\n \"endpoint_b\": \"F\",\n \"segment_length\": 187992.0\n },\n {\n \"endpoint_a\": \"S\",\n \"endpoint_b\": \"E\",\n \"segment_length\": 187149.0\n },\n {\n \"endpoint_a\": \"A\",\n \"endpoint_b\": \"V\",\n \"segment_length\": 565.0\n },\n {\n \"endpoint_a\": \"T\",\n \"endpoint_b\": \"U\",\n \"segment_length\": 253.0\n },\n {\n \"endpoint_a\": \"T\",\n \"endpoint_b\": \"Y\",\n \"segment_length\": 138.0\n },\n {\n \"endpoint_a\": \"T\",\n \"endpoint_b\": \"Q\",\n \"segment_length\": 447.0\n },\n {\n \"endpoint_a\": \"U\",\n \"endpoint_b\": \"Z\",\n \"segment_length\": 148.0\n },\n {\n \"endpoint_a\": \"U\",\n \"endpoint_b\": \"P\",\n \"segment_length\": 448.0\n },\n {\n \"endpoint_a\": \"B\",\n \"endpoint_b\": \"C\",\n \"segment_length\": 1030.0\n },\n {\n \"endpoint_a\": \"B\",\n \"endpoint_b\": \"D\",\n \"segment_length\": 662.0\n },\n {\n \"endpoint_a\": \"C\",\n \"endpoint_b\": \"X\",\n \"segment_length\": 665.0\n },\n {\n \"endpoint_a\": \"C\",\n \"endpoint_b\": \"K\",\n \"segment_length\": 1220.0\n },\n {\n \"endpoint_a\": \"D\",\n \"endpoint_b\": \"Y\",\n \"segment_length\": 92.0\n },\n {\n \"endpoint_a\": \"D\",\n \"endpoint_b\": \"H\",\n \"segment_length\": 1547.0\n },\n {\n \"endpoint_a\": \"E\",\n \"endpoint_b\": \"AA\",\n \"segment_length\": 1571.0\n },\n {\n \"endpoint_a\": \"E\",\n \"endpoint_b\": \"G\",\n \"segment_length\": 1663.0\n },\n {\n \"endpoint_a\": \"F\",\n \"endpoint_b\": \"G\",\n \"segment_length\": 667.0\n },\n {\n \"endpoint_a\": \"F\",\n \"endpoint_b\": \"H\",\n \"segment_length\": 227.0\n },\n {\n \"endpoint_a\": \"G\",\n \"endpoint_b\": \"V\",\n \"segment_length\": 255.0\n },\n {\n \"endpoint_a\": \"H\",\n \"endpoint_b\": \"V\",\n \"segment_length\": 677.0\n },\n {\n \"endpoint_a\": \"I\",\n \"endpoint_b\": \"J\",\n \"segment_length\": 1018.0\n },\n {\n \"endpoint_a\": \"I\",\n \"endpoint_b\": \"K\",\n \"segment_length\": 220.0\n },\n {\n \"endpoint_a\": \"J\",\n \"endpoint_b\": \"W\",\n \"segment_length\": 212.0\n },\n {\n \"endpoint_a\": \"J\",\n \"endpoint_b\": \"M\",\n \"segment_length\": 227.0\n },\n {\n \"endpoint_a\": \"K\",\n \"endpoint_b\": \"W\",\n \"segment_length\": 1016.0\n },\n {\n \"endpoint_a\": \"L\",\n \"endpoint_b\": \"X\",\n \"segment_length\": 505.0\n },\n {\n \"endpoint_a\": \"L\",\n \"endpoint_b\": \"N\",\n \"segment_length\": 297.0\n },\n {\n \"endpoint_a\": \"M\",\n \"endpoint_b\": \"N\",\n \"segment_length\": 1648.0\n },\n {\n \"endpoint_a\": \"O\",\n \"endpoint_b\": \"W\",\n \"segment_length\": 742.0\n },\n {\n \"endpoint_a\": \"X\",\n \"endpoint_b\": \"Q\",\n \"segment_length\": 353.0\n },\n {\n \"endpoint_a\": \"P\",\n \"endpoint_b\": \"Q\",\n \"segment_length\": 272.0\n },\n {\n \"endpoint_a\": \"Y\",\n \"endpoint_b\": \"Z\",\n \"segment_length\": 247.0\n },\n {\n \"endpoint_a\": \"Z\",\n \"endpoint_b\": \"AA\",\n \"segment_length\": 935.0\n }\n ],\n \"vendor_booth_list\": [\n \"B\",\n \"G\",\n \"J\",\n \"O\",\n \"Q\"\n ]\n}\n\nJust so we're on the same page, when you give the final plan please use this simple JSON layout:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nHere \"solution\" is a list of walkway segments to put down. Each pair [X, Y] is the two labeled spots (a vendor booth or an existing plaza/crossroad) that should be connected by that piece of path. Treat it like filling out a little checklist: list each connection you want us to build.\n\nThis is only a sketch of the shape I expect the answer to take — not the actual plan itself.\n\nPlease make sure to use the exact identifiers from the instance input, with no renaming and no new labels. \n- 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 27, "num_edges": 35, "edges": [ { "u": 18, "v": 9, "w": 200281.0 }, { "u": 18, "v": 12, "w": 201621.0 }, { "u": 19, "v": 6, "w": 187992.0 }, { "u": 19, "v": 5, "w": 187149.0 }, { "u": 1, "v": 22, "w": 565.0 }, { "u": 20, "v": 21, "w": 253.0 }, { "u": 20, "v": 25, "w": 138.0 }, { "u": 20, "v": 17, "w": 447.0 }, { "u": 21, "v": 26, "w": 148.0 }, { "u": 21, "v": 16, "w": 448.0 }, { "u": 2, "v": 3, "w": 1030.0 }, { "u": 2, "v": 4, "w": 662.0 }, { "u": 3, "v": 24, "w": 665.0 }, { "u": 3, "v": 11, "w": 1220.0 }, { "u": 4, "v": 25, "w": 92.0 }, { "u": 4, "v": 8, "w": 1547.0 }, { "u": 5, "v": 27, "w": 1571.0 }, { "u": 5, "v": 7, "w": 1663.0 }, { "u": 6, "v": 7, "w": 667.0 }, { "u": 6, "v": 8, "w": 227.0 }, { "u": 7, "v": 22, "w": 255.0 }, { "u": 8, "v": 22, "w": 677.0 }, { "u": 9, "v": 10, "w": 1018.0 }, { "u": 9, "v": 11, "w": 220.0 }, { "u": 10, "v": 23, "w": 212.0 }, { "u": 10, "v": 13, "w": 227.0 }, { "u": 11, "v": 23, "w": 1016.0 }, { "u": 12, "v": 24, "w": 505.0 }, { "u": 12, "v": 14, "w": 297.0 }, { "u": 13, "v": 14, "w": 1648.0 }, { "u": 15, "v": 23, "w": 742.0 }, { "u": 24, "v": 17, "w": 353.0 }, { "u": 16, "v": 17, "w": 272.0 }, { "u": 25, "v": 26, "w": 247.0 }, { "u": 26, "v": 27, "w": 935.0 } ], "terminals": [ 2, 7, 10, 15, 17 ], "source_file": "I031.stp", "density": 0.09971509971509972, "viz_instance": "generated_data/STP/viz/STP_L/instance_0005.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0005.png" }, "solution": [ [ 20, 25 ], [ 17, 20 ], [ 2, 4 ], [ 4, 25 ], [ 4, 8 ], [ 6, 7 ], [ 6, 8 ], [ 10, 23 ], [ 10, 13 ], [ 12, 24 ], [ 12, 14 ], [ 13, 14 ], [ 15, 23 ], [ 17, 24 ] ], "obj": 7764.0, "instance_variant": { "problem_type": "STP", "num_nodes": 27, "num_edges": 35, "edges": [ { "u": "R", "v": "I", "w": 200281.0 }, { "u": "R", "v": "L", "w": 201621.0 }, { "u": "S", "v": "F", "w": 187992.0 }, { "u": "S", "v": "E", "w": 187149.0 }, { "u": "A", "v": "V", "w": 565.0 }, { "u": "T", "v": "U", "w": 253.0 }, { "u": "T", "v": "Y", "w": 138.0 }, { "u": "T", "v": "Q", "w": 447.0 }, { "u": "U", "v": "Z", "w": 148.0 }, { "u": "U", "v": "P", "w": 448.0 }, { "u": "B", "v": "C", "w": 1030.0 }, { "u": "B", "v": "D", "w": 662.0 }, { "u": "C", "v": "X", "w": 665.0 }, { "u": "C", "v": "K", "w": 1220.0 }, { "u": "D", "v": "Y", "w": 92.0 }, { "u": "D", "v": "H", "w": 1547.0 }, { "u": "E", "v": "AA", "w": 1571.0 }, { "u": "E", "v": "G", "w": 1663.0 }, { "u": "F", "v": "G", "w": 667.0 }, { "u": "F", "v": "H", "w": 227.0 }, { "u": "G", "v": "V", "w": 255.0 }, { "u": "H", "v": "V", "w": 677.0 }, { "u": "I", "v": "J", "w": 1018.0 }, { "u": "I", "v": "K", "w": 220.0 }, { "u": "J", "v": "W", "w": 212.0 }, { "u": "J", "v": "M", "w": 227.0 }, { "u": "K", "v": "W", "w": 1016.0 }, { "u": "L", "v": "X", "w": 505.0 }, { "u": "L", "v": "N", "w": 297.0 }, { "u": "M", "v": "N", "w": 1648.0 }, { "u": "O", "v": "W", "w": 742.0 }, { "u": "X", "v": "Q", "w": 353.0 }, { "u": "P", "v": "Q", "w": 272.0 }, { "u": "Y", "v": "Z", "w": 247.0 }, { "u": "Z", "v": "AA", "w": 935.0 } ], "density": 0.09971509971509972, "source_file": "I031.stp", "terminals": [ "B", "G", "J", "O", "Q" ] }, "solution_variant": [ [ "T", "Y" ], [ "Q", "T" ], [ "B", "D" ], [ "D", "Y" ], [ "D", "H" ], [ "F", "G" ], [ "F", "H" ], [ "J", "W" ], [ "J", "M" ], [ "L", "X" ], [ "L", "N" ], [ "M", "N" ], [ "O", "W" ], [ "Q", "X" ] ], "context_index": 6, "input_format": "json", "input_index_base": "names" }, { "task_name": "STP", "problem_type": "STP", "instruction": "There’s a neighborhood project with poles and service panels laid out, and the challenge is to choose which conduit runs to build so every panel is part of a single, unbroken electrical path. Crews can drop in extra junction boxes to make the connections cleaner, and the measure of success is straightforward: the sum of the costs of the chosen conduit runs should be as small as it can be. No required panel can be left disconnected, and adding needless duplicate runs just increases cost. The exact map and prices are listed below.\n\nThe site map lists 21 locations, 25 available conduit runs, and required service panels 2 5 16 19.\nCrews can build a conduit between 0 and 14 for 3024.0.\nCrews can build a conduit between 1 and 5 for 1211.0.\nCrews can build a conduit between 2 and 4 for 597.0.\nCrews can build a conduit between 3 and 4 for 1869.0.\nCrews can build a conduit between 3 and 16 for 219.0.\nCrews can build a conduit between 3 and 19 for 59.0.\nCrews can build a conduit between 4 and 8 for 1135.0.\nCrews can build a conduit between 5 and 13 for 203881.0.\nCrews can build a conduit between 5 and 17 for 952.0.\nCrews can build a conduit between 6 and 13 for 203795.0.\nCrews can build a conduit between 7 and 8 for 1387.0.\nCrews can build a conduit between 7 and 20 for 554.0.\nCrews can build a conduit between 7 and 9 for 621.0.\nCrews can build a conduit between 8 and 12 for 1832.0.\nCrews can build a conduit between 9 and 18 for 563.0.\nCrews can build a conduit between 9 and 10 for 1838.0.\nCrews can build a conduit between 10 and 11 for 913.0.\nCrews can build a conduit between 10 and 12 for 903.0.\nCrews can build a conduit between 11 and 12 for 152.0.\nCrews can build a conduit between 11 and 14 for 1735.0.\nCrews can build a conduit between 14 and 15 for 1490.0.\nCrews can build a conduit between 17 and 18 for 485.0.\nCrews can build a conduit between 17 and 19 for 523.0.\nCrews can build a conduit between 18 and 20 for 598.0.\nCrews can build a conduit between 19 and 20 for 498.0.\nNo required panel may be left disconnected; choose runs that minimize the total installation cost.\n\nIf you want to hand over the chosen runs in a tidy, machine-friendly way, just stick to a tiny JSON object like this:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nHere \"solution\" is a list of conduit runs to build — each inner pair is a connection between two poles/panels (use the exact node IDs from the map). Think of it like a short shopping list: each [u, v] is one run you want the crew to lay down. This block is just a sketch of the shape I expect, not the actual final answer.\n\nPlease make sure every identifier you use matches the instance input exactly — no renaming and no new labels.\n- 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 21, "num_edges": 25, "edges": [ { "u": 1, "v": 15, "w": 3024.0 }, { "u": 2, "v": 6, "w": 1211.0 }, { "u": 3, "v": 5, "w": 597.0 }, { "u": 4, "v": 5, "w": 1869.0 }, { "u": 4, "v": 17, "w": 219.0 }, { "u": 4, "v": 20, "w": 59.0 }, { "u": 5, "v": 9, "w": 1135.0 }, { "u": 6, "v": 14, "w": 203881.0 }, { "u": 6, "v": 18, "w": 952.0 }, { "u": 7, "v": 14, "w": 203795.0 }, { "u": 8, "v": 9, "w": 1387.0 }, { "u": 8, "v": 21, "w": 554.0 }, { "u": 8, "v": 10, "w": 621.0 }, { "u": 9, "v": 13, "w": 1832.0 }, { "u": 10, "v": 19, "w": 563.0 }, { "u": 10, "v": 11, "w": 1838.0 }, { "u": 11, "v": 12, "w": 913.0 }, { "u": 11, "v": 13, "w": 903.0 }, { "u": 12, "v": 13, "w": 152.0 }, { "u": 12, "v": 15, "w": 1735.0 }, { "u": 15, "v": 16, "w": 1490.0 }, { "u": 18, "v": 19, "w": 485.0 }, { "u": 18, "v": 20, "w": 523.0 }, { "u": 19, "v": 21, "w": 598.0 }, { "u": 20, "v": 21, "w": 498.0 } ], "terminals": [ 3, 6, 17, 20 ], "source_file": "I052.stp", "density": 0.11904761904761904, "viz_instance": "generated_data/STP/viz/STP_L/instance_0006.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0006.png" }, "solution": [ [ 3, 5 ], [ 4, 5 ], [ 4, 17 ], [ 4, 20 ], [ 6, 18 ], [ 18, 20 ] ], "obj": 4219.0, "instance_variant": { "problem_type": "STP", "num_nodes": 21, "num_edges": 25, "edges": [ { "u": 0, "v": 14, "w": 3024.0 }, { "u": 1, "v": 5, "w": 1211.0 }, { "u": 2, "v": 4, "w": 597.0 }, { "u": 3, "v": 4, "w": 1869.0 }, { "u": 3, "v": 16, "w": 219.0 }, { "u": 3, "v": 19, "w": 59.0 }, { "u": 4, "v": 8, "w": 1135.0 }, { "u": 5, "v": 13, "w": 203881.0 }, { "u": 5, "v": 17, "w": 952.0 }, { "u": 6, "v": 13, "w": 203795.0 }, { "u": 7, "v": 8, "w": 1387.0 }, { "u": 7, "v": 20, "w": 554.0 }, { "u": 7, "v": 9, "w": 621.0 }, { "u": 8, "v": 12, "w": 1832.0 }, { "u": 9, "v": 18, "w": 563.0 }, { "u": 9, "v": 10, "w": 1838.0 }, { "u": 10, "v": 11, "w": 913.0 }, { "u": 10, "v": 12, "w": 903.0 }, { "u": 11, "v": 12, "w": 152.0 }, { "u": 11, "v": 14, "w": 1735.0 }, { "u": 14, "v": 15, "w": 1490.0 }, { "u": 17, "v": 18, "w": 485.0 }, { "u": 17, "v": 19, "w": 523.0 }, { "u": 18, "v": 20, "w": 598.0 }, { "u": 19, "v": 20, "w": 498.0 } ], "density": 0.11904761904761904, "source_file": "I052.stp", "terminals": [ 2, 5, 16, 19 ] }, "solution_variant": [ [ 2, 4 ], [ 3, 4 ], [ 3, 16 ], [ 3, 19 ], [ 5, 17 ], [ 17, 19 ] ], "context_index": 7, "input_format": "markdown_table", "input_index_base": 0 }, { "task_name": "STP", "problem_type": "STP", "instruction": "We’re planning a simple maintenance route: pick a set of trail segments so that all the flagged viewpoints end up connected by trails, and it’s okay to route through clearings that aren’t viewpoints. What makes one plan better than another is how much trail needs work — add up the lengths of every segment kept, and the smaller that sum, the better the plan. All marked viewpoints must be on that continuous trail system, intermediate clearings may be used to bridge gaps, and each chosen trail piece contributes its length only once. The exact map and numbers follow below.\n\nThe map we're using has 24 locations and 34 trail segments; the flagged viewpoints to connect are 2 3 5 10 13 17 19 21 22.\nKeep the segment between 8 and 7 (length 736.0).\nKeep the segment between 8 and 0 (length 1305.0).\nKeep the segment between 8 and 12 (length 2612.0).\nKeep the segment between 9 and 10 (length 1533.0).\nKeep the segment between 9 and 14 (length 2144.0).\nKeep the segment between 9 and 21 (length 2385.0).\nKeep the segment between 10 and 15 (length 3746.0).\nKeep the segment between 10 and 21 (length 1068.0).\nKeep the segment between 10 and 23 (length 2538.0).\nKeep the segment between 21 and 22 (length 1558.0).\nKeep the segment between 22 and 16 (length 2350.0).\nKeep the segment between 22 and 17 (length 327.0).\nKeep the segment between 23 and 16 (length 2570.0).\nKeep the segment between 23 and 3 (length 3739.0).\nKeep the segment between 11 and 6 (length 2821.0).\nKeep the segment between 11 and 16 (length 4309.0).\nKeep the segment between 11 and 19 (length 4311.0).\nKeep the segment between 12 and 7 (length 2893.0).\nKeep the segment between 13 and 7 (length 1134.0).\nKeep the segment between 13 and 18 (length 5563.0).\nKeep the segment between 0 and 1 (length 407.0).\nKeep the segment between 0 and 7 (length 1727.0).\nKeep the segment between 0 and 5 (length 444.0).\nKeep the segment between 1 and 5 (length 407.0).\nKeep the segment between 1 and 6 (length 927.0).\nKeep the segment between 2 and 3 (length 227554.0).\nKeep the segment between 2 and 4 (length 228495.0).\nKeep the segment between 3 and 4 (length 1434.0).\nKeep the segment between 18 and 19 (length 537.0).\nKeep the segment between 19 and 20 (length 113.0).\nKeep the segment between 14 and 15 (length 2101.0).\nKeep the segment between 20 and 17 (length 2320.0).\nKeep the segment between 16 and 6 (length 5322.0).\nKeep the segment between 4 and 5 (length 568.0).\nWe'll count each chosen segment's length once and seek the smallest total while ensuring all 2 3 5 10 13 17 19 21 22 are connected.\n\nAlso, when you send back the selected trail pieces, please use this simple JSON layout so it's easy to parse:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nHere the idea is straightforward: \"solution\" is a list of trail segments, and each segment is written as a pair [endpoint1, endpoint2] using the node identifiers from the map. Think of it like filling out a short form — each line is just one piece of trail you want to keep. This JSON is just the expected shape (a sketch), not the final contents you should submit.\n\nPlease use the identifiers exactly as they appear in the instance input — do not rename them or introduce new labels. \n- 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\".", "instance": { "problem_type": "STP", "num_nodes": 24, "num_edges": 34, "edges": [ { "u": 9, "v": 8, "w": 736.0 }, { "u": 9, "v": 1, "w": 1305.0 }, { "u": 9, "v": 13, "w": 2612.0 }, { "u": 10, "v": 11, "w": 1533.0 }, { "u": 10, "v": 15, "w": 2144.0 }, { "u": 10, "v": 22, "w": 2385.0 }, { "u": 11, "v": 16, "w": 3746.0 }, { "u": 11, "v": 22, "w": 1068.0 }, { "u": 11, "v": 24, "w": 2538.0 }, { "u": 22, "v": 23, "w": 1558.0 }, { "u": 23, "v": 17, "w": 2350.0 }, { "u": 23, "v": 18, "w": 327.0 }, { "u": 24, "v": 17, "w": 2570.0 }, { "u": 24, "v": 4, "w": 3739.0 }, { "u": 12, "v": 7, "w": 2821.0 }, { "u": 12, "v": 17, "w": 4309.0 }, { "u": 12, "v": 20, "w": 4311.0 }, { "u": 13, "v": 8, "w": 2893.0 }, { "u": 14, "v": 8, "w": 1134.0 }, { "u": 14, "v": 19, "w": 5563.0 }, { "u": 1, "v": 2, "w": 407.0 }, { "u": 1, "v": 8, "w": 1727.0 }, { "u": 1, "v": 6, "w": 444.0 }, { "u": 2, "v": 6, "w": 407.0 }, { "u": 2, "v": 7, "w": 927.0 }, { "u": 3, "v": 4, "w": 227554.0 }, { "u": 3, "v": 5, "w": 228495.0 }, { "u": 4, "v": 5, "w": 1434.0 }, { "u": 19, "v": 20, "w": 537.0 }, { "u": 20, "v": 21, "w": 113.0 }, { "u": 15, "v": 16, "w": 2101.0 }, { "u": 21, "v": 18, "w": 2320.0 }, { "u": 17, "v": 7, "w": 5322.0 }, { "u": 5, "v": 6, "w": 568.0 } ], "terminals": [ 3, 4, 6, 11, 14, 18, 20, 22, 23 ], "source_file": "I037.stp", "density": 0.12318840579710146, "viz_instance": "generated_data/STP/viz/STP_L/instance_0007.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0007.png" }, "solution": [ [ 11, 22 ], [ 22, 23 ], [ 18, 23 ], [ 8, 14 ], [ 14, 19 ], [ 1, 8 ], [ 1, 6 ], [ 3, 4 ], [ 4, 5 ], [ 19, 20 ], [ 20, 21 ], [ 18, 21 ], [ 5, 6 ] ], "obj": 244347.0, "instance_variant": { "problem_type": "STP", "num_nodes": 24, "num_edges": 34, "edges": [ { "u": 8, "v": 7, "w": 736.0 }, { "u": 8, "v": 0, "w": 1305.0 }, { "u": 8, "v": 12, "w": 2612.0 }, { "u": 9, "v": 10, "w": 1533.0 }, { "u": 9, "v": 14, "w": 2144.0 }, { "u": 9, "v": 21, "w": 2385.0 }, { "u": 10, "v": 15, "w": 3746.0 }, { "u": 10, "v": 21, "w": 1068.0 }, { "u": 10, "v": 23, "w": 2538.0 }, { "u": 21, "v": 22, "w": 1558.0 }, { "u": 22, "v": 16, "w": 2350.0 }, { "u": 22, "v": 17, "w": 327.0 }, { "u": 23, "v": 16, "w": 2570.0 }, { "u": 23, "v": 3, "w": 3739.0 }, { "u": 11, "v": 6, "w": 2821.0 }, { "u": 11, "v": 16, "w": 4309.0 }, { "u": 11, "v": 19, "w": 4311.0 }, { "u": 12, "v": 7, "w": 2893.0 }, { "u": 13, "v": 7, "w": 1134.0 }, { "u": 13, "v": 18, "w": 5563.0 }, { "u": 0, "v": 1, "w": 407.0 }, { "u": 0, "v": 7, "w": 1727.0 }, { "u": 0, "v": 5, "w": 444.0 }, { "u": 1, "v": 5, "w": 407.0 }, { "u": 1, "v": 6, "w": 927.0 }, { "u": 2, "v": 3, "w": 227554.0 }, { "u": 2, "v": 4, "w": 228495.0 }, { "u": 3, "v": 4, "w": 1434.0 }, { "u": 18, "v": 19, "w": 537.0 }, { "u": 19, "v": 20, "w": 113.0 }, { "u": 14, "v": 15, "w": 2101.0 }, { "u": 20, "v": 17, "w": 2320.0 }, { "u": 16, "v": 6, "w": 5322.0 }, { "u": 4, "v": 5, "w": 568.0 } ], "density": 0.12318840579710146, "source_file": "I037.stp", "terminals": [ 2, 3, 5, 10, 13, 17, 19, 21, 22 ] }, "solution_variant": [ [ 10, 21 ], [ 21, 22 ], [ 17, 22 ], [ 7, 13 ], [ 13, 18 ], [ 0, 7 ], [ 0, 5 ], [ 2, 3 ], [ 3, 4 ], [ 18, 19 ], [ 19, 20 ], [ 17, 20 ], [ 4, 5 ] ], "context_index": 8, "input_format": "nl", "input_index_base": 0 }, { "task_name": "STP", "problem_type": "STP", "instruction": "Someone at city hall has to draw up a repair plan so all the designated school entrances are connected by repaired sidewalks. It’s allowed to fix sidewalks at other street corners to let entrances link through those points instead of fixing direct paths every time. A smarter repair plan is the cheaper one that still gets every entrance into the same repaired web — the total expense is simply the sum of the individual repair prices for the chosen sidewalk pieces. No listed entrance can be left out, and repaired pieces are counted once in that total. The specifics and numbers are shown below.\n\n{\n \"total_intersections\": 29,\n \"total_sidewalk_segments\": 38,\n \"edges\": [\n {\n \"endpoint_a\": 27,\n \"endpoint_b\": 26,\n \"repair_cost\": 1135.0\n },\n {\n \"endpoint_a\": 27,\n \"endpoint_b\": 28,\n \"repair_cost\": 226.0\n },\n {\n \"endpoint_a\": 14,\n \"endpoint_b\": 4,\n \"repair_cost\": 964.0\n },\n {\n \"endpoint_a\": 14,\n \"endpoint_b\": 16,\n \"repair_cost\": 707.0\n },\n {\n \"endpoint_a\": 14,\n \"endpoint_b\": 1,\n \"repair_cost\": 1386.0\n },\n {\n \"endpoint_a\": 15,\n \"endpoint_b\": 5,\n \"repair_cost\": 517.0\n },\n {\n \"endpoint_a\": 15,\n \"endpoint_b\": 4,\n \"repair_cost\": 1134.0\n },\n {\n \"endpoint_a\": 15,\n \"endpoint_b\": 8,\n \"repair_cost\": 1376.0\n },\n {\n \"endpoint_a\": 16,\n \"endpoint_b\": 2,\n \"repair_cost\": 492.0\n },\n {\n \"endpoint_a\": 16,\n \"endpoint_b\": 17,\n \"repair_cost\": 165.0\n },\n {\n \"endpoint_a\": 17,\n \"endpoint_b\": 18,\n \"repair_cost\": 1155.0\n },\n {\n \"endpoint_a\": 17,\n \"endpoint_b\": 3,\n \"repair_cost\": 790.0\n },\n {\n \"endpoint_a\": 19,\n \"endpoint_b\": 20,\n \"repair_cost\": 500.0\n },\n {\n \"endpoint_a\": 19,\n \"endpoint_b\": 3,\n \"repair_cost\": 1015.0\n },\n {\n \"endpoint_a\": 19,\n \"endpoint_b\": 11,\n \"repair_cost\": 828.0\n },\n {\n \"endpoint_a\": 20,\n \"endpoint_b\": 5,\n \"repair_cost\": 331.0\n },\n {\n \"endpoint_a\": 20,\n \"endpoint_b\": 23,\n \"repair_cost\": 1079.0\n },\n {\n \"endpoint_a\": 21,\n \"endpoint_b\": 22,\n \"repair_cost\": 53.0\n },\n {\n \"endpoint_a\": 21,\n \"endpoint_b\": 10,\n \"repair_cost\": 339.0\n },\n {\n \"endpoint_a\": 22,\n \"endpoint_b\": 11,\n \"repair_cost\": 338.0\n },\n {\n \"endpoint_a\": 22,\n \"endpoint_b\": 26,\n \"repair_cost\": 1076.0\n },\n {\n \"endpoint_a\": 0,\n \"endpoint_b\": 1,\n \"repair_cost\": 466.0\n },\n {\n \"endpoint_a\": 0,\n \"endpoint_b\": 9,\n \"repair_cost\": 314428.0\n },\n {\n \"endpoint_a\": 2,\n \"endpoint_b\": 9,\n \"repair_cost\": 314574.0\n },\n {\n \"endpoint_a\": 10,\n \"endpoint_b\": 11,\n \"repair_cost\": 56.0\n },\n {\n \"endpoint_a\": 3,\n \"endpoint_b\": 4,\n \"repair_cost\": 1089.0\n },\n {\n \"endpoint_a\": 23,\n \"endpoint_b\": 12,\n \"repair_cost\": 254.0\n },\n {\n \"endpoint_a\": 23,\n \"endpoint_b\": 25,\n \"repair_cost\": 794.0\n },\n {\n \"endpoint_a\": 12,\n \"endpoint_b\": 13,\n \"repair_cost\": 318.0\n },\n {\n \"endpoint_a\": 12,\n \"endpoint_b\": 7,\n \"repair_cost\": 121.0\n },\n {\n \"endpoint_a\": 13,\n \"endpoint_b\": 24,\n \"repair_cost\": 1045.0\n },\n {\n \"endpoint_a\": 13,\n \"endpoint_b\": 6,\n \"repair_cost\": 1199.0\n },\n {\n \"endpoint_a\": 13,\n \"endpoint_b\": 7,\n \"repair_cost\": 438.0\n },\n {\n \"endpoint_a\": 28,\n \"endpoint_b\": 6,\n \"repair_cost\": 1611.0\n },\n {\n \"endpoint_a\": 24,\n \"endpoint_b\": 25,\n \"repair_cost\": 329.0\n },\n {\n \"endpoint_a\": 24,\n \"endpoint_b\": 6,\n \"repair_cost\": 157.0\n },\n {\n \"endpoint_a\": 25,\n \"endpoint_b\": 26,\n \"repair_cost\": 864.0\n },\n {\n \"endpoint_a\": 7,\n \"endpoint_b\": 8,\n \"repair_cost\": 346.0\n }\n ],\n \"school_entrances\": [\n 0,\n 2,\n 3,\n 5,\n 8,\n 9,\n 11,\n 13,\n 15,\n 16,\n 17,\n 18,\n 20,\n 21\n ]\n}\n\nAlso, when you hand the repair plan back, please use this simple JSON layout so it's easy to parse:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nHere \"solution\" is just a list of sidewalk pieces to fix. Each pair like [u1, v1] means \"repair the path between corner u1 and corner v1\" — think of u1 and v1 as the labels the city used on the map. This JSON is only a sketch of the shape I expect, not the actual repaired-edges answer.\n\nPlease make sure all identifiers in your final list match the instance input exactly — don't rename them or make up new labels. \n- 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 29, "num_edges": 38, "edges": [ { "u": 28, "v": 27, "w": 1135.0 }, { "u": 28, "v": 29, "w": 226.0 }, { "u": 15, "v": 5, "w": 964.0 }, { "u": 15, "v": 17, "w": 707.0 }, { "u": 15, "v": 2, "w": 1386.0 }, { "u": 16, "v": 6, "w": 517.0 }, { "u": 16, "v": 5, "w": 1134.0 }, { "u": 16, "v": 9, "w": 1376.0 }, { "u": 17, "v": 3, "w": 492.0 }, { "u": 17, "v": 18, "w": 165.0 }, { "u": 18, "v": 19, "w": 1155.0 }, { "u": 18, "v": 4, "w": 790.0 }, { "u": 20, "v": 21, "w": 500.0 }, { "u": 20, "v": 4, "w": 1015.0 }, { "u": 20, "v": 12, "w": 828.0 }, { "u": 21, "v": 6, "w": 331.0 }, { "u": 21, "v": 24, "w": 1079.0 }, { "u": 22, "v": 23, "w": 53.0 }, { "u": 22, "v": 11, "w": 339.0 }, { "u": 23, "v": 12, "w": 338.0 }, { "u": 23, "v": 27, "w": 1076.0 }, { "u": 1, "v": 2, "w": 466.0 }, { "u": 1, "v": 10, "w": 314428.0 }, { "u": 3, "v": 10, "w": 314574.0 }, { "u": 11, "v": 12, "w": 56.0 }, { "u": 4, "v": 5, "w": 1089.0 }, { "u": 24, "v": 13, "w": 254.0 }, { "u": 24, "v": 26, "w": 794.0 }, { "u": 13, "v": 14, "w": 318.0 }, { "u": 13, "v": 8, "w": 121.0 }, { "u": 14, "v": 25, "w": 1045.0 }, { "u": 14, "v": 7, "w": 1199.0 }, { "u": 14, "v": 8, "w": 438.0 }, { "u": 29, "v": 7, "w": 1611.0 }, { "u": 25, "v": 26, "w": 329.0 }, { "u": 25, "v": 7, "w": 157.0 }, { "u": 26, "v": 27, "w": 864.0 }, { "u": 8, "v": 9, "w": 346.0 } ], "terminals": [ 1, 3, 4, 6, 9, 10, 12, 14, 16, 17, 18, 19, 21, 22 ], "source_file": "I050.stp", "density": 0.09359605911330049, "viz_instance": "generated_data/STP/viz/STP_L/instance_0008.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0008.png" }, "solution": [ [ 15, 17 ], [ 2, 15 ], [ 6, 16 ], [ 3, 17 ], [ 17, 18 ], [ 18, 19 ], [ 4, 18 ], [ 20, 21 ], [ 4, 20 ], [ 12, 20 ], [ 6, 21 ], [ 21, 24 ], [ 22, 23 ], [ 12, 23 ], [ 1, 2 ], [ 1, 10 ], [ 13, 24 ], [ 13, 14 ], [ 8, 13 ], [ 8, 9 ] ], "obj": 325289.0, "instance_variant": { "problem_type": "STP", "num_nodes": 29, "num_edges": 38, "edges": [ { "u": 27, "v": 26, "w": 1135.0 }, { "u": 27, "v": 28, "w": 226.0 }, { "u": 14, "v": 4, "w": 964.0 }, { "u": 14, "v": 16, "w": 707.0 }, { "u": 14, "v": 1, "w": 1386.0 }, { "u": 15, "v": 5, "w": 517.0 }, { "u": 15, "v": 4, "w": 1134.0 }, { "u": 15, "v": 8, "w": 1376.0 }, { "u": 16, "v": 2, "w": 492.0 }, { "u": 16, "v": 17, "w": 165.0 }, { "u": 17, "v": 18, "w": 1155.0 }, { "u": 17, "v": 3, "w": 790.0 }, { "u": 19, "v": 20, "w": 500.0 }, { "u": 19, "v": 3, "w": 1015.0 }, { "u": 19, "v": 11, "w": 828.0 }, { "u": 20, "v": 5, "w": 331.0 }, { "u": 20, "v": 23, "w": 1079.0 }, { "u": 21, "v": 22, "w": 53.0 }, { "u": 21, "v": 10, "w": 339.0 }, { "u": 22, "v": 11, "w": 338.0 }, { "u": 22, "v": 26, "w": 1076.0 }, { "u": 0, "v": 1, "w": 466.0 }, { "u": 0, "v": 9, "w": 314428.0 }, { "u": 2, "v": 9, "w": 314574.0 }, { "u": 10, "v": 11, "w": 56.0 }, { "u": 3, "v": 4, "w": 1089.0 }, { "u": 23, "v": 12, "w": 254.0 }, { "u": 23, "v": 25, "w": 794.0 }, { "u": 12, "v": 13, "w": 318.0 }, { "u": 12, "v": 7, "w": 121.0 }, { "u": 13, "v": 24, "w": 1045.0 }, { "u": 13, "v": 6, "w": 1199.0 }, { "u": 13, "v": 7, "w": 438.0 }, { "u": 28, "v": 6, "w": 1611.0 }, { "u": 24, "v": 25, "w": 329.0 }, { "u": 24, "v": 6, "w": 157.0 }, { "u": 25, "v": 26, "w": 864.0 }, { "u": 7, "v": 8, "w": 346.0 } ], "density": 0.09359605911330049, "source_file": "I050.stp", "terminals": [ 0, 2, 3, 5, 8, 9, 11, 13, 15, 16, 17, 18, 20, 21 ] }, "solution_variant": [ [ 14, 16 ], [ 1, 14 ], [ 5, 15 ], [ 2, 16 ], [ 16, 17 ], [ 17, 18 ], [ 3, 17 ], [ 19, 20 ], [ 3, 19 ], [ 11, 19 ], [ 5, 20 ], [ 20, 23 ], [ 21, 22 ], [ 11, 22 ], [ 0, 1 ], [ 0, 9 ], [ 12, 23 ], [ 12, 13 ], [ 7, 12 ], [ 7, 8 ] ], "context_index": 9, "input_format": "json", "input_index_base": 0 }, { "task_name": "STP", "problem_type": "STP", "instruction": "I’m picturing a busy warehouse with a handful of storage bays flagged as top priority. The task is to decide which aisles to keep clear so every one of those priority bays can be reached by walking through a single connected corridor system, and it’s okay to use other aisles as connectors between them. A better choice is simply the one that ends up with the least total cleared distance — add up the length of every cleared aisle (count each stretch once) and smaller totals win — and every priority bay has to be reachable, no bay can be left out. The concrete layout and distances are shown below.\n\n# num_aisle_nodes=21\n# num_aisle_segments=25\n# priority_bay_nodes=B C D F J K L Q\naisle_endpoint_u,aisle_endpoint_v,aisle_length\nU,A,692.0\nU,T,464.0\nQ,K,1243.0\nQ,G,425.0\nQ,P,1588.0\nR,N,886.0\nA,C,390.0\nB,N,213.0\nB,C,870.0\nC,M,306.0\nS,G,68.0\nH,T,480.0\nI,P,306.0\nJ,E,539.0\nJ,O,196.0\nJ,F,1040.0\nK,E,540.0\nK,L,1152.0\nL,F,546.0\nL,M,707.0\nM,N,590.0\nD,E,232561.0\nD,F,232790.0\nT,O,641.0\nO,P,586.0\n\nAlso, when you reply with which aisles to keep clear, just use this simple JSON shape so it's easy to read and parse:\n\n{\n \"solution\": [[bay1, aisle1], [bay2, bay3], ...]\n}\n\nThis little block is just saying: \"solution\" is a list, and each item in the list is a pair naming the two ends of an aisle segment to keep clear. Think of each pair as one stretch of corridor between two labeled locations in the warehouse. It’s only a sketch of the expected shape — not the actual final answer.\n\nPlease be sure to use the exact identifiers from the instance 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”.", "instance": { "problem_type": "STP", "num_nodes": 21, "num_edges": 25, "edges": [ { "u": 21, "v": 1, "w": 692.0 }, { "u": 21, "v": 20, "w": 464.0 }, { "u": 17, "v": 11, "w": 1243.0 }, { "u": 17, "v": 7, "w": 425.0 }, { "u": 17, "v": 16, "w": 1588.0 }, { "u": 18, "v": 14, "w": 886.0 }, { "u": 1, "v": 3, "w": 390.0 }, { "u": 2, "v": 14, "w": 213.0 }, { "u": 2, "v": 3, "w": 870.0 }, { "u": 3, "v": 13, "w": 306.0 }, { "u": 19, "v": 7, "w": 68.0 }, { "u": 8, "v": 20, "w": 480.0 }, { "u": 9, "v": 16, "w": 306.0 }, { "u": 10, "v": 5, "w": 539.0 }, { "u": 10, "v": 15, "w": 196.0 }, { "u": 10, "v": 6, "w": 1040.0 }, { "u": 11, "v": 5, "w": 540.0 }, { "u": 11, "v": 12, "w": 1152.0 }, { "u": 12, "v": 6, "w": 546.0 }, { "u": 12, "v": 13, "w": 707.0 }, { "u": 13, "v": 14, "w": 590.0 }, { "u": 4, "v": 5, "w": 232561.0 }, { "u": 4, "v": 6, "w": 232790.0 }, { "u": 20, "v": 15, "w": 641.0 }, { "u": 15, "v": 16, "w": 586.0 } ], "terminals": [ 2, 3, 4, 6, 10, 11, 12, 17 ], "source_file": "I061.stp", "density": 0.11904761904761904, "viz_instance": "generated_data/STP/viz/STP_L/instance_0009.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0009.png" }, "solution": [ [ 11, 17 ], [ 2, 14 ], [ 3, 13 ], [ 5, 10 ], [ 6, 10 ], [ 5, 11 ], [ 6, 12 ], [ 12, 13 ], [ 13, 14 ], [ 4, 5 ] ], "obj": 238285.0, "instance_variant": { "problem_type": "STP", "num_nodes": 21, "num_edges": 25, "edges": [ { "u": "U", "v": "A", "w": 692.0 }, { "u": "U", "v": "T", "w": 464.0 }, { "u": "Q", "v": "K", "w": 1243.0 }, { "u": "Q", "v": "G", "w": 425.0 }, { "u": "Q", "v": "P", "w": 1588.0 }, { "u": "R", "v": "N", "w": 886.0 }, { "u": "A", "v": "C", "w": 390.0 }, { "u": "B", "v": "N", "w": 213.0 }, { "u": "B", "v": "C", "w": 870.0 }, { "u": "C", "v": "M", "w": 306.0 }, { "u": "S", "v": "G", "w": 68.0 }, { "u": "H", "v": "T", "w": 480.0 }, { "u": "I", "v": "P", "w": 306.0 }, { "u": "J", "v": "E", "w": 539.0 }, { "u": "J", "v": "O", "w": 196.0 }, { "u": "J", "v": "F", "w": 1040.0 }, { "u": "K", "v": "E", "w": 540.0 }, { "u": "K", "v": "L", "w": 1152.0 }, { "u": "L", "v": "F", "w": 546.0 }, { "u": "L", "v": "M", "w": 707.0 }, { "u": "M", "v": "N", "w": 590.0 }, { "u": "D", "v": "E", "w": 232561.0 }, { "u": "D", "v": "F", "w": 232790.0 }, { "u": "T", "v": "O", "w": 641.0 }, { "u": "O", "v": "P", "w": 586.0 } ], "density": 0.11904761904761904, "source_file": "I061.stp", "terminals": [ "B", "C", "D", "F", "J", "K", "L", "Q" ] }, "solution_variant": [ [ "K", "Q" ], [ "B", "N" ], [ "C", "M" ], [ "E", "J" ], [ "F", "J" ], [ "E", "K" ], [ "F", "L" ], [ "L", "M" ], [ "M", "N" ], [ "D", "E" ] ], "context_index": 10, "input_format": "csv", "input_index_base": "names" }, { "task_name": "STP", "problem_type": "STP", "instruction": "Someone on the reserve staff needs to map out repairs to get all the marsh observation platforms back onto one connected trail. They’ll choose which footbridges and boardwalk pieces to put back in service, and they can also repair non-viewing platforms to make the path work. The idea is to keep the repair tab as small as possible — just total up the cost of the pieces you commit to fixing, and that total is what you try to keep lowest. Every key observation point must be included in the continuous route, and each segment is either fixed or not (no double repairs). The concrete sections and their costs are listed below.\n\nThere are 24 distinct platforms and junctions and 31 repairable segments listed; the required observation platforms to include on the continuous route are 2 3 4 6 7 11 20.\nRepair the segment connecting 21 and 20 at a cost of 1121.0.\nRepair the segment connecting 8 and 5 at a cost of 207900.0.\nRepair the segment connecting 8 and 7 at a cost of 210155.0.\nRepair the segment connecting 0 and 1 at a cost of 773.0.\nRepair the segment connecting 0 and 11 at a cost of 3202.0.\nRepair the segment connecting 0 and 18 at a cost of 2761.0.\nRepair the segment connecting 1 and 12 at a cost of 152.0.\nRepair the segment connecting 1 and 9 at a cost of 2574.0.\nRepair the segment connecting 18 and 10 at a cost of 938.0.\nRepair the segment connecting 18 and 22 at a cost of 2389.0.\nRepair the segment connecting 5 and 6 at a cost of 2316.0.\nRepair the segment connecting 5 and 17 at a cost of 6325.0.\nRepair the segment connecting 6 and 14 at a cost of 576.0.\nRepair the segment connecting 6 and 19 at a cost of 3325.0.\nRepair the segment connecting 7 and 14 at a cost of 350.0.\nRepair the segment connecting 7 and 15 at a cost of 815.0.\nRepair the segment connecting 22 and 11 at a cost of 1453.0.\nRepair the segment connecting 3 and 2 at a cost of 876.0.\nRepair the segment connecting 3 and 13 at a cost of 1610.0.\nRepair the segment connecting 3 and 23 at a cost of 4261.0.\nRepair the segment connecting 16 and 19 at a cost of 1353.0.\nRepair the segment connecting 16 and 20 at a cost of 1234.0.\nRepair the segment connecting 16 and 14 at a cost of 3120.0.\nRepair the segment connecting 4 and 2 at a cost of 1234.0.\nRepair the segment connecting 4 and 13 at a cost of 760.0.\nRepair the segment connecting 4 and 12 at a cost of 2066.0.\nRepair the segment connecting 9 and 10 at a cost of 1338.0.\nRepair the segment connecting 9 and 20 at a cost of 240.0.\nRepair the segment connecting 13 and 15 at a cost of 1107.0.\nRepair the segment connecting 17 and 23 at a cost of 4304.0.\nRepair the segment connecting 23 and 15 at a cost of 2427.0.\nThey should total the repair costs and minimize that sum while ensuring every required observation platform 2 3 4 6 7 11 20 is on the final continuous route.\n\nWhen you're ready to tell the crew which pieces to repair, just give the answer in this simple JSON layout:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nThis means \"solution\" should be a list of edge pairs — each pair [u1, v1] is the boardwalk or bridge segment between those two platform/node identifiers that you'll fix. Think of it like filling in a form: list the connections you want repaired so everything connects.\n\nThis JSON is just the shape I expect, not the actual repair plan itself.\n\nPlease make sure you use the exact identifiers from the problem input — don't rename them or invent new labels. \nFor 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 24, "num_edges": 31, "edges": [ { "u": 22, "v": 21, "w": 1121.0 }, { "u": 9, "v": 6, "w": 207900.0 }, { "u": 9, "v": 8, "w": 210155.0 }, { "u": 1, "v": 2, "w": 773.0 }, { "u": 1, "v": 12, "w": 3202.0 }, { "u": 1, "v": 19, "w": 2761.0 }, { "u": 2, "v": 13, "w": 152.0 }, { "u": 2, "v": 10, "w": 2574.0 }, { "u": 19, "v": 11, "w": 938.0 }, { "u": 19, "v": 23, "w": 2389.0 }, { "u": 6, "v": 7, "w": 2316.0 }, { "u": 6, "v": 18, "w": 6325.0 }, { "u": 7, "v": 15, "w": 576.0 }, { "u": 7, "v": 20, "w": 3325.0 }, { "u": 8, "v": 15, "w": 350.0 }, { "u": 8, "v": 16, "w": 815.0 }, { "u": 23, "v": 12, "w": 1453.0 }, { "u": 4, "v": 3, "w": 876.0 }, { "u": 4, "v": 14, "w": 1610.0 }, { "u": 4, "v": 24, "w": 4261.0 }, { "u": 17, "v": 20, "w": 1353.0 }, { "u": 17, "v": 21, "w": 1234.0 }, { "u": 17, "v": 15, "w": 3120.0 }, { "u": 5, "v": 3, "w": 1234.0 }, { "u": 5, "v": 14, "w": 760.0 }, { "u": 5, "v": 13, "w": 2066.0 }, { "u": 10, "v": 11, "w": 1338.0 }, { "u": 10, "v": 21, "w": 240.0 }, { "u": 14, "v": 16, "w": 1107.0 }, { "u": 18, "v": 24, "w": 4304.0 }, { "u": 24, "v": 16, "w": 2427.0 } ], "terminals": [ 3, 4, 5, 7, 8, 12, 21 ], "source_file": "I075.stp", "density": 0.11231884057971014, "viz_instance": "generated_data/STP/viz/STP_L/instance_0010.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0010.png" }, "solution": [ [ 1, 2 ], [ 1, 12 ], [ 2, 13 ], [ 2, 10 ], [ 7, 15 ], [ 8, 15 ], [ 8, 16 ], [ 3, 4 ], [ 3, 5 ], [ 5, 14 ], [ 5, 13 ], [ 10, 21 ], [ 14, 16 ] ], "obj": 14725.0, "instance_variant": { "problem_type": "STP", "num_nodes": 24, "num_edges": 31, "edges": [ { "u": 21, "v": 20, "w": 1121.0 }, { "u": 8, "v": 5, "w": 207900.0 }, { "u": 8, "v": 7, "w": 210155.0 }, { "u": 0, "v": 1, "w": 773.0 }, { "u": 0, "v": 11, "w": 3202.0 }, { "u": 0, "v": 18, "w": 2761.0 }, { "u": 1, "v": 12, "w": 152.0 }, { "u": 1, "v": 9, "w": 2574.0 }, { "u": 18, "v": 10, "w": 938.0 }, { "u": 18, "v": 22, "w": 2389.0 }, { "u": 5, "v": 6, "w": 2316.0 }, { "u": 5, "v": 17, "w": 6325.0 }, { "u": 6, "v": 14, "w": 576.0 }, { "u": 6, "v": 19, "w": 3325.0 }, { "u": 7, "v": 14, "w": 350.0 }, { "u": 7, "v": 15, "w": 815.0 }, { "u": 22, "v": 11, "w": 1453.0 }, { "u": 3, "v": 2, "w": 876.0 }, { "u": 3, "v": 13, "w": 1610.0 }, { "u": 3, "v": 23, "w": 4261.0 }, { "u": 16, "v": 19, "w": 1353.0 }, { "u": 16, "v": 20, "w": 1234.0 }, { "u": 16, "v": 14, "w": 3120.0 }, { "u": 4, "v": 2, "w": 1234.0 }, { "u": 4, "v": 13, "w": 760.0 }, { "u": 4, "v": 12, "w": 2066.0 }, { "u": 9, "v": 10, "w": 1338.0 }, { "u": 9, "v": 20, "w": 240.0 }, { "u": 13, "v": 15, "w": 1107.0 }, { "u": 17, "v": 23, "w": 4304.0 }, { "u": 23, "v": 15, "w": 2427.0 } ], "density": 0.11231884057971014, "source_file": "I075.stp", "terminals": [ 2, 3, 4, 6, 7, 11, 20 ] }, "solution_variant": [ [ 0, 1 ], [ 0, 11 ], [ 1, 12 ], [ 1, 9 ], [ 6, 14 ], [ 7, 14 ], [ 7, 15 ], [ 2, 3 ], [ 2, 4 ], [ 4, 13 ], [ 4, 12 ], [ 9, 20 ], [ 13, 15 ] ], "context_index": 11, "input_format": "markdown_table", "input_index_base": 0 }, { "task_name": "STP", "problem_type": "STP", "instruction": "We’ve got a campus map with a handful of important buildings that must be connected, and the team needs to pick which backbone links to activate so those buildings all end up on a single live path. Other building connections can serve as intermediate hops, but better plans are the ones that achieve full connectivity while keeping the sum of the activated cable lengths as low as possible — calculated by summing the length of every turned-on link. All listed key buildings must be included in the network, each active link is counted toward the total, and the specific link lengths and layout are shown below.\n\n# campus_node_count=29\n# available_link_count=33\n# key_buildings=0 3 7 9 14 16 21 22\nlink_endpoint_a,link_endpoint_b,link_length\n3,21,1599.0\n3,2,651.0\n19,20,749.0\n19,21,210.0\n19,25,1277.0\n20,6,2042.0\n20,4,1297.0\n16,17,631.0\n16,26,886.0\n16,22,2692.0\n17,5,1332.0\n17,7,2297.0\n5,24,658.0\n5,4,3624.0\n4,2,396.0\n18,24,2572.0\n18,22,2966.0\n6,1,446.0\n6,10,1609.0\n7,0,1212.0\n7,9,420.0\n8,12,1070.0\n8,11,1087.0\n9,12,153.0\n9,26,853.0\n10,11,1023.0\n10,23,2276.0\n11,28,843.0\n12,14,364.0\n13,22,36.0\n0,1,2499.0\n26,27,655.0\n15,28,850.0\n\nQuick note — when you give your chosen set of links, please use this simple JSON layout so it’s easy to parse:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nHere, \"solution\" is just a list of link pairs. Each pair [u, v] means “turn on the cable between building/node u and building/node v.” Think of it like listing the specific edges you want active — just the pairs, nothing extra. The JSON above is only a sketch of the expected shape, not your final answer.\n\nPlease make sure to use the node identifiers exactly as they appear in the problem instance — don’t rename them or invent new labels. \n- 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 29, "num_edges": 33, "edges": [ { "u": 4, "v": 22, "w": 1599.0 }, { "u": 4, "v": 3, "w": 651.0 }, { "u": 20, "v": 21, "w": 749.0 }, { "u": 20, "v": 22, "w": 210.0 }, { "u": 20, "v": 26, "w": 1277.0 }, { "u": 21, "v": 7, "w": 2042.0 }, { "u": 21, "v": 5, "w": 1297.0 }, { "u": 17, "v": 18, "w": 631.0 }, { "u": 17, "v": 27, "w": 886.0 }, { "u": 17, "v": 23, "w": 2692.0 }, { "u": 18, "v": 6, "w": 1332.0 }, { "u": 18, "v": 8, "w": 2297.0 }, { "u": 6, "v": 25, "w": 658.0 }, { "u": 6, "v": 5, "w": 3624.0 }, { "u": 5, "v": 3, "w": 396.0 }, { "u": 19, "v": 25, "w": 2572.0 }, { "u": 19, "v": 23, "w": 2966.0 }, { "u": 7, "v": 2, "w": 446.0 }, { "u": 7, "v": 11, "w": 1609.0 }, { "u": 8, "v": 1, "w": 1212.0 }, { "u": 8, "v": 10, "w": 420.0 }, { "u": 9, "v": 13, "w": 1070.0 }, { "u": 9, "v": 12, "w": 1087.0 }, { "u": 10, "v": 13, "w": 153.0 }, { "u": 10, "v": 27, "w": 853.0 }, { "u": 11, "v": 12, "w": 1023.0 }, { "u": 11, "v": 24, "w": 2276.0 }, { "u": 12, "v": 29, "w": 843.0 }, { "u": 13, "v": 15, "w": 364.0 }, { "u": 14, "v": 23, "w": 36.0 }, { "u": 1, "v": 2, "w": 2499.0 }, { "u": 27, "v": 28, "w": 655.0 }, { "u": 16, "v": 29, "w": 850.0 } ], "terminals": [ 1, 4, 8, 10, 15, 17, 22, 23 ], "source_file": "I023.stp", "density": 0.0812807881773399, "viz_instance": "generated_data/STP/viz/STP_L/instance_0011.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0011.png" }, "solution": [ [ 4, 22 ], [ 20, 21 ], [ 20, 22 ], [ 7, 21 ], [ 17, 27 ], [ 17, 23 ], [ 2, 7 ], [ 1, 8 ], [ 8, 10 ], [ 10, 13 ], [ 10, 27 ], [ 13, 15 ], [ 1, 2 ] ], "obj": 14125.0, "instance_variant": { "problem_type": "STP", "num_nodes": 29, "num_edges": 33, "edges": [ { "u": 3, "v": 21, "w": 1599.0 }, { "u": 3, "v": 2, "w": 651.0 }, { "u": 19, "v": 20, "w": 749.0 }, { "u": 19, "v": 21, "w": 210.0 }, { "u": 19, "v": 25, "w": 1277.0 }, { "u": 20, "v": 6, "w": 2042.0 }, { "u": 20, "v": 4, "w": 1297.0 }, { "u": 16, "v": 17, "w": 631.0 }, { "u": 16, "v": 26, "w": 886.0 }, { "u": 16, "v": 22, "w": 2692.0 }, { "u": 17, "v": 5, "w": 1332.0 }, { "u": 17, "v": 7, "w": 2297.0 }, { "u": 5, "v": 24, "w": 658.0 }, { "u": 5, "v": 4, "w": 3624.0 }, { "u": 4, "v": 2, "w": 396.0 }, { "u": 18, "v": 24, "w": 2572.0 }, { "u": 18, "v": 22, "w": 2966.0 }, { "u": 6, "v": 1, "w": 446.0 }, { "u": 6, "v": 10, "w": 1609.0 }, { "u": 7, "v": 0, "w": 1212.0 }, { "u": 7, "v": 9, "w": 420.0 }, { "u": 8, "v": 12, "w": 1070.0 }, { "u": 8, "v": 11, "w": 1087.0 }, { "u": 9, "v": 12, "w": 153.0 }, { "u": 9, "v": 26, "w": 853.0 }, { "u": 10, "v": 11, "w": 1023.0 }, { "u": 10, "v": 23, "w": 2276.0 }, { "u": 11, "v": 28, "w": 843.0 }, { "u": 12, "v": 14, "w": 364.0 }, { "u": 13, "v": 22, "w": 36.0 }, { "u": 0, "v": 1, "w": 2499.0 }, { "u": 26, "v": 27, "w": 655.0 }, { "u": 15, "v": 28, "w": 850.0 } ], "density": 0.0812807881773399, "source_file": "I023.stp", "terminals": [ 0, 3, 7, 9, 14, 16, 21, 22 ] }, "solution_variant": [ [ 3, 21 ], [ 19, 20 ], [ 19, 21 ], [ 6, 20 ], [ 16, 26 ], [ 16, 22 ], [ 1, 6 ], [ 0, 7 ], [ 7, 9 ], [ 9, 12 ], [ 9, 26 ], [ 12, 14 ], [ 0, 1 ] ], "context_index": 12, "input_format": "csv", "input_index_base": 0 }, { "task_name": "STP", "problem_type": "STP", "instruction": "Imagine pruning the delivery map: pick a set of links between stores that keeps every flagship connected, letting trucks pass through regional hubs when helpful. The way to tell which pruning worked best is to total the lengths of the links that were left open — the smaller that total, the better the pruning. No flagship is allowed to be disconnected and no lane is counted more than once. The concrete store locations and route distances are shown below.\n\nThere are 24 locations, 29 candidate lanes, and these flagship stores: 11 20.\nConsider the lane between 3 and 1 with distance 432.0.\nConsider the lane between 24 and 13 with distance 661.0.\nConsider the lane between 24 and 16 with distance 5447.0.\nConsider the lane between 24 and 15 with distance 1668.0.\nConsider the lane between 20 and 12 with distance 1471.0.\nConsider the lane between 20 and 23 with distance 1624.0.\nConsider the lane between 20 and 15 with distance 1621.0.\nConsider the lane between 21 and 22 with distance 1344.0.\nConsider the lane between 21 and 18 with distance 2650.0.\nConsider the lane between 21 and 7 with distance 3872.0.\nConsider the lane between 4 and 10 with distance 405.0.\nConsider the lane between 4 and 16 with distance 6342.0.\nConsider the lane between 23 and 1 with distance 8368.0.\nConsider the lane between 23 and 16 with distance 5424.0.\nConsider the lane between 11 and 9 with distance 869.0.\nConsider the lane between 11 and 15 with distance 1376.0.\nConsider the lane between 11 and 7 with distance 1652.0.\nConsider the lane between 12 and 9 with distance 730.0.\nConsider the lane between 12 and 7 with distance 1456.0.\nConsider the lane between 13 and 6 with distance 1077.0.\nConsider the lane between 13 and 15 with distance 1347.0.\nConsider the lane between 6 and 15 with distance 1551.0.\nConsider the lane between 7 and 14 with distance 1399.0.\nConsider the lane between 5 and 17 with distance 3762.0.\nConsider the lane between 5 and 16 with distance 3964.0.\nConsider the lane between 14 and 19 with distance 577.0.\nConsider the lane between 14 and 8 with distance 948.0.\nConsider the lane between 18 and 19 with distance 3331.0.\nConsider the lane between 1 and 2 with distance 414.0.\nKeep in mind that no flagship in 11 20 may be disconnected and no lane is counted more than once; minimize the total distance of the lanes you keep.\n\nWhen you send the pruned map back, please use this JSON layout so it's easy to read by both people and tools:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nHere \"solution\" is just a list of the links you decided to keep open. Each inner pair [u, v] represents a single link between two locations — think of it as \"leave the lane between u and v open.\" This block is only a sketch of the shape I expect, not the actual answer — replace the placeholders with the real pairs from your work.\n\nPlease use the exact identifiers from the instance input — do not rename them or invent new labels. \n- 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\".", "instance": { "problem_type": "STP", "num_nodes": 24, "num_edges": 29, "edges": [ { "u": 3, "v": 1, "w": 432.0 }, { "u": 24, "v": 13, "w": 661.0 }, { "u": 24, "v": 16, "w": 5447.0 }, { "u": 24, "v": 15, "w": 1668.0 }, { "u": 20, "v": 12, "w": 1471.0 }, { "u": 20, "v": 23, "w": 1624.0 }, { "u": 20, "v": 15, "w": 1621.0 }, { "u": 21, "v": 22, "w": 1344.0 }, { "u": 21, "v": 18, "w": 2650.0 }, { "u": 21, "v": 7, "w": 3872.0 }, { "u": 4, "v": 10, "w": 405.0 }, { "u": 4, "v": 16, "w": 6342.0 }, { "u": 23, "v": 1, "w": 8368.0 }, { "u": 23, "v": 16, "w": 5424.0 }, { "u": 11, "v": 9, "w": 869.0 }, { "u": 11, "v": 15, "w": 1376.0 }, { "u": 11, "v": 7, "w": 1652.0 }, { "u": 12, "v": 9, "w": 730.0 }, { "u": 12, "v": 7, "w": 1456.0 }, { "u": 13, "v": 6, "w": 1077.0 }, { "u": 13, "v": 15, "w": 1347.0 }, { "u": 6, "v": 15, "w": 1551.0 }, { "u": 7, "v": 14, "w": 1399.0 }, { "u": 5, "v": 17, "w": 3762.0 }, { "u": 5, "v": 16, "w": 3964.0 }, { "u": 14, "v": 19, "w": 577.0 }, { "u": 14, "v": 8, "w": 948.0 }, { "u": 18, "v": 19, "w": 3331.0 }, { "u": 1, "v": 2, "w": 414.0 } ], "terminals": [ 11, 20 ], "source_file": "I045.stp", "density": 0.10507246376811594, "viz_instance": "generated_data/STP/viz/STP_L/instance_0012.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0012.png" }, "solution": [ [ 15, 20 ], [ 11, 15 ] ], "obj": 2997.0, "instance_variant": { "problem_type": "STP", "num_nodes": 24, "num_edges": 29, "edges": [ { "u": 3, "v": 1, "w": 432.0 }, { "u": 24, "v": 13, "w": 661.0 }, { "u": 24, "v": 16, "w": 5447.0 }, { "u": 24, "v": 15, "w": 1668.0 }, { "u": 20, "v": 12, "w": 1471.0 }, { "u": 20, "v": 23, "w": 1624.0 }, { "u": 20, "v": 15, "w": 1621.0 }, { "u": 21, "v": 22, "w": 1344.0 }, { "u": 21, "v": 18, "w": 2650.0 }, { "u": 21, "v": 7, "w": 3872.0 }, { "u": 4, "v": 10, "w": 405.0 }, { "u": 4, "v": 16, "w": 6342.0 }, { "u": 23, "v": 1, "w": 8368.0 }, { "u": 23, "v": 16, "w": 5424.0 }, { "u": 11, "v": 9, "w": 869.0 }, { "u": 11, "v": 15, "w": 1376.0 }, { "u": 11, "v": 7, "w": 1652.0 }, { "u": 12, "v": 9, "w": 730.0 }, { "u": 12, "v": 7, "w": 1456.0 }, { "u": 13, "v": 6, "w": 1077.0 }, { "u": 13, "v": 15, "w": 1347.0 }, { "u": 6, "v": 15, "w": 1551.0 }, { "u": 7, "v": 14, "w": 1399.0 }, { "u": 5, "v": 17, "w": 3762.0 }, { "u": 5, "v": 16, "w": 3964.0 }, { "u": 14, "v": 19, "w": 577.0 }, { "u": 14, "v": 8, "w": 948.0 }, { "u": 18, "v": 19, "w": 3331.0 }, { "u": 1, "v": 2, "w": 414.0 } ], "density": 0.10507246376811594, "source_file": "I045.stp", "terminals": [ 11, 20 ] }, "solution_variant": [ [ 15, 20 ], [ 11, 15 ] ], "context_index": 13, "input_format": "nl", "input_index_base": 1 }, { "task_name": "STP", "problem_type": "STP", "instruction": "We have a set of treatment plants and a bunch of possible pipe pieces that could be installed between places. The decision is which pieces to actually put in so that all the plants are part of one continuous pipeline, with any intersections happening only at current valve stations; the best option is the one with the smallest combined pipe length, which you get by summing the lengths of the chosen pieces. All named sites must be included and no segment should be counted twice. The specific layout and numbers are listed below.\n\n{\n \"total_locations\": 30,\n \"available_pipe_segments\": 35,\n \"edges\": [\n {\n \"endpoint_a\": 1,\n \"endpoint_b\": 2,\n \"segment_length\": 1355.0\n },\n {\n \"endpoint_a\": 1,\n \"endpoint_b\": 3,\n \"segment_length\": 568.0\n },\n {\n \"endpoint_a\": 2,\n \"endpoint_b\": 14,\n \"segment_length\": 384.0\n },\n {\n \"endpoint_a\": 2,\n \"endpoint_b\": 15,\n \"segment_length\": 2667.0\n },\n {\n \"endpoint_a\": 3,\n \"endpoint_b\": 5,\n \"segment_length\": 406.0\n },\n {\n \"endpoint_a\": 3,\n \"endpoint_b\": 14,\n \"segment_length\": 1289.0\n },\n {\n \"endpoint_a\": 4,\n \"endpoint_b\": 11,\n \"segment_length\": 464.0\n },\n {\n \"endpoint_a\": 4,\n \"endpoint_b\": 5,\n \"segment_length\": 810.0\n },\n {\n \"endpoint_a\": 4,\n \"endpoint_b\": 15,\n \"segment_length\": 1407.0\n },\n {\n \"endpoint_a\": 5,\n \"endpoint_b\": 10,\n \"segment_length\": 314.0\n },\n {\n \"endpoint_a\": 9,\n \"endpoint_b\": 10,\n \"segment_length\": 1978.0\n },\n {\n \"endpoint_a\": 9,\n \"endpoint_b\": 13,\n \"segment_length\": 641.0\n },\n {\n \"endpoint_a\": 9,\n \"endpoint_b\": 28,\n \"segment_length\": 453.0\n },\n {\n \"endpoint_a\": 29,\n \"endpoint_b\": 8,\n \"segment_length\": 3982.0\n },\n {\n \"endpoint_a\": 7,\n \"endpoint_b\": 27,\n \"segment_length\": 1138.0\n },\n {\n \"endpoint_a\": 7,\n \"endpoint_b\": 28,\n \"segment_length\": 2258.0\n },\n {\n \"endpoint_a\": 6,\n \"endpoint_b\": 19,\n \"segment_length\": 502.0\n },\n {\n \"endpoint_a\": 6,\n \"endpoint_b\": 18,\n \"segment_length\": 1552.0\n },\n {\n \"endpoint_a\": 8,\n \"endpoint_b\": 11,\n \"segment_length\": 1312.0\n },\n {\n \"endpoint_a\": 8,\n \"endpoint_b\": 28,\n \"segment_length\": 2541.0\n },\n {\n \"endpoint_a\": 26,\n \"endpoint_b\": 25,\n \"segment_length\": 2185.0\n },\n {\n \"endpoint_a\": 13,\n \"endpoint_b\": 0,\n \"segment_length\": 142.0\n },\n {\n \"endpoint_a\": 14,\n \"endpoint_b\": 24,\n \"segment_length\": 1007.0\n },\n {\n \"endpoint_a\": 15,\n \"endpoint_b\": 16,\n \"segment_length\": 1016.0\n },\n {\n \"endpoint_a\": 23,\n \"endpoint_b\": 25,\n \"segment_length\": 710.0\n },\n {\n \"endpoint_a\": 24,\n \"endpoint_b\": 25,\n \"segment_length\": 1712.0\n },\n {\n \"endpoint_a\": 24,\n \"endpoint_b\": 17,\n \"segment_length\": 2365.0\n },\n {\n \"endpoint_a\": 16,\n \"endpoint_b\": 17,\n \"segment_length\": 2349.0\n },\n {\n \"endpoint_a\": 16,\n \"endpoint_b\": 19,\n \"segment_length\": 1994.0\n },\n {\n \"endpoint_a\": 17,\n \"endpoint_b\": 18,\n \"segment_length\": 2144.0\n },\n {\n \"endpoint_a\": 10,\n \"endpoint_b\": 11,\n \"segment_length\": 219.0\n },\n {\n \"endpoint_a\": 18,\n \"endpoint_b\": 22,\n \"segment_length\": 1533.0\n },\n {\n \"endpoint_a\": 12,\n \"endpoint_b\": 20,\n \"segment_length\": 570.0\n },\n {\n \"endpoint_a\": 19,\n \"endpoint_b\": 20,\n \"segment_length\": 1259.0\n },\n {\n \"endpoint_a\": 20,\n \"endpoint_b\": 21,\n \"segment_length\": 343.0\n }\n ],\n \"required_treatment_plants\": [\n 13,\n 18,\n 20\n ]\n}\n\nIf you want to hand me back a proposed set of pipe pieces, just send it in this simple JSON shape:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nHere \"solution\" is a list of the pipe segments you choose; each pair [uX, vX] is one piece connecting site uX to site vX. Think of it like a form where you tick off each connection you want — one pair per segment, and don't list the same segment twice. This block is just a sketch of the shape I expect, not the actual answer.\n\nAnd please use the exact identifiers from the instance input — don't rename or invent new labels. \n- 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 30, "num_edges": 35, "edges": [ { "u": 2, "v": 3, "w": 1355.0 }, { "u": 2, "v": 4, "w": 568.0 }, { "u": 3, "v": 15, "w": 384.0 }, { "u": 3, "v": 16, "w": 2667.0 }, { "u": 4, "v": 6, "w": 406.0 }, { "u": 4, "v": 15, "w": 1289.0 }, { "u": 5, "v": 12, "w": 464.0 }, { "u": 5, "v": 6, "w": 810.0 }, { "u": 5, "v": 16, "w": 1407.0 }, { "u": 6, "v": 11, "w": 314.0 }, { "u": 10, "v": 11, "w": 1978.0 }, { "u": 10, "v": 14, "w": 641.0 }, { "u": 10, "v": 29, "w": 453.0 }, { "u": 30, "v": 9, "w": 3982.0 }, { "u": 8, "v": 28, "w": 1138.0 }, { "u": 8, "v": 29, "w": 2258.0 }, { "u": 7, "v": 20, "w": 502.0 }, { "u": 7, "v": 19, "w": 1552.0 }, { "u": 9, "v": 12, "w": 1312.0 }, { "u": 9, "v": 29, "w": 2541.0 }, { "u": 27, "v": 26, "w": 2185.0 }, { "u": 14, "v": 1, "w": 142.0 }, { "u": 15, "v": 25, "w": 1007.0 }, { "u": 16, "v": 17, "w": 1016.0 }, { "u": 24, "v": 26, "w": 710.0 }, { "u": 25, "v": 26, "w": 1712.0 }, { "u": 25, "v": 18, "w": 2365.0 }, { "u": 17, "v": 18, "w": 2349.0 }, { "u": 17, "v": 20, "w": 1994.0 }, { "u": 18, "v": 19, "w": 2144.0 }, { "u": 11, "v": 12, "w": 219.0 }, { "u": 19, "v": 23, "w": 1533.0 }, { "u": 13, "v": 21, "w": 570.0 }, { "u": 20, "v": 21, "w": 1259.0 }, { "u": 21, "v": 22, "w": 343.0 } ], "terminals": [ 14, 19, 21 ], "source_file": "I044.stp", "density": 0.08045977011494253, "viz_instance": "generated_data/STP/viz/STP_L/instance_0013.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0013.png" }, "solution": [ [ 5, 12 ], [ 5, 16 ], [ 10, 11 ], [ 10, 14 ], [ 7, 20 ], [ 7, 19 ], [ 16, 17 ], [ 17, 20 ], [ 11, 12 ], [ 20, 21 ] ], "obj": 11032.0, "instance_variant": { "problem_type": "STP", "num_nodes": 30, "num_edges": 35, "edges": [ { "u": 1, "v": 2, "w": 1355.0 }, { "u": 1, "v": 3, "w": 568.0 }, { "u": 2, "v": 14, "w": 384.0 }, { "u": 2, "v": 15, "w": 2667.0 }, { "u": 3, "v": 5, "w": 406.0 }, { "u": 3, "v": 14, "w": 1289.0 }, { "u": 4, "v": 11, "w": 464.0 }, { "u": 4, "v": 5, "w": 810.0 }, { "u": 4, "v": 15, "w": 1407.0 }, { "u": 5, "v": 10, "w": 314.0 }, { "u": 9, "v": 10, "w": 1978.0 }, { "u": 9, "v": 13, "w": 641.0 }, { "u": 9, "v": 28, "w": 453.0 }, { "u": 29, "v": 8, "w": 3982.0 }, { "u": 7, "v": 27, "w": 1138.0 }, { "u": 7, "v": 28, "w": 2258.0 }, { "u": 6, "v": 19, "w": 502.0 }, { "u": 6, "v": 18, "w": 1552.0 }, { "u": 8, "v": 11, "w": 1312.0 }, { "u": 8, "v": 28, "w": 2541.0 }, { "u": 26, "v": 25, "w": 2185.0 }, { "u": 13, "v": 0, "w": 142.0 }, { "u": 14, "v": 24, "w": 1007.0 }, { "u": 15, "v": 16, "w": 1016.0 }, { "u": 23, "v": 25, "w": 710.0 }, { "u": 24, "v": 25, "w": 1712.0 }, { "u": 24, "v": 17, "w": 2365.0 }, { "u": 16, "v": 17, "w": 2349.0 }, { "u": 16, "v": 19, "w": 1994.0 }, { "u": 17, "v": 18, "w": 2144.0 }, { "u": 10, "v": 11, "w": 219.0 }, { "u": 18, "v": 22, "w": 1533.0 }, { "u": 12, "v": 20, "w": 570.0 }, { "u": 19, "v": 20, "w": 1259.0 }, { "u": 20, "v": 21, "w": 343.0 } ], "density": 0.08045977011494253, "source_file": "I044.stp", "terminals": [ 13, 18, 20 ] }, "solution_variant": [ [ 4, 11 ], [ 4, 15 ], [ 9, 10 ], [ 9, 13 ], [ 6, 19 ], [ 6, 18 ], [ 15, 16 ], [ 16, 19 ], [ 10, 11 ], [ 19, 20 ] ], "context_index": 14, "input_format": "json", "input_index_base": 0 }, { "task_name": "STP", "problem_type": "STP", "instruction": "Many people think of it as a puzzle of holiday wiring: there are landmark trees to light, lamp posts that can join things, and a set of candidate runs between them. The task is to pick which runs to put in so every landmark tree is on the same continuous power circuit, using posts as connectors where useful. Better solutions are simply those that use less total wiring — the total is the sum of the lengths of the installed runs — and nothing can be left out or wired twice. The exact map and numbers are provided below.\n\n# total_landmarks_and_posts=21\n# available_runs=26\n# required_landmark_trees=A C E F G H K L M O\nrun_endpoint_u,run_endpoint_v,run_length\nU,Q,1508.0\nU,T,866.0\nA,M,781.0\nA,N,647.0\nA,B,1542.0\nB,N,921.0\nB,O,28.0\nC,M,1249.0\nC,I,229.0\nC,G,215426.0\nD,F,517.0\nD,P,96.0\nD,E,1081.0\nE,I,75.0\nE,R,422.0\nF,O,231.0\nF,G,214445.0\nM,L,1477.0\nN,K,1436.0\nO,T,1232.0\nJ,L,83.0\nJ,K,1551.0\nP,S,845.0\nP,Q,1794.0\nH,I,1310.0\nR,S,811.0\n\nIf you want to hand the wiring plan back to me, just stick it in a tiny JSON snippet like this — nice and simple so I can read it straight away.\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nThis just means \"solution\" is a list of runs to install; each inner pair [u, v] is an edge connecting two locations (think: between two trees or a tree and a lamp post). It's just a sketch of the shape I expect, not the actual answer — fill in the real pairs from the instance.\n\nPlease use the exact identifiers from the instance input — don't rename them or invent new labels. \n- 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 21, "num_edges": 26, "edges": [ { "u": 21, "v": 17, "w": 1508.0 }, { "u": 21, "v": 20, "w": 866.0 }, { "u": 1, "v": 13, "w": 781.0 }, { "u": 1, "v": 14, "w": 647.0 }, { "u": 1, "v": 2, "w": 1542.0 }, { "u": 2, "v": 14, "w": 921.0 }, { "u": 2, "v": 15, "w": 28.0 }, { "u": 3, "v": 13, "w": 1249.0 }, { "u": 3, "v": 9, "w": 229.0 }, { "u": 3, "v": 7, "w": 215426.0 }, { "u": 4, "v": 6, "w": 517.0 }, { "u": 4, "v": 16, "w": 96.0 }, { "u": 4, "v": 5, "w": 1081.0 }, { "u": 5, "v": 9, "w": 75.0 }, { "u": 5, "v": 18, "w": 422.0 }, { "u": 6, "v": 15, "w": 231.0 }, { "u": 6, "v": 7, "w": 214445.0 }, { "u": 13, "v": 12, "w": 1477.0 }, { "u": 14, "v": 11, "w": 1436.0 }, { "u": 15, "v": 20, "w": 1232.0 }, { "u": 10, "v": 12, "w": 83.0 }, { "u": 10, "v": 11, "w": 1551.0 }, { "u": 16, "v": 19, "w": 845.0 }, { "u": 16, "v": 17, "w": 1794.0 }, { "u": 8, "v": 9, "w": 1310.0 }, { "u": 18, "v": 19, "w": 811.0 } ], "terminals": [ 1, 3, 5, 6, 7, 8, 11, 12, 13, 15 ], "source_file": "I019.stp", "density": 0.12380952380952381, "viz_instance": "generated_data/STP/viz/STP_L/instance_0014.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0014.png" }, "solution": [ [ 1, 13 ], [ 1, 14 ], [ 2, 14 ], [ 2, 15 ], [ 3, 13 ], [ 3, 9 ], [ 5, 9 ], [ 6, 15 ], [ 6, 7 ], [ 12, 13 ], [ 11, 14 ], [ 8, 9 ] ], "obj": 222829.0, "instance_variant": { "problem_type": "STP", "num_nodes": 21, "num_edges": 26, "edges": [ { "u": "U", "v": "Q", "w": 1508.0 }, { "u": "U", "v": "T", "w": 866.0 }, { "u": "A", "v": "M", "w": 781.0 }, { "u": "A", "v": "N", "w": 647.0 }, { "u": "A", "v": "B", "w": 1542.0 }, { "u": "B", "v": "N", "w": 921.0 }, { "u": "B", "v": "O", "w": 28.0 }, { "u": "C", "v": "M", "w": 1249.0 }, { "u": "C", "v": "I", "w": 229.0 }, { "u": "C", "v": "G", "w": 215426.0 }, { "u": "D", "v": "F", "w": 517.0 }, { "u": "D", "v": "P", "w": 96.0 }, { "u": "D", "v": "E", "w": 1081.0 }, { "u": "E", "v": "I", "w": 75.0 }, { "u": "E", "v": "R", "w": 422.0 }, { "u": "F", "v": "O", "w": 231.0 }, { "u": "F", "v": "G", "w": 214445.0 }, { "u": "M", "v": "L", "w": 1477.0 }, { "u": "N", "v": "K", "w": 1436.0 }, { "u": "O", "v": "T", "w": 1232.0 }, { "u": "J", "v": "L", "w": 83.0 }, { "u": "J", "v": "K", "w": 1551.0 }, { "u": "P", "v": "S", "w": 845.0 }, { "u": "P", "v": "Q", "w": 1794.0 }, { "u": "H", "v": "I", "w": 1310.0 }, { "u": "R", "v": "S", "w": 811.0 } ], "density": 0.12380952380952381, "source_file": "I019.stp", "terminals": [ "A", "C", "E", "F", "G", "H", "K", "L", "M", "O" ] }, "solution_variant": [ [ "A", "M" ], [ "A", "N" ], [ "B", "N" ], [ "B", "O" ], [ "C", "M" ], [ "C", "I" ], [ "E", "I" ], [ "F", "O" ], [ "F", "G" ], [ "L", "M" ], [ "K", "N" ], [ "H", "I" ] ], "context_index": 15, "input_format": "csv", "input_index_base": "names" }, { "task_name": "STP", "problem_type": "STP", "instruction": "Out in the subdivision the idea is to shut off some access roads but keep enough streets so all the fire hydrants can still be reached, using small residential streets where needed to connect things. The decision is which road segments to preserve so every hydrant sits on the same usable street network; a plan is judged by the total length of the roads that remain — simply add up those lengths, and the lower the total the better. The preserved streets must let crews get to every hydrant (none left out) and avoid keeping unnecessary extra loops. The specific roads and distances are shown below.\n\nThere are 27 intersections and 32 road segments, and the hydrants are at 0 3 6 8 22.\nPreserve the segment between 14 and 13 (length 4573.0).\nPreserve the segment between 14 and 24 (length 1876.0).\nPreserve the segment between 25 and 24 (length 538.0).\nPreserve the segment between 25 and 15 (length 3989.0).\nPreserve the segment between 26 and 23 (length 515.0).\nPreserve the segment between 26 and 0 (length 236.0).\nPreserve the segment between 26 and 10 (length 1898.0).\nPreserve the segment between 15 and 8 (length 897.0).\nPreserve the segment between 15 and 13 (length 4854.0).\nPreserve the segment between 22 and 18 (length 2621.0).\nPreserve the segment between 0 and 9 (length 479.0).\nPreserve the segment between 0 and 23 (length 699.0).\nPreserve the segment between 1 and 4 (length 2292.0).\nPreserve the segment between 1 and 18 (length 4285.0).\nPreserve the segment between 16 and 17 (length 63.0).\nPreserve the segment between 4 and 5 (length 5453.0).\nPreserve the segment between 4 and 3 (length 9321.0).\nPreserve the segment between 5 and 9 (length 1306.0).\nPreserve the segment between 5 and 6 (length 666.0).\nPreserve the segment between 17 and 11 (length 2523.0).\nPreserve the segment between 17 and 20 (length 4332.0).\nPreserve the segment between 6 and 7 (length 2762.0).\nPreserve the segment between 6 and 10 (length 395.0).\nPreserve the segment between 8 and 2 (length 3934.0).\nPreserve the segment between 2 and 18 (length 5190.0).\nPreserve the segment between 3 and 12 (length 1337.0).\nPreserve the segment between 9 and 19 (length 2192.0).\nPreserve the segment between 11 and 12 (length 2962.0).\nPreserve the segment between 11 and 19 (length 3251.0).\nPreserve the segment between 19 and 20 (length 2200.0).\nPreserve the segment between 20 and 21 (length 1572.0).\nPreserve the segment between 12 and 13 (length 1278.0).\nPreserve a set of segments that connects every hydrant 0 3 6 8 22 without unnecessary loops while minimizing the total kept road length.\n\nWhen you send the plan back, just stick to this simple JSON shape so it's easy to read by the rest of the tools:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nHere \"solution\" is just a list of road segments you want to keep; each pair [u1, v1] describes a street between the two intersections u1 and v1. Think of it like filling out a quick form: one line per kept street. This JSON is only a sketch of the expected shape — not the final answer itself.\n\nPlease make sure to use the exact intersection identifiers from the instance input — no renaming and no new labels.\n- 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 27, "num_edges": 32, "edges": [ { "u": 15, "v": 14, "w": 4573.0 }, { "u": 15, "v": 25, "w": 1876.0 }, { "u": 26, "v": 25, "w": 538.0 }, { "u": 26, "v": 16, "w": 3989.0 }, { "u": 27, "v": 24, "w": 515.0 }, { "u": 27, "v": 1, "w": 236.0 }, { "u": 27, "v": 11, "w": 1898.0 }, { "u": 16, "v": 9, "w": 897.0 }, { "u": 16, "v": 14, "w": 4854.0 }, { "u": 23, "v": 19, "w": 2621.0 }, { "u": 1, "v": 10, "w": 479.0 }, { "u": 1, "v": 24, "w": 699.0 }, { "u": 2, "v": 5, "w": 2292.0 }, { "u": 2, "v": 19, "w": 4285.0 }, { "u": 17, "v": 18, "w": 63.0 }, { "u": 5, "v": 6, "w": 5453.0 }, { "u": 5, "v": 4, "w": 9321.0 }, { "u": 6, "v": 10, "w": 1306.0 }, { "u": 6, "v": 7, "w": 666.0 }, { "u": 18, "v": 12, "w": 2523.0 }, { "u": 18, "v": 21, "w": 4332.0 }, { "u": 7, "v": 8, "w": 2762.0 }, { "u": 7, "v": 11, "w": 395.0 }, { "u": 9, "v": 3, "w": 3934.0 }, { "u": 3, "v": 19, "w": 5190.0 }, { "u": 4, "v": 13, "w": 1337.0 }, { "u": 10, "v": 20, "w": 2192.0 }, { "u": 12, "v": 13, "w": 2962.0 }, { "u": 12, "v": 20, "w": 3251.0 }, { "u": 20, "v": 21, "w": 2200.0 }, { "u": 21, "v": 22, "w": 1572.0 }, { "u": 13, "v": 14, "w": 1278.0 } ], "terminals": [ 1, 4, 7, 9, 23 ], "source_file": "I047.stp", "density": 0.09116809116809117, "viz_instance": "generated_data/STP/viz/STP_L/instance_0015.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0015.png" }, "solution": [ [ 9, 16 ], [ 14, 16 ], [ 19, 23 ], [ 1, 10 ], [ 6, 10 ], [ 6, 7 ], [ 3, 9 ], [ 3, 19 ], [ 4, 13 ], [ 10, 20 ], [ 12, 13 ], [ 12, 20 ], [ 13, 14 ] ], "obj": 30967.0, "instance_variant": { "problem_type": "STP", "num_nodes": 27, "num_edges": 32, "edges": [ { "u": 14, "v": 13, "w": 4573.0 }, { "u": 14, "v": 24, "w": 1876.0 }, { "u": 25, "v": 24, "w": 538.0 }, { "u": 25, "v": 15, "w": 3989.0 }, { "u": 26, "v": 23, "w": 515.0 }, { "u": 26, "v": 0, "w": 236.0 }, { "u": 26, "v": 10, "w": 1898.0 }, { "u": 15, "v": 8, "w": 897.0 }, { "u": 15, "v": 13, "w": 4854.0 }, { "u": 22, "v": 18, "w": 2621.0 }, { "u": 0, "v": 9, "w": 479.0 }, { "u": 0, "v": 23, "w": 699.0 }, { "u": 1, "v": 4, "w": 2292.0 }, { "u": 1, "v": 18, "w": 4285.0 }, { "u": 16, "v": 17, "w": 63.0 }, { "u": 4, "v": 5, "w": 5453.0 }, { "u": 4, "v": 3, "w": 9321.0 }, { "u": 5, "v": 9, "w": 1306.0 }, { "u": 5, "v": 6, "w": 666.0 }, { "u": 17, "v": 11, "w": 2523.0 }, { "u": 17, "v": 20, "w": 4332.0 }, { "u": 6, "v": 7, "w": 2762.0 }, { "u": 6, "v": 10, "w": 395.0 }, { "u": 8, "v": 2, "w": 3934.0 }, { "u": 2, "v": 18, "w": 5190.0 }, { "u": 3, "v": 12, "w": 1337.0 }, { "u": 9, "v": 19, "w": 2192.0 }, { "u": 11, "v": 12, "w": 2962.0 }, { "u": 11, "v": 19, "w": 3251.0 }, { "u": 19, "v": 20, "w": 2200.0 }, { "u": 20, "v": 21, "w": 1572.0 }, { "u": 12, "v": 13, "w": 1278.0 } ], "density": 0.09116809116809117, "source_file": "I047.stp", "terminals": [ 0, 3, 6, 8, 22 ] }, "solution_variant": [ [ 8, 15 ], [ 13, 15 ], [ 18, 22 ], [ 0, 9 ], [ 5, 9 ], [ 5, 6 ], [ 2, 8 ], [ 2, 18 ], [ 3, 12 ], [ 9, 19 ], [ 11, 12 ], [ 11, 19 ], [ 12, 13 ] ], "context_index": 16, "input_format": "nl", "input_index_base": 0 }, { "task_name": "STP", "problem_type": "STP", "instruction": "There’s a shift where the plow crew must make a choice: which parts of the taxiway system to clear so that a set of assigned gates are all reachable from one another. Using other aprons as shortcuts is allowed if it saves on clearing, but every assigned gate must sit on the cleared network and the plan shouldn’t include redundant cleared stretches. A good plan is the one that minimizes how much pavement is cleared in total — you figure that out by summing the distances of all cleared segments. The specific layout and numbers are shown below.\n\nFor the plow crew: 25 total pavement nodes, 30 possible clear segments, assigned gates 9 11 19 21 25.\nSegment between 22 and 8: clearing length 1737.0 m.\nSegment between 22 and 4: clearing length 276.0 m.\nSegment between 22 and 17: clearing length 2771.0 m.\nSegment between 23 and 8: clearing length 3825.0 m.\nSegment between 23 and 24: clearing length 1633.0 m.\nSegment between 23 and 9: clearing length 1605.0 m.\nSegment between 24 and 20: clearing length 2819.0 m.\nSegment between 24 and 18: clearing length 1645.0 m.\nSegment between 25 and 15: clearing length 1182.0 m.\nSegment between 25 and 21: clearing length 1247.0 m.\nSegment between 25 and 14: clearing length 1002.0 m.\nSegment between 17 and 11: clearing length 1216.0 m.\nSegment between 17 and 21: clearing length 1597.0 m.\nSegment between 8 and 7: clearing length 2059.0 m.\nSegment between 9 and 7: clearing length 4939.0 m.\nSegment between 9 and 18: clearing length 1672.0 m.\nSegment between 10 and 11: clearing length 2571.0 m.\nSegment between 10 and 5: clearing length 4610.0 m.\nSegment between 11 and 14: clearing length 2738.0 m.\nSegment between 12 and 14: clearing length 7027.0 m.\nSegment between 3 and 4: clearing length 915.0 m.\nSegment between 3 and 2: clearing length 1023.0 m.\nSegment between 3 and 21: clearing length 3767.0 m.\nSegment between 4 and 1: clearing length 342.0 m.\nSegment between 6 and 7: clearing length 1143.0 m.\nSegment between 18 and 13: clearing length 2702.0 m.\nSegment between 1 and 2: clearing length 2029.0 m.\nSegment between 19 and 20: clearing length 937.0 m.\nSegment between 19 and 15: clearing length 2319.0 m.\nSegment between 15 and 16: clearing length 3398.0 m.\nThe plow crew must select a subset of these segments that places all 9 11 19 21 25 on one cleared network without redundant stretches, minimizing the total cleared meters.\n\nWhen you're ready to give the plan, just use the tiny JSON layout below so it's easy to parse:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nHere \"solution\" is a list of the taxiway segments to clear; each pair like [u1, v1] is one segment connecting two pavement nodes. Think of it like filling out a short form: list the connecting pairs you want cleared so all assigned gates are connected.\n\nThis is only a sketch of the expected shape, not the actual answer—fill in the actual node identifiers from the instance.\n\nPlease use the identifiers exactly as they appear in the instance input — no renaming and no new labels.\n- 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 25, "num_edges": 30, "edges": [ { "u": 22, "v": 8, "w": 1737.0 }, { "u": 22, "v": 4, "w": 276.0 }, { "u": 22, "v": 17, "w": 2771.0 }, { "u": 23, "v": 8, "w": 3825.0 }, { "u": 23, "v": 24, "w": 1633.0 }, { "u": 23, "v": 9, "w": 1605.0 }, { "u": 24, "v": 20, "w": 2819.0 }, { "u": 24, "v": 18, "w": 1645.0 }, { "u": 25, "v": 15, "w": 1182.0 }, { "u": 25, "v": 21, "w": 1247.0 }, { "u": 25, "v": 14, "w": 1002.0 }, { "u": 17, "v": 11, "w": 1216.0 }, { "u": 17, "v": 21, "w": 1597.0 }, { "u": 8, "v": 7, "w": 2059.0 }, { "u": 9, "v": 7, "w": 4939.0 }, { "u": 9, "v": 18, "w": 1672.0 }, { "u": 10, "v": 11, "w": 2571.0 }, { "u": 10, "v": 5, "w": 4610.0 }, { "u": 11, "v": 14, "w": 2738.0 }, { "u": 12, "v": 14, "w": 7027.0 }, { "u": 3, "v": 4, "w": 915.0 }, { "u": 3, "v": 2, "w": 1023.0 }, { "u": 3, "v": 21, "w": 3767.0 }, { "u": 4, "v": 1, "w": 342.0 }, { "u": 6, "v": 7, "w": 1143.0 }, { "u": 18, "v": 13, "w": 2702.0 }, { "u": 1, "v": 2, "w": 2029.0 }, { "u": 19, "v": 20, "w": 937.0 }, { "u": 19, "v": 15, "w": 2319.0 }, { "u": 15, "v": 16, "w": 3398.0 } ], "terminals": [ 9, 11, 19, 21, 25 ], "source_file": "I017.stp", "density": 0.1, "viz_instance": "generated_data/STP/viz/STP_L/instance_0016.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0016.png" }, "solution": [ [ 23, 24 ], [ 9, 23 ], [ 20, 24 ], [ 15, 25 ], [ 21, 25 ], [ 11, 17 ], [ 17, 21 ], [ 19, 20 ], [ 15, 19 ] ], "obj": 14555.0, "instance_variant": { "problem_type": "STP", "num_nodes": 25, "num_edges": 30, "edges": [ { "u": 22, "v": 8, "w": 1737.0 }, { "u": 22, "v": 4, "w": 276.0 }, { "u": 22, "v": 17, "w": 2771.0 }, { "u": 23, "v": 8, "w": 3825.0 }, { "u": 23, "v": 24, "w": 1633.0 }, { "u": 23, "v": 9, "w": 1605.0 }, { "u": 24, "v": 20, "w": 2819.0 }, { "u": 24, "v": 18, "w": 1645.0 }, { "u": 25, "v": 15, "w": 1182.0 }, { "u": 25, "v": 21, "w": 1247.0 }, { "u": 25, "v": 14, "w": 1002.0 }, { "u": 17, "v": 11, "w": 1216.0 }, { "u": 17, "v": 21, "w": 1597.0 }, { "u": 8, "v": 7, "w": 2059.0 }, { "u": 9, "v": 7, "w": 4939.0 }, { "u": 9, "v": 18, "w": 1672.0 }, { "u": 10, "v": 11, "w": 2571.0 }, { "u": 10, "v": 5, "w": 4610.0 }, { "u": 11, "v": 14, "w": 2738.0 }, { "u": 12, "v": 14, "w": 7027.0 }, { "u": 3, "v": 4, "w": 915.0 }, { "u": 3, "v": 2, "w": 1023.0 }, { "u": 3, "v": 21, "w": 3767.0 }, { "u": 4, "v": 1, "w": 342.0 }, { "u": 6, "v": 7, "w": 1143.0 }, { "u": 18, "v": 13, "w": 2702.0 }, { "u": 1, "v": 2, "w": 2029.0 }, { "u": 19, "v": 20, "w": 937.0 }, { "u": 19, "v": 15, "w": 2319.0 }, { "u": 15, "v": 16, "w": 3398.0 } ], "density": 0.1, "source_file": "I017.stp", "terminals": [ 9, 11, 19, 21, 25 ] }, "solution_variant": [ [ 23, 24 ], [ 9, 23 ], [ 20, 24 ], [ 15, 25 ], [ 21, 25 ], [ 11, 17 ], [ 17, 21 ], [ 19, 20 ], [ 15, 19 ] ], "context_index": 17, "input_format": "markdown_table", "input_index_base": 1 }, { "task_name": "STP", "problem_type": "STP", "instruction": "Imagine a landscape of protected pockets and a web of possible restoration strips — the task is to choose which strips to fix up so every protected pocket can be reached from any other via those strips, allowing hops across unprotected land where needed. The best setup is the one that uses the least restoration area: sum the area of each corridor that gets restored (shared sections aren’t counted twice) and pick the combination with the smallest total, while making sure no protected site is left out. The concrete details are shown below.\n\n{\n \"total_patches\": 24,\n \"total_candidate_corridors\": 31,\n \"edges\": [\n {\n \"patch_a\": 0,\n \"patch_b\": 1,\n \"restoration_area\": 168286.0\n },\n {\n \"patch_a\": 0,\n \"patch_b\": 2,\n \"restoration_area\": 167275.0\n },\n {\n \"patch_a\": 1,\n \"patch_b\": 6,\n \"restoration_area\": 231.0\n },\n {\n \"patch_a\": 1,\n \"patch_b\": 7,\n \"restoration_area\": 246.0\n },\n {\n \"patch_a\": 2,\n \"patch_b\": 23,\n \"restoration_area\": 1303.0\n },\n {\n \"patch_a\": 3,\n \"patch_b\": 5,\n \"restoration_area\": 251.0\n },\n {\n \"patch_a\": 3,\n \"patch_b\": 14,\n \"restoration_area\": 1305.0\n },\n {\n \"patch_a\": 22,\n \"patch_b\": 11,\n \"restoration_area\": 472.0\n },\n {\n \"patch_a\": 22,\n \"patch_b\": 14,\n \"restoration_area\": 790.0\n },\n {\n \"patch_a\": 22,\n \"patch_b\": 17,\n \"restoration_area\": 647.0\n },\n {\n \"patch_a\": 23,\n \"patch_b\": 14,\n \"restoration_area\": 476.0\n },\n {\n \"patch_a\": 23,\n \"patch_b\": 11,\n \"restoration_area\": 799.0\n },\n {\n \"patch_a\": 23,\n \"patch_b\": 8,\n \"restoration_area\": 472.0\n },\n {\n \"patch_a\": 21,\n \"patch_b\": 16,\n \"restoration_area\": 718.0\n },\n {\n \"patch_a\": 5,\n \"patch_b\": 6,\n \"restoration_area\": 470.0\n },\n {\n \"patch_a\": 5,\n \"patch_b\": 13,\n \"restoration_area\": 208.0\n },\n {\n \"patch_a\": 17,\n \"patch_b\": 18,\n \"restoration_area\": 753.0\n },\n {\n \"patch_a\": 17,\n \"patch_b\": 20,\n \"restoration_area\": 720.0\n },\n {\n \"patch_a\": 18,\n \"patch_b\": 19,\n \"restoration_area\": 710.0\n },\n {\n \"patch_a\": 6,\n \"patch_b\": 10,\n \"restoration_area\": 235.0\n },\n {\n \"patch_a\": 19,\n \"patch_b\": 20,\n \"restoration_area\": 746.0\n },\n {\n \"patch_a\": 20,\n \"patch_b\": 15,\n \"restoration_area\": 59.0\n },\n {\n \"patch_a\": 7,\n \"patch_b\": 12,\n \"restoration_area\": 212.0\n },\n {\n \"patch_a\": 13,\n \"patch_b\": 10,\n \"restoration_area\": 456.0\n },\n {\n \"patch_a\": 13,\n \"patch_b\": 16,\n \"restoration_area\": 699.0\n },\n {\n \"patch_a\": 14,\n \"patch_b\": 15,\n \"restoration_area\": 663.0\n },\n {\n \"patch_a\": 15,\n \"patch_b\": 16,\n \"restoration_area\": 813.0\n },\n {\n \"patch_a\": 8,\n \"patch_b\": 9,\n \"restoration_area\": 806.0\n },\n {\n \"patch_a\": 12,\n \"patch_b\": 10,\n \"restoration_area\": 470.0\n },\n {\n \"patch_a\": 4,\n \"patch_b\": 11,\n \"restoration_area\": 468.0\n },\n {\n \"patch_a\": 4,\n \"patch_b\": 9,\n \"restoration_area\": 5.0\n }\n ],\n \"protected_patches\": [\n 3,\n 5,\n 6,\n 14,\n 15,\n 16,\n 17,\n 19,\n 20\n ]\n}\n\nIf you want to hand in a candidate set of strips to restore, just follow this little JSON layout — super simple, just a list of edge pairs that you'd like to include:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nPretty casual mapping: \"solution\" is the list of corridors you’d repair, and each pair like [u1, v1] is one corridor connecting two sites (write them in the exact identifier form the instance uses). This block is just a sketch of the shape I expect, not the actual answer itself.\n\nQuick reminder: use the exact identifiers from the instance input — don’t rename them and don’t invent new labels.\n\n- 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 24, "num_edges": 31, "edges": [ { "u": 1, "v": 2, "w": 168286.0 }, { "u": 1, "v": 3, "w": 167275.0 }, { "u": 2, "v": 7, "w": 231.0 }, { "u": 2, "v": 8, "w": 246.0 }, { "u": 3, "v": 24, "w": 1303.0 }, { "u": 4, "v": 6, "w": 251.0 }, { "u": 4, "v": 15, "w": 1305.0 }, { "u": 23, "v": 12, "w": 472.0 }, { "u": 23, "v": 15, "w": 790.0 }, { "u": 23, "v": 18, "w": 647.0 }, { "u": 24, "v": 15, "w": 476.0 }, { "u": 24, "v": 12, "w": 799.0 }, { "u": 24, "v": 9, "w": 472.0 }, { "u": 22, "v": 17, "w": 718.0 }, { "u": 6, "v": 7, "w": 470.0 }, { "u": 6, "v": 14, "w": 208.0 }, { "u": 18, "v": 19, "w": 753.0 }, { "u": 18, "v": 21, "w": 720.0 }, { "u": 19, "v": 20, "w": 710.0 }, { "u": 7, "v": 11, "w": 235.0 }, { "u": 20, "v": 21, "w": 746.0 }, { "u": 21, "v": 16, "w": 59.0 }, { "u": 8, "v": 13, "w": 212.0 }, { "u": 14, "v": 11, "w": 456.0 }, { "u": 14, "v": 17, "w": 699.0 }, { "u": 15, "v": 16, "w": 663.0 }, { "u": 16, "v": 17, "w": 813.0 }, { "u": 9, "v": 10, "w": 806.0 }, { "u": 13, "v": 11, "w": 470.0 }, { "u": 5, "v": 12, "w": 468.0 }, { "u": 5, "v": 10, "w": 5.0 } ], "terminals": [ 4, 6, 7, 15, 16, 17, 18, 20, 21 ], "source_file": "I047.stp", "density": 0.11231884057971014, "viz_instance": "generated_data/STP/viz/STP_L/instance_0017.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0017.png" }, "solution": [ [ 4, 6 ], [ 6, 7 ], [ 6, 14 ], [ 18, 21 ], [ 20, 21 ], [ 16, 21 ], [ 14, 17 ], [ 15, 16 ], [ 16, 17 ] ], "obj": 4629.0, "instance_variant": { "problem_type": "STP", "num_nodes": 24, "num_edges": 31, "edges": [ { "u": 0, "v": 1, "w": 168286.0 }, { "u": 0, "v": 2, "w": 167275.0 }, { "u": 1, "v": 6, "w": 231.0 }, { "u": 1, "v": 7, "w": 246.0 }, { "u": 2, "v": 23, "w": 1303.0 }, { "u": 3, "v": 5, "w": 251.0 }, { "u": 3, "v": 14, "w": 1305.0 }, { "u": 22, "v": 11, "w": 472.0 }, { "u": 22, "v": 14, "w": 790.0 }, { "u": 22, "v": 17, "w": 647.0 }, { "u": 23, "v": 14, "w": 476.0 }, { "u": 23, "v": 11, "w": 799.0 }, { "u": 23, "v": 8, "w": 472.0 }, { "u": 21, "v": 16, "w": 718.0 }, { "u": 5, "v": 6, "w": 470.0 }, { "u": 5, "v": 13, "w": 208.0 }, { "u": 17, "v": 18, "w": 753.0 }, { "u": 17, "v": 20, "w": 720.0 }, { "u": 18, "v": 19, "w": 710.0 }, { "u": 6, "v": 10, "w": 235.0 }, { "u": 19, "v": 20, "w": 746.0 }, { "u": 20, "v": 15, "w": 59.0 }, { "u": 7, "v": 12, "w": 212.0 }, { "u": 13, "v": 10, "w": 456.0 }, { "u": 13, "v": 16, "w": 699.0 }, { "u": 14, "v": 15, "w": 663.0 }, { "u": 15, "v": 16, "w": 813.0 }, { "u": 8, "v": 9, "w": 806.0 }, { "u": 12, "v": 10, "w": 470.0 }, { "u": 4, "v": 11, "w": 468.0 }, { "u": 4, "v": 9, "w": 5.0 } ], "density": 0.11231884057971014, "source_file": "I047.stp", "terminals": [ 3, 5, 6, 14, 15, 16, 17, 19, 20 ] }, "solution_variant": [ [ 3, 5 ], [ 5, 6 ], [ 5, 13 ], [ 17, 20 ], [ 19, 20 ], [ 15, 20 ], [ 13, 16 ], [ 14, 15 ], [ 15, 16 ] ], "context_index": 18, "input_format": "json", "input_index_base": 0 }, { "task_name": "STP", "problem_type": "STP", "instruction": "Someone’s designing the overhead rigging for a small art walk and wants every highlighted work to sit on the same accessible skeleton of truss. The practical decision is which truss segments to assemble so the whole set of installations is connected — extra support junctions can be inserted where they make things shorter or neater. A smarter assembly uses the least truss overall: tally the length of each chosen piece and keep that grand total as low as possible, while ensuring every installation is part of the same continuous structure and nothing important is omitted or needlessly doubled. The detailed map and dimensions are shown below.\n\n# total_support_junctions=22\n# total_truss_segments=30\n# featured_installation_nodes=2 6 8 10 12 15 18 21\njunction_u,junction_v,segment_length\n0,1,584.0\n0,2,14481.0\n0,14,1351.0\n1,3,14386.0\n1,14,1925.0\n2,3,532.0\n2,6,147.0\n3,5,105.0\n4,5,14820.0\n4,6,14500.0\n4,7,2555.0\n4,10,456.0\n4,11,2935.0\n5,6,440.0\n19,14,4329.0\n7,15,1242.0\n7,16,4770.0\n7,20,2759.0\n8,9,879.0\n8,10,679.0\n8,13,142358.0\n9,15,661.0\n9,11,1373.0\n10,15,865.0\n11,13,142992.0\n20,18,5606.0\n20,21,2157.0\n21,16,1676.0\n12,18,2015.0\n16,17,839.0\n\nWhen you send the list of chosen truss pieces back, please stick to this simple JSON layout so it's easy to check which segments you picked.\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nHere \"solution\" is just a list of the truss segments to assemble; each inner pair [u, v] names the two junctions that a piece connects. Think of it like filling out a short form: each entry says \"connect this spot to that spot.\" This block is only a sketch of the expected shape, not the actual answer.\n\nPlease use the exact identifiers from the instance input — do not rename them or make up new labels.\n- 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 22, "num_edges": 30, "edges": [ { "u": 1, "v": 2, "w": 584.0 }, { "u": 1, "v": 3, "w": 14481.0 }, { "u": 1, "v": 15, "w": 1351.0 }, { "u": 2, "v": 4, "w": 14386.0 }, { "u": 2, "v": 15, "w": 1925.0 }, { "u": 3, "v": 4, "w": 532.0 }, { "u": 3, "v": 7, "w": 147.0 }, { "u": 4, "v": 6, "w": 105.0 }, { "u": 5, "v": 6, "w": 14820.0 }, { "u": 5, "v": 7, "w": 14500.0 }, { "u": 5, "v": 8, "w": 2555.0 }, { "u": 5, "v": 11, "w": 456.0 }, { "u": 5, "v": 12, "w": 2935.0 }, { "u": 6, "v": 7, "w": 440.0 }, { "u": 20, "v": 15, "w": 4329.0 }, { "u": 8, "v": 16, "w": 1242.0 }, { "u": 8, "v": 17, "w": 4770.0 }, { "u": 8, "v": 21, "w": 2759.0 }, { "u": 9, "v": 10, "w": 879.0 }, { "u": 9, "v": 11, "w": 679.0 }, { "u": 9, "v": 14, "w": 142358.0 }, { "u": 10, "v": 16, "w": 661.0 }, { "u": 10, "v": 12, "w": 1373.0 }, { "u": 11, "v": 16, "w": 865.0 }, { "u": 12, "v": 14, "w": 142992.0 }, { "u": 21, "v": 19, "w": 5606.0 }, { "u": 21, "v": 22, "w": 2157.0 }, { "u": 22, "v": 17, "w": 1676.0 }, { "u": 13, "v": 19, "w": 2015.0 }, { "u": 17, "v": 18, "w": 839.0 } ], "terminals": [ 3, 7, 9, 11, 13, 16, 19, 22 ], "source_file": "I052.stp", "density": 0.12987012987012986, "viz_instance": "generated_data/STP/viz/STP_L/instance_0018.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0018.png" }, "solution": [ [ 3, 7 ], [ 5, 7 ], [ 5, 11 ], [ 8, 16 ], [ 8, 21 ], [ 9, 11 ], [ 11, 16 ], [ 19, 21 ], [ 21, 22 ], [ 13, 19 ] ], "obj": 30426.0, "instance_variant": { "problem_type": "STP", "num_nodes": 22, "num_edges": 30, "edges": [ { "u": 0, "v": 1, "w": 584.0 }, { "u": 0, "v": 2, "w": 14481.0 }, { "u": 0, "v": 14, "w": 1351.0 }, { "u": 1, "v": 3, "w": 14386.0 }, { "u": 1, "v": 14, "w": 1925.0 }, { "u": 2, "v": 3, "w": 532.0 }, { "u": 2, "v": 6, "w": 147.0 }, { "u": 3, "v": 5, "w": 105.0 }, { "u": 4, "v": 5, "w": 14820.0 }, { "u": 4, "v": 6, "w": 14500.0 }, { "u": 4, "v": 7, "w": 2555.0 }, { "u": 4, "v": 10, "w": 456.0 }, { "u": 4, "v": 11, "w": 2935.0 }, { "u": 5, "v": 6, "w": 440.0 }, { "u": 19, "v": 14, "w": 4329.0 }, { "u": 7, "v": 15, "w": 1242.0 }, { "u": 7, "v": 16, "w": 4770.0 }, { "u": 7, "v": 20, "w": 2759.0 }, { "u": 8, "v": 9, "w": 879.0 }, { "u": 8, "v": 10, "w": 679.0 }, { "u": 8, "v": 13, "w": 142358.0 }, { "u": 9, "v": 15, "w": 661.0 }, { "u": 9, "v": 11, "w": 1373.0 }, { "u": 10, "v": 15, "w": 865.0 }, { "u": 11, "v": 13, "w": 142992.0 }, { "u": 20, "v": 18, "w": 5606.0 }, { "u": 20, "v": 21, "w": 2157.0 }, { "u": 21, "v": 16, "w": 1676.0 }, { "u": 12, "v": 18, "w": 2015.0 }, { "u": 16, "v": 17, "w": 839.0 } ], "density": 0.12987012987012986, "source_file": "I052.stp", "terminals": [ 2, 6, 8, 10, 12, 15, 18, 21 ] }, "solution_variant": [ [ 2, 6 ], [ 4, 6 ], [ 4, 10 ], [ 7, 15 ], [ 7, 20 ], [ 8, 10 ], [ 10, 15 ], [ 18, 20 ], [ 20, 21 ], [ 12, 18 ] ], "context_index": 19, "input_format": "csv", "input_index_base": 0 }, { "task_name": "STP", "problem_type": "STP", "instruction": "On a quiet street a few households agreed to join certain gardens with decorative fence sections so they’d form one continuous fenced area for the whole group. The question is which specific fence links to put up so every agreed garden is part of that single connected system, and corners can share gate posts to avoid extra hardware. The measure of a good layout is how little fencing it takes overall — just add up the lengths of all the installed sections to see the total. Each agreed garden must be connected and no fence section may be counted or built twice. The concrete plan and measurements appear below.\n\n{\n \"total_gate_posts\": 27,\n \"total_possible_sections\": 31,\n \"edges\": [\n {\n \"endpoint_a\": 15,\n \"endpoint_b\": 13,\n \"section_length\": 1508.0\n },\n {\n \"endpoint_a\": 15,\n \"endpoint_b\": 6,\n \"section_length\": 2605.0\n },\n {\n \"endpoint_a\": 15,\n \"endpoint_b\": 14,\n \"section_length\": 366.0\n },\n {\n \"endpoint_a\": 16,\n \"endpoint_b\": 18,\n \"section_length\": 3645.0\n },\n {\n \"endpoint_a\": 17,\n \"endpoint_b\": 7,\n \"section_length\": 1154.0\n },\n {\n \"endpoint_a\": 17,\n \"endpoint_b\": 18,\n \"section_length\": 170.0\n },\n {\n \"endpoint_a\": 6,\n \"endpoint_b\": 10,\n \"section_length\": 988.0\n },\n {\n \"endpoint_a\": 0,\n \"endpoint_b\": 1,\n \"section_length\": 513.0\n },\n {\n \"endpoint_a\": 0,\n \"endpoint_b\": 2,\n \"section_length\": 558.0\n },\n {\n \"endpoint_a\": 1,\n \"endpoint_b\": 4,\n \"section_length\": 310.0\n },\n {\n \"endpoint_a\": 1,\n \"endpoint_b\": 12,\n \"section_length\": 583.0\n },\n {\n \"endpoint_a\": 18,\n \"endpoint_b\": 26,\n \"section_length\": 815.0\n },\n {\n \"endpoint_a\": 2,\n \"endpoint_b\": 12,\n \"section_length\": 541.0\n },\n {\n \"endpoint_a\": 2,\n \"endpoint_b\": 11,\n \"section_length\": 583.0\n },\n {\n \"endpoint_a\": 3,\n \"endpoint_b\": 5,\n \"section_length\": 362.0\n },\n {\n \"endpoint_a\": 4,\n \"endpoint_b\": 13,\n \"section_length\": 346.0\n },\n {\n \"endpoint_a\": 4,\n \"endpoint_b\": 5,\n \"section_length\": 511.0\n },\n {\n \"endpoint_a\": 5,\n \"endpoint_b\": 13,\n \"section_length\": 173.0\n },\n {\n \"endpoint_a\": 19,\n \"endpoint_b\": 10,\n \"section_length\": 267.0\n },\n {\n \"endpoint_a\": 21,\n \"endpoint_b\": 22,\n \"section_length\": 762.0\n },\n {\n \"endpoint_a\": 21,\n \"endpoint_b\": 24,\n \"section_length\": 1981.0\n },\n {\n \"endpoint_a\": 22,\n \"endpoint_b\": 23,\n \"section_length\": 1650.0\n },\n {\n \"endpoint_a\": 7,\n \"endpoint_b\": 8,\n \"section_length\": 156.0\n },\n {\n \"endpoint_a\": 12,\n \"endpoint_b\": 20,\n \"section_length\": 625.0\n },\n {\n \"endpoint_a\": 23,\n \"endpoint_b\": 24,\n \"section_length\": 390.0\n },\n {\n \"endpoint_a\": 24,\n \"endpoint_b\": 25,\n \"section_length\": 1898.0\n },\n {\n \"endpoint_a\": 25,\n \"endpoint_b\": 26,\n \"section_length\": 221.0\n },\n {\n \"endpoint_a\": 25,\n \"endpoint_b\": 20,\n \"section_length\": 640.0\n },\n {\n \"endpoint_a\": 26,\n \"endpoint_b\": 14,\n \"section_length\": 386.0\n },\n {\n \"endpoint_a\": 9,\n \"endpoint_b\": 10,\n \"section_length\": 752.0\n },\n {\n \"endpoint_a\": 20,\n \"endpoint_b\": 14,\n \"section_length\": 778.0\n }\n ],\n \"terminal_gardens\": [\n 0,\n 2,\n 3,\n 4,\n 6,\n 7,\n 13,\n 19,\n 22,\n 23,\n 24,\n 25,\n 26\n ]\n}\n\nIf you want to tell me which exact fence links to build, a nice simple way to send that back is in this little JSON shape:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nHere \"solution\" is just a list of fence sections to install; each little pair like [u1, v1] means \"connect corner u1 to corner v1\" (one fence section between those two spots). Think of it as filling in a checklist of which links to put up — nothing fancy, just the pairs of endpoints.\n\nThis JSON is only a sketch of the shape I expect, not the actual answer. When you fill it in, use the exact node identifiers from the instance input — do not rename them or invent new labels. \n- 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 27, "num_edges": 31, "edges": [ { "u": 16, "v": 14, "w": 1508.0 }, { "u": 16, "v": 7, "w": 2605.0 }, { "u": 16, "v": 15, "w": 366.0 }, { "u": 17, "v": 19, "w": 3645.0 }, { "u": 18, "v": 8, "w": 1154.0 }, { "u": 18, "v": 19, "w": 170.0 }, { "u": 7, "v": 11, "w": 988.0 }, { "u": 1, "v": 2, "w": 513.0 }, { "u": 1, "v": 3, "w": 558.0 }, { "u": 2, "v": 5, "w": 310.0 }, { "u": 2, "v": 13, "w": 583.0 }, { "u": 19, "v": 27, "w": 815.0 }, { "u": 3, "v": 13, "w": 541.0 }, { "u": 3, "v": 12, "w": 583.0 }, { "u": 4, "v": 6, "w": 362.0 }, { "u": 5, "v": 14, "w": 346.0 }, { "u": 5, "v": 6, "w": 511.0 }, { "u": 6, "v": 14, "w": 173.0 }, { "u": 20, "v": 11, "w": 267.0 }, { "u": 22, "v": 23, "w": 762.0 }, { "u": 22, "v": 25, "w": 1981.0 }, { "u": 23, "v": 24, "w": 1650.0 }, { "u": 8, "v": 9, "w": 156.0 }, { "u": 13, "v": 21, "w": 625.0 }, { "u": 24, "v": 25, "w": 390.0 }, { "u": 25, "v": 26, "w": 1898.0 }, { "u": 26, "v": 27, "w": 221.0 }, { "u": 26, "v": 21, "w": 640.0 }, { "u": 27, "v": 15, "w": 386.0 }, { "u": 10, "v": 11, "w": 752.0 }, { "u": 21, "v": 15, "w": 778.0 } ], "terminals": [ 1, 3, 4, 5, 7, 8, 14, 20, 23, 24, 25, 26, 27 ], "source_file": "I008.stp", "density": 0.08831908831908832, "viz_instance": "generated_data/STP/viz/STP_L/instance_0019.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0019.png" }, "solution": [ [ 14, 16 ], [ 7, 16 ], [ 15, 16 ], [ 8, 18 ], [ 18, 19 ], [ 7, 11 ], [ 1, 2 ], [ 1, 3 ], [ 2, 5 ], [ 19, 27 ], [ 4, 6 ], [ 5, 14 ], [ 6, 14 ], [ 11, 20 ], [ 23, 24 ], [ 24, 25 ], [ 25, 26 ], [ 26, 27 ], [ 15, 27 ] ], "obj": 14680.0, "instance_variant": { "problem_type": "STP", "num_nodes": 27, "num_edges": 31, "edges": [ { "u": 15, "v": 13, "w": 1508.0 }, { "u": 15, "v": 6, "w": 2605.0 }, { "u": 15, "v": 14, "w": 366.0 }, { "u": 16, "v": 18, "w": 3645.0 }, { "u": 17, "v": 7, "w": 1154.0 }, { "u": 17, "v": 18, "w": 170.0 }, { "u": 6, "v": 10, "w": 988.0 }, { "u": 0, "v": 1, "w": 513.0 }, { "u": 0, "v": 2, "w": 558.0 }, { "u": 1, "v": 4, "w": 310.0 }, { "u": 1, "v": 12, "w": 583.0 }, { "u": 18, "v": 26, "w": 815.0 }, { "u": 2, "v": 12, "w": 541.0 }, { "u": 2, "v": 11, "w": 583.0 }, { "u": 3, "v": 5, "w": 362.0 }, { "u": 4, "v": 13, "w": 346.0 }, { "u": 4, "v": 5, "w": 511.0 }, { "u": 5, "v": 13, "w": 173.0 }, { "u": 19, "v": 10, "w": 267.0 }, { "u": 21, "v": 22, "w": 762.0 }, { "u": 21, "v": 24, "w": 1981.0 }, { "u": 22, "v": 23, "w": 1650.0 }, { "u": 7, "v": 8, "w": 156.0 }, { "u": 12, "v": 20, "w": 625.0 }, { "u": 23, "v": 24, "w": 390.0 }, { "u": 24, "v": 25, "w": 1898.0 }, { "u": 25, "v": 26, "w": 221.0 }, { "u": 25, "v": 20, "w": 640.0 }, { "u": 26, "v": 14, "w": 386.0 }, { "u": 9, "v": 10, "w": 752.0 }, { "u": 20, "v": 14, "w": 778.0 } ], "density": 0.08831908831908832, "source_file": "I008.stp", "terminals": [ 0, 2, 3, 4, 6, 7, 13, 19, 22, 23, 24, 25, 26 ] }, "solution_variant": [ [ 13, 15 ], [ 6, 15 ], [ 14, 15 ], [ 7, 17 ], [ 17, 18 ], [ 6, 10 ], [ 0, 1 ], [ 0, 2 ], [ 1, 4 ], [ 18, 26 ], [ 3, 5 ], [ 4, 13 ], [ 5, 13 ], [ 10, 19 ], [ 22, 23 ], [ 23, 24 ], [ 24, 25 ], [ 25, 26 ], [ 14, 26 ] ], "context_index": 20, "input_format": "json", "input_index_base": 0 }, { "task_name": "STP", "problem_type": "STP", "instruction": "Someone at the municipal office needs a trenching route that links all the listed public buildings with fiber; the trick is to pick streets so the whole set becomes one connected network while keeping the total length of new trenches as small as possible. To see which idea is better, add together the lengths of all the streets chosen — the smaller that sum, the better the plan. Every specified building has to be on the connected route, and any intermediate intersections can be used to save digging. The specific sites and street lengths are shown below.\n\nThe city's street graph has 26 nodes and 31 street segments, and the buildings to connect are C D H J M P Q R W Z.\nStreet between intersections I and F with trench length 2357.0.\nStreet between intersections U and Z with trench length 883.0.\nStreet between intersections J and T with trench length 1139.0.\nStreet between intersections J and V with trench length 1899.0.\nStreet between intersections J and E with trench length 955.0.\nStreet between intersections W and V with trench length 176.0.\nStreet between intersections W and Z with trench length 1823.0.\nStreet between intersections W and T with trench length 714.0.\nStreet between intersections V and H with trench length 293.0.\nStreet between intersections K and E with trench length 581.0.\nStreet between intersections K and S with trench length 1115.0.\nStreet between intersections K and L with trench length 1685.0.\nStreet between intersections S and X with trench length 583.0.\nStreet between intersections S and P with trench length 136.0.\nStreet between intersections L and M with trench length 306.0.\nStreet between intersections L and F with trench length 1443.0.\nStreet between intersections M and D with trench length 627.0.\nStreet between intersections M and N with trench length 686.0.\nStreet between intersections O and P with trench length 561.0.\nStreet between intersections O and R with trench length 1129.0.\nStreet between intersections P and Q with trench length 1120.0.\nStreet between intersections Y and Q with trench length 607.0.\nStreet between intersections Y and Z with trench length 681.0.\nStreet between intersections Y and X with trench length 1235.0.\nStreet between intersections N and C with trench length 628.0.\nStreet between intersections T and X with trench length 611.0.\nStreet between intersections Q and R with trench length 506.0.\nStreet between intersections A and G with trench length 256.0.\nStreet between intersections A and H with trench length 610.0.\nStreet between intersections A and B with trench length 934.0.\nStreet between intersections B and H with trench length 484.0.\nEvery listed building in C D H J M P Q R W Z must lie on the chosen connected route; minimize the sum of trench lengths across the selected streets.\n\nAlso, when you send your plan back, please use this simple JSON layout so it's easy for the office to read automatically:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nThink of \"solution\" as just a list of street segments to trench. Each inner pair like [u1, v1] is one chosen street, given by its two end intersections or building IDs. This block is just a sketch of the shape I need — not your final trenching choices — so fill it with the actual pairs from the map when you submit the plan.\n\nPlease use the exact node identifiers from 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”.", "instance": { "problem_type": "STP", "num_nodes": 26, "num_edges": 31, "edges": [ { "u": 9, "v": 6, "w": 2357.0 }, { "u": 21, "v": 26, "w": 883.0 }, { "u": 10, "v": 20, "w": 1139.0 }, { "u": 10, "v": 22, "w": 1899.0 }, { "u": 10, "v": 5, "w": 955.0 }, { "u": 23, "v": 22, "w": 176.0 }, { "u": 23, "v": 26, "w": 1823.0 }, { "u": 23, "v": 20, "w": 714.0 }, { "u": 22, "v": 8, "w": 293.0 }, { "u": 11, "v": 5, "w": 581.0 }, { "u": 11, "v": 19, "w": 1115.0 }, { "u": 11, "v": 12, "w": 1685.0 }, { "u": 19, "v": 24, "w": 583.0 }, { "u": 19, "v": 16, "w": 136.0 }, { "u": 12, "v": 13, "w": 306.0 }, { "u": 12, "v": 6, "w": 1443.0 }, { "u": 13, "v": 4, "w": 627.0 }, { "u": 13, "v": 14, "w": 686.0 }, { "u": 15, "v": 16, "w": 561.0 }, { "u": 15, "v": 18, "w": 1129.0 }, { "u": 16, "v": 17, "w": 1120.0 }, { "u": 25, "v": 17, "w": 607.0 }, { "u": 25, "v": 26, "w": 681.0 }, { "u": 25, "v": 24, "w": 1235.0 }, { "u": 14, "v": 3, "w": 628.0 }, { "u": 20, "v": 24, "w": 611.0 }, { "u": 17, "v": 18, "w": 506.0 }, { "u": 1, "v": 7, "w": 256.0 }, { "u": 1, "v": 8, "w": 610.0 }, { "u": 1, "v": 2, "w": 934.0 }, { "u": 2, "v": 8, "w": 484.0 } ], "terminals": [ 3, 4, 8, 10, 13, 16, 17, 18, 23, 26 ], "source_file": "I001.stp", "density": 0.09538461538461539, "viz_instance": "generated_data/STP/viz/STP_L/instance_0020.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0020.png" }, "solution": [ [ 10, 20 ], [ 22, 23 ], [ 20, 23 ], [ 8, 22 ], [ 11, 19 ], [ 11, 12 ], [ 19, 24 ], [ 16, 19 ], [ 12, 13 ], [ 4, 13 ], [ 13, 14 ], [ 16, 17 ], [ 17, 25 ], [ 25, 26 ], [ 3, 14 ], [ 20, 24 ], [ 17, 18 ] ], "obj": 11613.0, "instance_variant": { "problem_type": "STP", "num_nodes": 26, "num_edges": 31, "edges": [ { "u": "I", "v": "F", "w": 2357.0 }, { "u": "U", "v": "Z", "w": 883.0 }, { "u": "J", "v": "T", "w": 1139.0 }, { "u": "J", "v": "V", "w": 1899.0 }, { "u": "J", "v": "E", "w": 955.0 }, { "u": "W", "v": "V", "w": 176.0 }, { "u": "W", "v": "Z", "w": 1823.0 }, { "u": "W", "v": "T", "w": 714.0 }, { "u": "V", "v": "H", "w": 293.0 }, { "u": "K", "v": "E", "w": 581.0 }, { "u": "K", "v": "S", "w": 1115.0 }, { "u": "K", "v": "L", "w": 1685.0 }, { "u": "S", "v": "X", "w": 583.0 }, { "u": "S", "v": "P", "w": 136.0 }, { "u": "L", "v": "M", "w": 306.0 }, { "u": "L", "v": "F", "w": 1443.0 }, { "u": "M", "v": "D", "w": 627.0 }, { "u": "M", "v": "N", "w": 686.0 }, { "u": "O", "v": "P", "w": 561.0 }, { "u": "O", "v": "R", "w": 1129.0 }, { "u": "P", "v": "Q", "w": 1120.0 }, { "u": "Y", "v": "Q", "w": 607.0 }, { "u": "Y", "v": "Z", "w": 681.0 }, { "u": "Y", "v": "X", "w": 1235.0 }, { "u": "N", "v": "C", "w": 628.0 }, { "u": "T", "v": "X", "w": 611.0 }, { "u": "Q", "v": "R", "w": 506.0 }, { "u": "A", "v": "G", "w": 256.0 }, { "u": "A", "v": "H", "w": 610.0 }, { "u": "A", "v": "B", "w": 934.0 }, { "u": "B", "v": "H", "w": 484.0 } ], "density": 0.09538461538461539, "source_file": "I001.stp", "terminals": [ "C", "D", "H", "J", "M", "P", "Q", "R", "W", "Z" ] }, "solution_variant": [ [ "J", "T" ], [ "V", "W" ], [ "T", "W" ], [ "H", "V" ], [ "K", "S" ], [ "K", "L" ], [ "S", "X" ], [ "P", "S" ], [ "L", "M" ], [ "D", "M" ], [ "M", "N" ], [ "P", "Q" ], [ "Q", "Y" ], [ "Y", "Z" ], [ "C", "N" ], [ "T", "X" ], [ "Q", "R" ] ], "context_index": 21, "input_format": "markdown_table", "input_index_base": "names" }, { "task_name": "STP", "problem_type": "STP", "instruction": "A homeowner has marked several beds and asked for a piping layout that reaches them all while using as little pipe as possible. The choice to make is which paths to install so the marked beds are all linked together in one continuous network, with the option to branch through other garden points to save material. Better plans are those with a smaller total run of pipe — total length is found by adding up each installed segment — and every marked bed must be connected; no bed can be left out and the system can’t be split into separate pieces. The precise site plan and lengths are shown below.\n\n{\n \"total_site_points\": 30,\n \"possible_pipe_segments\": 35,\n \"edges\": [\n {\n \"endpoint_a\": 6,\n \"endpoint_b\": 7,\n \"segment_length\": 3680.0\n },\n {\n \"endpoint_a\": 6,\n \"endpoint_b\": 8,\n \"segment_length\": 2338.0\n },\n {\n \"endpoint_a\": 7,\n \"endpoint_b\": 29,\n \"segment_length\": 1556.0\n },\n {\n \"endpoint_a\": 20,\n \"endpoint_b\": 9,\n \"segment_length\": 2584.0\n },\n {\n \"endpoint_a\": 8,\n \"endpoint_b\": 13,\n \"segment_length\": 502.0\n },\n {\n \"endpoint_a\": 8,\n \"endpoint_b\": 12,\n \"segment_length\": 3080.0\n },\n {\n \"endpoint_a\": 26,\n \"endpoint_b\": 25,\n \"segment_length\": 471.0\n },\n {\n \"endpoint_a\": 26,\n \"endpoint_b\": 24,\n \"segment_length\": 950.0\n },\n {\n \"endpoint_a\": 26,\n \"endpoint_b\": 27,\n \"segment_length\": 272.0\n },\n {\n \"endpoint_a\": 27,\n \"endpoint_b\": 21,\n \"segment_length\": 1667.0\n },\n {\n \"endpoint_a\": 27,\n \"endpoint_b\": 2,\n \"segment_length\": 1537.0\n },\n {\n \"endpoint_a\": 5,\n \"endpoint_b\": 29,\n \"segment_length\": 57.0\n },\n {\n \"endpoint_a\": 5,\n \"endpoint_b\": 11,\n \"segment_length\": 2353.0\n },\n {\n \"endpoint_a\": 21,\n \"endpoint_b\": 2,\n \"segment_length\": 822.0\n },\n {\n \"endpoint_a\": 21,\n \"endpoint_b\": 3,\n \"segment_length\": 371.0\n },\n {\n \"endpoint_a\": 28,\n \"endpoint_b\": 18,\n \"segment_length\": 983.0\n },\n {\n \"endpoint_a\": 28,\n \"endpoint_b\": 4,\n \"segment_length\": 2202.0\n },\n {\n \"endpoint_a\": 28,\n \"endpoint_b\": 24,\n \"segment_length\": 2444.0\n },\n {\n \"endpoint_a\": 11,\n \"endpoint_b\": 15,\n \"segment_length\": 2362.0\n },\n {\n \"endpoint_a\": 0,\n \"endpoint_b\": 9,\n \"segment_length\": 1672.0\n },\n {\n \"endpoint_a\": 24,\n \"endpoint_b\": 22,\n \"segment_length\": 1332.0\n },\n {\n \"endpoint_a\": 25,\n \"endpoint_b\": 1,\n \"segment_length\": 1419.0\n },\n {\n \"endpoint_a\": 25,\n \"endpoint_b\": 12,\n \"segment_length\": 2095.0\n },\n {\n \"endpoint_a\": 12,\n \"endpoint_b\": 3,\n \"segment_length\": 1403.0\n },\n {\n \"endpoint_a\": 14,\n \"endpoint_b\": 17,\n \"segment_length\": 2313.0\n },\n {\n \"endpoint_a\": 14,\n \"endpoint_b\": 23,\n \"segment_length\": 2534.0\n },\n {\n \"endpoint_a\": 14,\n \"endpoint_b\": 15,\n \"segment_length\": 63.0\n },\n {\n \"endpoint_a\": 15,\n \"endpoint_b\": 16,\n \"segment_length\": 1832.0\n },\n {\n \"endpoint_a\": 17,\n \"endpoint_b\": 1,\n \"segment_length\": 2598.0\n },\n {\n \"endpoint_a\": 17,\n \"endpoint_b\": 29,\n \"segment_length\": 2804.0\n },\n {\n \"endpoint_a\": 1,\n \"endpoint_b\": 22,\n \"segment_length\": 1272.0\n },\n {\n \"endpoint_a\": 22,\n \"endpoint_b\": 10,\n \"segment_length\": 4377.0\n },\n {\n \"endpoint_a\": 18,\n \"endpoint_b\": 19,\n \"segment_length\": 1116.0\n },\n {\n \"endpoint_a\": 19,\n \"endpoint_b\": 10,\n \"segment_length\": 1128.0\n },\n {\n \"endpoint_a\": 9,\n \"endpoint_b\": 10,\n \"segment_length\": 2376.0\n }\n ],\n \"marked_bed_nodes\": [\n 3,\n 6,\n 8,\n 14,\n 15,\n 21\n ]\n}\n\nIf you want to hand me the proposed piping in a tidy, machine-friendly way, just follow this shape when you reply:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nThis shows the shape I expect: \"solution\" is a list of pipe segments, and each pair [u, v] is a single installed segment between point u and point v on the site plan. Think of it like ticking off which connections to lay pipe along — one pair per segment.\n\nJust so you know, that JSON is only a sketch of the shape I need, not the actual plan — fill it with the actual segment identifiers from the instance.\n\nPlease use the exact identifiers from the instance input with no renaming or invented labels — do not change them. 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”.", "instance": { "problem_type": "STP", "num_nodes": 30, "num_edges": 35, "edges": [ { "u": 7, "v": 8, "w": 3680.0 }, { "u": 7, "v": 9, "w": 2338.0 }, { "u": 8, "v": 30, "w": 1556.0 }, { "u": 21, "v": 10, "w": 2584.0 }, { "u": 9, "v": 14, "w": 502.0 }, { "u": 9, "v": 13, "w": 3080.0 }, { "u": 27, "v": 26, "w": 471.0 }, { "u": 27, "v": 25, "w": 950.0 }, { "u": 27, "v": 28, "w": 272.0 }, { "u": 28, "v": 22, "w": 1667.0 }, { "u": 28, "v": 3, "w": 1537.0 }, { "u": 6, "v": 30, "w": 57.0 }, { "u": 6, "v": 12, "w": 2353.0 }, { "u": 22, "v": 3, "w": 822.0 }, { "u": 22, "v": 4, "w": 371.0 }, { "u": 29, "v": 19, "w": 983.0 }, { "u": 29, "v": 5, "w": 2202.0 }, { "u": 29, "v": 25, "w": 2444.0 }, { "u": 12, "v": 16, "w": 2362.0 }, { "u": 1, "v": 10, "w": 1672.0 }, { "u": 25, "v": 23, "w": 1332.0 }, { "u": 26, "v": 2, "w": 1419.0 }, { "u": 26, "v": 13, "w": 2095.0 }, { "u": 13, "v": 4, "w": 1403.0 }, { "u": 15, "v": 18, "w": 2313.0 }, { "u": 15, "v": 24, "w": 2534.0 }, { "u": 15, "v": 16, "w": 63.0 }, { "u": 16, "v": 17, "w": 1832.0 }, { "u": 18, "v": 2, "w": 2598.0 }, { "u": 18, "v": 30, "w": 2804.0 }, { "u": 2, "v": 23, "w": 1272.0 }, { "u": 23, "v": 11, "w": 4377.0 }, { "u": 19, "v": 20, "w": 1116.0 }, { "u": 20, "v": 11, "w": 1128.0 }, { "u": 10, "v": 11, "w": 2376.0 } ], "terminals": [ 4, 7, 9, 15, 16, 22 ], "source_file": "I073.stp", "density": 0.08045977011494253, "viz_instance": "generated_data/STP/viz/STP_L/instance_0021.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0021.png" }, "solution": [ [ 7, 9 ], [ 9, 13 ], [ 4, 22 ], [ 2, 26 ], [ 13, 26 ], [ 4, 13 ], [ 15, 18 ], [ 15, 16 ], [ 2, 18 ] ], "obj": 15680.0, "instance_variant": { "problem_type": "STP", "num_nodes": 30, "num_edges": 35, "edges": [ { "u": 6, "v": 7, "w": 3680.0 }, { "u": 6, "v": 8, "w": 2338.0 }, { "u": 7, "v": 29, "w": 1556.0 }, { "u": 20, "v": 9, "w": 2584.0 }, { "u": 8, "v": 13, "w": 502.0 }, { "u": 8, "v": 12, "w": 3080.0 }, { "u": 26, "v": 25, "w": 471.0 }, { "u": 26, "v": 24, "w": 950.0 }, { "u": 26, "v": 27, "w": 272.0 }, { "u": 27, "v": 21, "w": 1667.0 }, { "u": 27, "v": 2, "w": 1537.0 }, { "u": 5, "v": 29, "w": 57.0 }, { "u": 5, "v": 11, "w": 2353.0 }, { "u": 21, "v": 2, "w": 822.0 }, { "u": 21, "v": 3, "w": 371.0 }, { "u": 28, "v": 18, "w": 983.0 }, { "u": 28, "v": 4, "w": 2202.0 }, { "u": 28, "v": 24, "w": 2444.0 }, { "u": 11, "v": 15, "w": 2362.0 }, { "u": 0, "v": 9, "w": 1672.0 }, { "u": 24, "v": 22, "w": 1332.0 }, { "u": 25, "v": 1, "w": 1419.0 }, { "u": 25, "v": 12, "w": 2095.0 }, { "u": 12, "v": 3, "w": 1403.0 }, { "u": 14, "v": 17, "w": 2313.0 }, { "u": 14, "v": 23, "w": 2534.0 }, { "u": 14, "v": 15, "w": 63.0 }, { "u": 15, "v": 16, "w": 1832.0 }, { "u": 17, "v": 1, "w": 2598.0 }, { "u": 17, "v": 29, "w": 2804.0 }, { "u": 1, "v": 22, "w": 1272.0 }, { "u": 22, "v": 10, "w": 4377.0 }, { "u": 18, "v": 19, "w": 1116.0 }, { "u": 19, "v": 10, "w": 1128.0 }, { "u": 9, "v": 10, "w": 2376.0 } ], "density": 0.08045977011494253, "source_file": "I073.stp", "terminals": [ 3, 6, 8, 14, 15, 21 ] }, "solution_variant": [ [ 6, 8 ], [ 8, 12 ], [ 3, 21 ], [ 1, 25 ], [ 12, 25 ], [ 3, 12 ], [ 14, 17 ], [ 14, 15 ], [ 1, 17 ] ], "context_index": 22, "input_format": "json", "input_index_base": 0 }, { "task_name": "STP", "problem_type": "STP", "instruction": "At the nature reserve the challenge is to recommend which footpaths to harden so the handful of trailheads become one connected network. The practical test for any recommendation is the total paving length: take the lengths of every path included in the plan, add them up, and the plan with the smallest total is preferred. Detouring the paved connections through other clearings or junctions is allowed if it saves overall length, but no trailhead can be omitted and no segment is counted more than once. The specific map and path lengths appear below.\n\nThe map shows 21 locations, 29 paths, and the trailheads to be joined are 3 13.\nFootpath segment joining 7 and 19 with length 2052.0.\nFootpath segment joining 7 and 8 with length 441.0.\nFootpath segment joining 7 and 6 with length 2106.0.\nFootpath segment joining 8 and 9 with length 2169.0.\nFootpath segment joining 9 and 10 with length 728.0.\nFootpath segment joining 10 and 11 with length 1647.0.\nFootpath segment joining 0 and 2 with length 818.0.\nFootpath segment joining 0 and 6 with length 689.0.\nFootpath segment joining 0 and 5 with length 1142.0.\nFootpath segment joining 0 and 1 with length 1077.0.\nFootpath segment joining 1 and 2 with length 483.0.\nFootpath segment joining 1 and 3 with length 1056.0.\nFootpath segment joining 1 and 4 with length 951.0.\nFootpath segment joining 2 and 11 with length 937.0.\nFootpath segment joining 3 and 11 with length 541.0.\nFootpath segment joining 3 and 14 with length 776.0.\nFootpath segment joining 4 and 13 with length 515.0.\nFootpath segment joining 4 and 15 with length 151.0.\nFootpath segment joining 6 and 5 with length 556.0.\nFootpath segment joining 5 and 12 with length 724.0.\nFootpath segment joining 12 and 17 with length 952.0.\nFootpath segment joining 12 and 13 with length 850.0.\nFootpath segment joining 13 and 17 with length 162.0.\nFootpath segment joining 14 and 15 with length 750.0.\nFootpath segment joining 14 and 20 with length 637.0.\nFootpath segment joining 15 and 16 with length 918.0.\nFootpath segment joining 17 and 16 with length 817.0.\nFootpath segment joining 16 and 18 with length 1601.0.\nFootpath segment joining 20 and 18 with length 749.0.\nRecommend the subset of paths that yields the smallest total length while connecting all 3 13.\n\nAlso, when you give your final recommendation, please use this simple JSON layout so it's clear which paths you're choosing:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nThe \"solution\" field is just a list of the path segments to harden; each little pair [u, v] is the two end points of a single trail to include. It's an easy checklist-like sketch — not the finished plan itself, just the shape I expect the answer to take.\n\nPlease make sure to use the exact identifiers from the instance input — don't rename them or invent new labels.\n- 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 21, "num_edges": 29, "edges": [ { "u": 8, "v": 20, "w": 2052.0 }, { "u": 8, "v": 9, "w": 441.0 }, { "u": 8, "v": 7, "w": 2106.0 }, { "u": 9, "v": 10, "w": 2169.0 }, { "u": 10, "v": 11, "w": 728.0 }, { "u": 11, "v": 12, "w": 1647.0 }, { "u": 1, "v": 3, "w": 818.0 }, { "u": 1, "v": 7, "w": 689.0 }, { "u": 1, "v": 6, "w": 1142.0 }, { "u": 1, "v": 2, "w": 1077.0 }, { "u": 2, "v": 3, "w": 483.0 }, { "u": 2, "v": 4, "w": 1056.0 }, { "u": 2, "v": 5, "w": 951.0 }, { "u": 3, "v": 12, "w": 937.0 }, { "u": 4, "v": 12, "w": 541.0 }, { "u": 4, "v": 15, "w": 776.0 }, { "u": 5, "v": 14, "w": 515.0 }, { "u": 5, "v": 16, "w": 151.0 }, { "u": 7, "v": 6, "w": 556.0 }, { "u": 6, "v": 13, "w": 724.0 }, { "u": 13, "v": 18, "w": 952.0 }, { "u": 13, "v": 14, "w": 850.0 }, { "u": 14, "v": 18, "w": 162.0 }, { "u": 15, "v": 16, "w": 750.0 }, { "u": 15, "v": 21, "w": 637.0 }, { "u": 16, "v": 17, "w": 918.0 }, { "u": 18, "v": 17, "w": 817.0 }, { "u": 17, "v": 19, "w": 1601.0 }, { "u": 21, "v": 19, "w": 749.0 } ], "terminals": [ 4, 14 ], "source_file": "I049.stp", "density": 0.1380952380952381, "viz_instance": "generated_data/STP/viz/STP_L/instance_0022.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0022.png" }, "solution": [ [ 4, 15 ], [ 5, 14 ], [ 5, 16 ], [ 15, 16 ] ], "obj": 2192.0, "instance_variant": { "problem_type": "STP", "num_nodes": 21, "num_edges": 29, "edges": [ { "u": 7, "v": 19, "w": 2052.0 }, { "u": 7, "v": 8, "w": 441.0 }, { "u": 7, "v": 6, "w": 2106.0 }, { "u": 8, "v": 9, "w": 2169.0 }, { "u": 9, "v": 10, "w": 728.0 }, { "u": 10, "v": 11, "w": 1647.0 }, { "u": 0, "v": 2, "w": 818.0 }, { "u": 0, "v": 6, "w": 689.0 }, { "u": 0, "v": 5, "w": 1142.0 }, { "u": 0, "v": 1, "w": 1077.0 }, { "u": 1, "v": 2, "w": 483.0 }, { "u": 1, "v": 3, "w": 1056.0 }, { "u": 1, "v": 4, "w": 951.0 }, { "u": 2, "v": 11, "w": 937.0 }, { "u": 3, "v": 11, "w": 541.0 }, { "u": 3, "v": 14, "w": 776.0 }, { "u": 4, "v": 13, "w": 515.0 }, { "u": 4, "v": 15, "w": 151.0 }, { "u": 6, "v": 5, "w": 556.0 }, { "u": 5, "v": 12, "w": 724.0 }, { "u": 12, "v": 17, "w": 952.0 }, { "u": 12, "v": 13, "w": 850.0 }, { "u": 13, "v": 17, "w": 162.0 }, { "u": 14, "v": 15, "w": 750.0 }, { "u": 14, "v": 20, "w": 637.0 }, { "u": 15, "v": 16, "w": 918.0 }, { "u": 17, "v": 16, "w": 817.0 }, { "u": 16, "v": 18, "w": 1601.0 }, { "u": 20, "v": 18, "w": 749.0 } ], "density": 0.1380952380952381, "source_file": "I049.stp", "terminals": [ 3, 13 ] }, "solution_variant": [ [ 3, 14 ], [ 4, 13 ], [ 4, 15 ], [ 14, 15 ] ], "context_index": 23, "input_format": "markdown_table", "input_index_base": 0 }, { "task_name": "STP", "problem_type": "STP", "instruction": "There’s a little puzzle at the museum: which runs of wire should be installed so that all the display cases are linked into a single, continuous security loop? It’s okay to route wiring through other rooms that don’t have displays if that helps shorten things, but every target case has to be included and there shouldn’t be redundant parallel cables. The winner is the plan with the smallest total cable length — add together the lengths of all selected runs to get that number — and the concrete map and lengths follow below.\n\n# total_locations=29\n# total_candidate_runs=36\n# required_display_cases=A E F J L M P W Y Z AA\nrun_endpoint_a,run_endpoint_b,run_length\nA,B,2323.0\nA,H,1663.0\nA,T,4329.0\nB,I,4932.0\nB,F,2200.0\nAA,U,28.0\nAA,X,2339.0\nAA,M,6044.0\nH,K,3300.0\nI,Z,5911.0\nM,N,2322.0\nM,D,2371.0\nN,O,189.0\nN,X,5993.0\nJ,K,1234553.0\nK,L,3782.0\nS,Z,7710.0\nS,D,5440.0\nL,Y,1955.0\nT,R,28.0\nT,U,2345.0\nU,F,2140.0\nV,G,3014.0\nV,C,5954.0\nW,X,2353.0\nW,R,2357.0\nO,P,2194.0\nP,D,2643.0\nAB,E,2162.0\nAB,AC,1339.0\nAB,F,2165.0\nAC,E,2194.0\nAC,F,2162.0\nY,Z,2553.0\nY,Q,4478.0\nG,R,3026.0\n\nAlso, when you send back the wiring plan, please use this simple JSON shape so I can read it automatically:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nPretty straightforward: \"solution\" holds a list of cable runs, and each little pair [u, v] says \"connect node u to node v\" on the museum map. Treat the block above as just a sketch of the shape I need — not the actual wiring plan.\n\nPlease use the exact identifiers from the instance input — no renaming and no new labels.\n- 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”.", "instance": { "problem_type": "STP", "num_nodes": 29, "num_edges": 36, "edges": [ { "u": 1, "v": 2, "w": 2323.0 }, { "u": 1, "v": 8, "w": 1663.0 }, { "u": 1, "v": 20, "w": 4329.0 }, { "u": 2, "v": 9, "w": 4932.0 }, { "u": 2, "v": 6, "w": 2200.0 }, { "u": 27, "v": 21, "w": 28.0 }, { "u": 27, "v": 24, "w": 2339.0 }, { "u": 27, "v": 13, "w": 6044.0 }, { "u": 8, "v": 11, "w": 3300.0 }, { "u": 9, "v": 26, "w": 5911.0 }, { "u": 13, "v": 14, "w": 2322.0 }, { "u": 13, "v": 4, "w": 2371.0 }, { "u": 14, "v": 15, "w": 189.0 }, { "u": 14, "v": 24, "w": 5993.0 }, { "u": 10, "v": 11, "w": 1234553.0 }, { "u": 11, "v": 12, "w": 3782.0 }, { "u": 19, "v": 26, "w": 7710.0 }, { "u": 19, "v": 4, "w": 5440.0 }, { "u": 12, "v": 25, "w": 1955.0 }, { "u": 20, "v": 18, "w": 28.0 }, { "u": 20, "v": 21, "w": 2345.0 }, { "u": 21, "v": 6, "w": 2140.0 }, { "u": 22, "v": 7, "w": 3014.0 }, { "u": 22, "v": 3, "w": 5954.0 }, { "u": 23, "v": 24, "w": 2353.0 }, { "u": 23, "v": 18, "w": 2357.0 }, { "u": 15, "v": 16, "w": 2194.0 }, { "u": 16, "v": 4, "w": 2643.0 }, { "u": 28, "v": 5, "w": 2162.0 }, { "u": 28, "v": 29, "w": 1339.0 }, { "u": 28, "v": 6, "w": 2165.0 }, { "u": 29, "v": 5, "w": 2194.0 }, { "u": 29, "v": 6, "w": 2162.0 }, { "u": 25, "v": 26, "w": 2553.0 }, { "u": 25, "v": 17, "w": 4478.0 }, { "u": 7, "v": 18, "w": 3026.0 } ], "terminals": [ 1, 5, 6, 10, 12, 13, 16, 23, 25, 26, 27 ], "source_file": "I004.stp", "density": 0.08866995073891626, "viz_instance": "generated_data/STP/viz/STP_L/instance_0023.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0023.png" }, "solution": [ [ 1, 8 ], [ 1, 20 ], [ 21, 27 ], [ 13, 27 ], [ 8, 11 ], [ 13, 14 ], [ 14, 15 ], [ 10, 11 ], [ 11, 12 ], [ 12, 25 ], [ 18, 20 ], [ 20, 21 ], [ 6, 21 ], [ 18, 23 ], [ 15, 16 ], [ 5, 28 ], [ 6, 28 ], [ 25, 26 ] ], "obj": 1274109.0, "instance_variant": { "problem_type": "STP", "num_nodes": 29, "num_edges": 36, "edges": [ { "u": "A", "v": "B", "w": 2323.0 }, { "u": "A", "v": "H", "w": 1663.0 }, { "u": "A", "v": "T", "w": 4329.0 }, { "u": "B", "v": "I", "w": 4932.0 }, { "u": "B", "v": "F", "w": 2200.0 }, { "u": "AA", "v": "U", "w": 28.0 }, { "u": "AA", "v": "X", "w": 2339.0 }, { "u": "AA", "v": "M", "w": 6044.0 }, { "u": "H", "v": "K", "w": 3300.0 }, { "u": "I", "v": "Z", "w": 5911.0 }, { "u": "M", "v": "N", "w": 2322.0 }, { "u": "M", "v": "D", "w": 2371.0 }, { "u": "N", "v": "O", "w": 189.0 }, { "u": "N", "v": "X", "w": 5993.0 }, { "u": "J", "v": "K", "w": 1234553.0 }, { "u": "K", "v": "L", "w": 3782.0 }, { "u": "S", "v": "Z", "w": 7710.0 }, { "u": "S", "v": "D", "w": 5440.0 }, { "u": "L", "v": "Y", "w": 1955.0 }, { "u": "T", "v": "R", "w": 28.0 }, { "u": "T", "v": "U", "w": 2345.0 }, { "u": "U", "v": "F", "w": 2140.0 }, { "u": "V", "v": "G", "w": 3014.0 }, { "u": "V", "v": "C", "w": 5954.0 }, { "u": "W", "v": "X", "w": 2353.0 }, { "u": "W", "v": "R", "w": 2357.0 }, { "u": "O", "v": "P", "w": 2194.0 }, { "u": "P", "v": "D", "w": 2643.0 }, { "u": "AB", "v": "E", "w": 2162.0 }, { "u": "AB", "v": "AC", "w": 1339.0 }, { "u": "AB", "v": "F", "w": 2165.0 }, { "u": "AC", "v": "E", "w": 2194.0 }, { "u": "AC", "v": "F", "w": 2162.0 }, { "u": "Y", "v": "Z", "w": 2553.0 }, { "u": "Y", "v": "Q", "w": 4478.0 }, { "u": "G", "v": "R", "w": 3026.0 } ], "density": 0.08866995073891626, "source_file": "I004.stp", "terminals": [ "A", "E", "F", "J", "L", "M", "P", "W", "Y", "Z", "AA" ] }, "solution_variant": [ [ "A", "H" ], [ "A", "T" ], [ "U", "AA" ], [ "M", "AA" ], [ "H", "K" ], [ "M", "N" ], [ "N", "O" ], [ "J", "K" ], [ "K", "L" ], [ "L", "Y" ], [ "R", "T" ], [ "T", "U" ], [ "F", "U" ], [ "R", "W" ], [ "O", "P" ], [ "E", "AB" ], [ "F", "AB" ], [ "Y", "Z" ] ], "context_index": 24, "input_format": "csv", "input_index_base": "names" }, { "task_name": "STP", "problem_type": "STP", "instruction": "There’s a telecom request to connect several crucial desks so they’re all on the same wired network; the team needs to choose which hallways to run the cable through. Passing the wire through other rooms is allowed to create links, and the goal is to end up with the smallest amount of cable possible — compute that by totaling the lengths of the corridors chosen. All required desks have to be part of the final connected route, and corridor lengths are accounted for once in that total. The detailed office layout and lengths are listed below.\n\nOffice plan: 27 total nodes, 32 corridor segments, required desks at nodes B H K P R V W X.\nCorridor connecting F and H, length 2809.0.\nCorridor connecting F and G, length 2899.0.\nCorridor connecting G and A, length 3403.0.\nCorridor connecting G and AA, length 3137.0.\nCorridor connecting I and B, length 681.0.\nCorridor connecting I and Y, length 1649.0.\nCorridor connecting I and W, length 64.0.\nCorridor connecting J and N, length 938.0.\nCorridor connecting J and Q, length 1696.0.\nCorridor connecting J and E, length 695.0.\nCorridor connecting K and W, length 1098.0.\nCorridor connecting K and P, length 226.0.\nCorridor connecting L and D, length 1061.0.\nCorridor connecting L and AA, length 1984.0.\nCorridor connecting L and Q, length 1510.0.\nCorridor connecting M and D, length 556.0.\nCorridor connecting M and U, length 2837.0.\nCorridor connecting M and O, length 492.0.\nCorridor connecting N and Z, length 937.0.\nCorridor connecting N and E, length 983.0.\nCorridor connecting O and T, length 2796.0.\nCorridor connecting O and Q, length 1392.0.\nCorridor connecting P and X, length 1779.0.\nCorridor connecting R and C, length 1009.0.\nCorridor connecting R and X, length 1721.0.\nCorridor connecting T and U, length 505.0.\nCorridor connecting T and S, length 6034.0.\nCorridor connecting U and A, length 5264.0.\nCorridor connecting Z and AA, length 477.0.\nCorridor connecting Z and Y, length 1237.0.\nCorridor connecting X and Y, length 604.0.\nCorridor connecting C and V, length 4411.0.\nRun cable along chosen corridors to connect all B H K P R V W X while minimizing the total of the listed corridor lengths.\n\nYou can just give the chosen corridors as a simple JSON list so I can read it automatically — nothing fancy, just a list of the hallway endpoints you picked.\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nEach pair [u, v] is a corridor between desk/room u and desk/room v that we’d run cable through, and \"solution\" is the whole set of corridors. This is just the shape I’m expecting — a sketch of how to format the answer, not the actual cable plan.\n\nPlease be sure to use the exact identifiers from the instance input — don’t rename or invent new labels. \n- 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”.", "instance": { "problem_type": "STP", "num_nodes": 27, "num_edges": 32, "edges": [ { "u": 6, "v": 8, "w": 2809.0 }, { "u": 6, "v": 7, "w": 2899.0 }, { "u": 7, "v": 1, "w": 3403.0 }, { "u": 7, "v": 27, "w": 3137.0 }, { "u": 9, "v": 2, "w": 681.0 }, { "u": 9, "v": 25, "w": 1649.0 }, { "u": 9, "v": 23, "w": 64.0 }, { "u": 10, "v": 14, "w": 938.0 }, { "u": 10, "v": 17, "w": 1696.0 }, { "u": 10, "v": 5, "w": 695.0 }, { "u": 11, "v": 23, "w": 1098.0 }, { "u": 11, "v": 16, "w": 226.0 }, { "u": 12, "v": 4, "w": 1061.0 }, { "u": 12, "v": 27, "w": 1984.0 }, { "u": 12, "v": 17, "w": 1510.0 }, { "u": 13, "v": 4, "w": 556.0 }, { "u": 13, "v": 21, "w": 2837.0 }, { "u": 13, "v": 15, "w": 492.0 }, { "u": 14, "v": 26, "w": 937.0 }, { "u": 14, "v": 5, "w": 983.0 }, { "u": 15, "v": 20, "w": 2796.0 }, { "u": 15, "v": 17, "w": 1392.0 }, { "u": 16, "v": 24, "w": 1779.0 }, { "u": 18, "v": 3, "w": 1009.0 }, { "u": 18, "v": 24, "w": 1721.0 }, { "u": 20, "v": 21, "w": 505.0 }, { "u": 20, "v": 19, "w": 6034.0 }, { "u": 21, "v": 1, "w": 5264.0 }, { "u": 26, "v": 27, "w": 477.0 }, { "u": 26, "v": 25, "w": 1237.0 }, { "u": 24, "v": 25, "w": 604.0 }, { "u": 3, "v": 22, "w": 4411.0 } ], "terminals": [ 2, 8, 11, 16, 18, 22, 23, 24 ], "source_file": "I010.stp", "density": 0.09116809116809117, "viz_instance": "generated_data/STP/viz/STP_L/instance_0024.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0024.png" }, "solution": [ [ 6, 8 ], [ 6, 7 ], [ 7, 27 ], [ 2, 9 ], [ 9, 25 ], [ 9, 23 ], [ 11, 23 ], [ 11, 16 ], [ 3, 18 ], [ 18, 24 ], [ 26, 27 ], [ 25, 26 ], [ 24, 25 ], [ 3, 22 ] ], "obj": 22022.0, "instance_variant": { "problem_type": "STP", "num_nodes": 27, "num_edges": 32, "edges": [ { "u": "F", "v": "H", "w": 2809.0 }, { "u": "F", "v": "G", "w": 2899.0 }, { "u": "G", "v": "A", "w": 3403.0 }, { "u": "G", "v": "AA", "w": 3137.0 }, { "u": "I", "v": "B", "w": 681.0 }, { "u": "I", "v": "Y", "w": 1649.0 }, { "u": "I", "v": "W", "w": 64.0 }, { "u": "J", "v": "N", "w": 938.0 }, { "u": "J", "v": "Q", "w": 1696.0 }, { "u": "J", "v": "E", "w": 695.0 }, { "u": "K", "v": "W", "w": 1098.0 }, { "u": "K", "v": "P", "w": 226.0 }, { "u": "L", "v": "D", "w": 1061.0 }, { "u": "L", "v": "AA", "w": 1984.0 }, { "u": "L", "v": "Q", "w": 1510.0 }, { "u": "M", "v": "D", "w": 556.0 }, { "u": "M", "v": "U", "w": 2837.0 }, { "u": "M", "v": "O", "w": 492.0 }, { "u": "N", "v": "Z", "w": 937.0 }, { "u": "N", "v": "E", "w": 983.0 }, { "u": "O", "v": "T", "w": 2796.0 }, { "u": "O", "v": "Q", "w": 1392.0 }, { "u": "P", "v": "X", "w": 1779.0 }, { "u": "R", "v": "C", "w": 1009.0 }, { "u": "R", "v": "X", "w": 1721.0 }, { "u": "T", "v": "U", "w": 505.0 }, { "u": "T", "v": "S", "w": 6034.0 }, { "u": "U", "v": "A", "w": 5264.0 }, { "u": "Z", "v": "AA", "w": 477.0 }, { "u": "Z", "v": "Y", "w": 1237.0 }, { "u": "X", "v": "Y", "w": 604.0 }, { "u": "C", "v": "V", "w": 4411.0 } ], "density": 0.09116809116809117, "source_file": "I010.stp", "terminals": [ "B", "H", "K", "P", "R", "V", "W", "X" ] }, "solution_variant": [ [ "F", "H" ], [ "F", "G" ], [ "G", "AA" ], [ "B", "I" ], [ "I", "Y" ], [ "I", "W" ], [ "K", "W" ], [ "K", "P" ], [ "C", "R" ], [ "R", "X" ], [ "Z", "AA" ], [ "Y", "Z" ], [ "X", "Y" ], [ "C", "V" ] ], "context_index": 25, "input_format": "markdown_table", "input_index_base": "names" }, { "task_name": "STP", "problem_type": "STP", "instruction": "There’s a campsite map with a few main sites and several commons, and the goal is to make a single tidy route that hits every campsite by using some of those commons as link points. The job is picking which paths to open and which commons to route through so that the campsites are all joined together. One plan beats another if the total amount of trail to cut and mark is less — simply total up the lengths of the picked segments to compare — and the plan has to include every campsite and avoid building any redundant, duplicated trails. The concrete layout and numbers appear below.\n\nThere are 29 locations, 35 potential trails, and required campsites 5 6 9 14 15 16 18 19 20 22 23 25 27 28.\nTrail between 9 and 6 with length 905.0.\nTrail between 9 and 8 with length 149.0.\nTrail between 9 and 0 with length 2799.0.\nTrail between 26 and 17 with length 900.0.\nTrail between 26 and 10 with length 130.0.\nTrail between 18 and 5 with length 334.0.\nTrail between 18 and 3 with length 3481.0.\nTrail between 18 and 28 with length 1733.0.\nTrail between 10 and 8 with length 624.0.\nTrail between 10 and 14 with length 2196.0.\nTrail between 11 and 17 with length 954.0.\nTrail between 11 and 12 with length 1453.0.\nTrail between 12 and 15 with length 3565.0.\nTrail between 12 and 16 with length 3449.0.\nTrail between 25 and 16 with length 985.0.\nTrail between 21 and 22 with length 66.0.\nTrail between 14 and 8 with length 2618.0.\nTrail between 27 and 22 with length 1116.0.\nTrail between 27 and 28 with length 139.0.\nTrail between 28 and 23 with length 1128.0.\nTrail between 0 and 3 with length 970.0.\nTrail between 0 and 7 with length 1595.0.\nTrail between 23 and 13 with length 109.0.\nTrail between 23 and 22 with length 313.0.\nTrail between 24 and 13 with length 988.0.\nTrail between 24 and 4 with length 335.0.\nTrail between 5 and 4 with length 1386.0.\nTrail between 5 and 2 with length 4573.0.\nTrail between 16 and 7 with length 4416.0.\nTrail between 17 and 6 with length 335.0.\nTrail between 2 and 1 with length 927.0.\nTrail between 2 and 20 with length 5950.0.\nTrail between 1 and 19 with length 3420.0.\nTrail between 6 and 7 with length 476.0.\nTrail between 19 and 4 with length 2202.0.\nPick a set of these trails that joins every required campsite, avoids redundant duplicate paths, and minimizes the total listed lengths.\n\nAlso, when you send back the plan, please use this simple JSON shape so I can read it straight away:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nThink of \"solution\" as a short list of the trail segments you want to open. Each pair like [u1, v1] is one segment connecting two spots on the map (the order doesn’t matter). This block is just a sketch of the shape I expect — you’ll replace the placeholders with the actual node labels from the instance.\n\nPlease use the exact node identifiers from the input — don’t rename them and don’t invent new labels. \n- 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 29, "num_edges": 35, "edges": [ { "u": 10, "v": 7, "w": 905.0 }, { "u": 10, "v": 9, "w": 149.0 }, { "u": 10, "v": 1, "w": 2799.0 }, { "u": 27, "v": 18, "w": 900.0 }, { "u": 27, "v": 11, "w": 130.0 }, { "u": 19, "v": 6, "w": 334.0 }, { "u": 19, "v": 4, "w": 3481.0 }, { "u": 19, "v": 29, "w": 1733.0 }, { "u": 11, "v": 9, "w": 624.0 }, { "u": 11, "v": 15, "w": 2196.0 }, { "u": 12, "v": 18, "w": 954.0 }, { "u": 12, "v": 13, "w": 1453.0 }, { "u": 13, "v": 16, "w": 3565.0 }, { "u": 13, "v": 17, "w": 3449.0 }, { "u": 26, "v": 17, "w": 985.0 }, { "u": 22, "v": 23, "w": 66.0 }, { "u": 15, "v": 9, "w": 2618.0 }, { "u": 28, "v": 23, "w": 1116.0 }, { "u": 28, "v": 29, "w": 139.0 }, { "u": 29, "v": 24, "w": 1128.0 }, { "u": 1, "v": 4, "w": 970.0 }, { "u": 1, "v": 8, "w": 1595.0 }, { "u": 24, "v": 14, "w": 109.0 }, { "u": 24, "v": 23, "w": 313.0 }, { "u": 25, "v": 14, "w": 988.0 }, { "u": 25, "v": 5, "w": 335.0 }, { "u": 6, "v": 5, "w": 1386.0 }, { "u": 6, "v": 3, "w": 4573.0 }, { "u": 17, "v": 8, "w": 4416.0 }, { "u": 18, "v": 7, "w": 335.0 }, { "u": 3, "v": 2, "w": 927.0 }, { "u": 3, "v": 21, "w": 5950.0 }, { "u": 2, "v": 20, "w": 3420.0 }, { "u": 7, "v": 8, "w": 476.0 }, { "u": 20, "v": 5, "w": 2202.0 } ], "terminals": [ 6, 7, 10, 15, 16, 17, 19, 20, 21, 23, 24, 26, 28, 29 ], "source_file": "I042.stp", "density": 0.08620689655172414, "viz_instance": "generated_data/STP/viz/STP_L/instance_0025.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0025.png" }, "solution": [ [ 7, 10 ], [ 9, 10 ], [ 6, 19 ], [ 4, 19 ], [ 12, 18 ], [ 12, 13 ], [ 13, 16 ], [ 13, 17 ], [ 17, 26 ], [ 9, 15 ], [ 23, 28 ], [ 28, 29 ], [ 1, 4 ], [ 1, 8 ], [ 14, 24 ], [ 23, 24 ], [ 14, 25 ], [ 5, 25 ], [ 5, 6 ], [ 7, 18 ], [ 2, 3 ], [ 3, 21 ], [ 2, 20 ], [ 7, 8 ], [ 5, 20 ] ], "obj": 38154.0, "instance_variant": { "problem_type": "STP", "num_nodes": 29, "num_edges": 35, "edges": [ { "u": 9, "v": 6, "w": 905.0 }, { "u": 9, "v": 8, "w": 149.0 }, { "u": 9, "v": 0, "w": 2799.0 }, { "u": 26, "v": 17, "w": 900.0 }, { "u": 26, "v": 10, "w": 130.0 }, { "u": 18, "v": 5, "w": 334.0 }, { "u": 18, "v": 3, "w": 3481.0 }, { "u": 18, "v": 28, "w": 1733.0 }, { "u": 10, "v": 8, "w": 624.0 }, { "u": 10, "v": 14, "w": 2196.0 }, { "u": 11, "v": 17, "w": 954.0 }, { "u": 11, "v": 12, "w": 1453.0 }, { "u": 12, "v": 15, "w": 3565.0 }, { "u": 12, "v": 16, "w": 3449.0 }, { "u": 25, "v": 16, "w": 985.0 }, { "u": 21, "v": 22, "w": 66.0 }, { "u": 14, "v": 8, "w": 2618.0 }, { "u": 27, "v": 22, "w": 1116.0 }, { "u": 27, "v": 28, "w": 139.0 }, { "u": 28, "v": 23, "w": 1128.0 }, { "u": 0, "v": 3, "w": 970.0 }, { "u": 0, "v": 7, "w": 1595.0 }, { "u": 23, "v": 13, "w": 109.0 }, { "u": 23, "v": 22, "w": 313.0 }, { "u": 24, "v": 13, "w": 988.0 }, { "u": 24, "v": 4, "w": 335.0 }, { "u": 5, "v": 4, "w": 1386.0 }, { "u": 5, "v": 2, "w": 4573.0 }, { "u": 16, "v": 7, "w": 4416.0 }, { "u": 17, "v": 6, "w": 335.0 }, { "u": 2, "v": 1, "w": 927.0 }, { "u": 2, "v": 20, "w": 5950.0 }, { "u": 1, "v": 19, "w": 3420.0 }, { "u": 6, "v": 7, "w": 476.0 }, { "u": 19, "v": 4, "w": 2202.0 } ], "density": 0.08620689655172414, "source_file": "I042.stp", "terminals": [ 5, 6, 9, 14, 15, 16, 18, 19, 20, 22, 23, 25, 27, 28 ] }, "solution_variant": [ [ 6, 9 ], [ 8, 9 ], [ 5, 18 ], [ 3, 18 ], [ 11, 17 ], [ 11, 12 ], [ 12, 15 ], [ 12, 16 ], [ 16, 25 ], [ 8, 14 ], [ 22, 27 ], [ 27, 28 ], [ 0, 3 ], [ 0, 7 ], [ 13, 23 ], [ 22, 23 ], [ 13, 24 ], [ 4, 24 ], [ 4, 5 ], [ 6, 17 ], [ 1, 2 ], [ 2, 20 ], [ 1, 19 ], [ 6, 7 ], [ 4, 19 ] ], "context_index": 26, "input_format": "nl", "input_index_base": 0 }, { "task_name": "STP", "problem_type": "STP", "instruction": "Many people think connecting substations means linking them directly, but the coordinator’s job is to pick which distribution lines to actually build so all substations become one connected network while using as little material as possible. The comparison is done by summing the cost (or length) of each selected line — lower totals are better. Intermediate junctions may be used to make cheaper connections, yet every substation must be included and a given physical line should only be built once. The concrete map and numbers are provided below.\n\n# total_junctions=30\n# total_candidate_lines=39\n# required_substations=6 14 23\nendpoint_node_a,endpoint_node_b,line_material_cost\n28,27,639.0\n28,23,723.0\n28,29,878.0\n17,18,551.0\n17,19,1636.0\n14,8,257803.0\n14,11,257447.0\n18,1,326.0\n19,10,838.0\n19,9,807.0\n20,3,440.0\n20,24,188.0\n20,1,820.0\n21,10,372.0\n21,22,91.0\n21,15,452.0\n22,16,400.0\n22,26,1446.0\n23,7,938.0\n23,6,486.0\n24,4,474.0\n24,7,635.0\n25,4,911.0\n0,1,470.0\n0,2,821.0\n2,3,28.0\n27,12,607.0\n27,13,1156.0\n3,4,1101.0\n5,6,897.0\n5,7,402.0\n6,9,277.0\n8,9,619.0\n8,10,577.0\n8,15,392.0\n11,13,616.0\n11,16,554.0\n12,13,579.0\n15,16,230.0\n\nWhen you send back the actual selection, just use a tiny JSON snippet like this so it's easy to parse:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nThis little object is just a sketch of the shape I need: \"solution\" holds a list of built lines, and each inner pair [u, v] means \"build the line between node u and node v.\" Super informal — think of it as filling out a checkbox form that says which connections get built. The example above is only the expected shape, not the real answer.\n\nPlease use the exact identifiers from the instance input with no renaming and no new labels. Valid identifiers look like:\n- plain numbers such as “1” or “23”\n- single capital letters like “A” or “B”\n- a capital letter followed by digits like “A1” or “X7”\n\nThanks — just paste the JSON shaped like that with the real node IDs and we’re good.", "instance": { "problem_type": "STP", "num_nodes": 30, "num_edges": 39, "edges": [ { "u": 29, "v": 28, "w": 639.0 }, { "u": 29, "v": 24, "w": 723.0 }, { "u": 29, "v": 30, "w": 878.0 }, { "u": 18, "v": 19, "w": 551.0 }, { "u": 18, "v": 20, "w": 1636.0 }, { "u": 15, "v": 9, "w": 257803.0 }, { "u": 15, "v": 12, "w": 257447.0 }, { "u": 19, "v": 2, "w": 326.0 }, { "u": 20, "v": 11, "w": 838.0 }, { "u": 20, "v": 10, "w": 807.0 }, { "u": 21, "v": 4, "w": 440.0 }, { "u": 21, "v": 25, "w": 188.0 }, { "u": 21, "v": 2, "w": 820.0 }, { "u": 22, "v": 11, "w": 372.0 }, { "u": 22, "v": 23, "w": 91.0 }, { "u": 22, "v": 16, "w": 452.0 }, { "u": 23, "v": 17, "w": 400.0 }, { "u": 23, "v": 27, "w": 1446.0 }, { "u": 24, "v": 8, "w": 938.0 }, { "u": 24, "v": 7, "w": 486.0 }, { "u": 25, "v": 5, "w": 474.0 }, { "u": 25, "v": 8, "w": 635.0 }, { "u": 26, "v": 5, "w": 911.0 }, { "u": 1, "v": 2, "w": 470.0 }, { "u": 1, "v": 3, "w": 821.0 }, { "u": 3, "v": 4, "w": 28.0 }, { "u": 28, "v": 13, "w": 607.0 }, { "u": 28, "v": 14, "w": 1156.0 }, { "u": 4, "v": 5, "w": 1101.0 }, { "u": 6, "v": 7, "w": 897.0 }, { "u": 6, "v": 8, "w": 402.0 }, { "u": 7, "v": 10, "w": 277.0 }, { "u": 9, "v": 10, "w": 619.0 }, { "u": 9, "v": 11, "w": 577.0 }, { "u": 9, "v": 16, "w": 392.0 }, { "u": 12, "v": 14, "w": 616.0 }, { "u": 12, "v": 17, "w": 554.0 }, { "u": 13, "v": 14, "w": 579.0 }, { "u": 16, "v": 17, "w": 230.0 } ], "terminals": [ 7, 15, 24 ], "source_file": "I067.stp", "density": 0.0896551724137931, "viz_instance": "generated_data/STP/viz/STP_L/instance_0026.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0026.png" }, "solution": [ [ 9, 15 ], [ 7, 24 ], [ 7, 10 ], [ 9, 10 ] ], "obj": 259185.0, "instance_variant": { "problem_type": "STP", "num_nodes": 30, "num_edges": 39, "edges": [ { "u": 28, "v": 27, "w": 639.0 }, { "u": 28, "v": 23, "w": 723.0 }, { "u": 28, "v": 29, "w": 878.0 }, { "u": 17, "v": 18, "w": 551.0 }, { "u": 17, "v": 19, "w": 1636.0 }, { "u": 14, "v": 8, "w": 257803.0 }, { "u": 14, "v": 11, "w": 257447.0 }, { "u": 18, "v": 1, "w": 326.0 }, { "u": 19, "v": 10, "w": 838.0 }, { "u": 19, "v": 9, "w": 807.0 }, { "u": 20, "v": 3, "w": 440.0 }, { "u": 20, "v": 24, "w": 188.0 }, { "u": 20, "v": 1, "w": 820.0 }, { "u": 21, "v": 10, "w": 372.0 }, { "u": 21, "v": 22, "w": 91.0 }, { "u": 21, "v": 15, "w": 452.0 }, { "u": 22, "v": 16, "w": 400.0 }, { "u": 22, "v": 26, "w": 1446.0 }, { "u": 23, "v": 7, "w": 938.0 }, { "u": 23, "v": 6, "w": 486.0 }, { "u": 24, "v": 4, "w": 474.0 }, { "u": 24, "v": 7, "w": 635.0 }, { "u": 25, "v": 4, "w": 911.0 }, { "u": 0, "v": 1, "w": 470.0 }, { "u": 0, "v": 2, "w": 821.0 }, { "u": 2, "v": 3, "w": 28.0 }, { "u": 27, "v": 12, "w": 607.0 }, { "u": 27, "v": 13, "w": 1156.0 }, { "u": 3, "v": 4, "w": 1101.0 }, { "u": 5, "v": 6, "w": 897.0 }, { "u": 5, "v": 7, "w": 402.0 }, { "u": 6, "v": 9, "w": 277.0 }, { "u": 8, "v": 9, "w": 619.0 }, { "u": 8, "v": 10, "w": 577.0 }, { "u": 8, "v": 15, "w": 392.0 }, { "u": 11, "v": 13, "w": 616.0 }, { "u": 11, "v": 16, "w": 554.0 }, { "u": 12, "v": 13, "w": 579.0 }, { "u": 15, "v": 16, "w": 230.0 } ], "density": 0.0896551724137931, "source_file": "I067.stp", "terminals": [ 6, 14, 23 ] }, "solution_variant": [ [ 8, 14 ], [ 6, 23 ], [ 6, 9 ], [ 8, 9 ] ], "context_index": 27, "input_format": "csv", "input_index_base": 0 }, { "task_name": "STP", "problem_type": "STP", "instruction": "Someone in facilities asked for a plan that shows exactly which corridors to expand so all program classrooms are connected by one accessible corridor system. The choice comes down to selecting certain hallways and possibly using lobbies or other public spots as links so every target classroom sits on the same continuous path. The winner is the plan with the smallest total renovation length — simply add up the lengths of each chosen hallway and public area to compare plans. It’s essential that every classroom on the program list is included in that single network and that no corridor gets counted more than once. The concrete map and classroom details follow below.\n\nThere are 22 locations and 28 corridor segments; the program classrooms to connect are 0 2 4 6 8 9 12 13 15 18 21.\nChoose corridor linking 11 and 19 with renovation length 429.0.\nChoose corridor linking 12 and 3 with renovation length 448.0.\nChoose corridor linking 12 and 15 with renovation length 1279.0.\nChoose corridor linking 12 and 20 with renovation length 1646.0.\nChoose corridor linking 13 and 19 with renovation length 3110.0.\nChoose corridor linking 13 and 2 with renovation length 453.0.\nChoose corridor linking 13 and 6 with renovation length 1444.0.\nChoose corridor linking 14 and 6 with renovation length 123.0.\nChoose corridor linking 14 and 5 with renovation length 465.0.\nChoose corridor linking 15 and 16 with renovation length 70.0.\nChoose corridor linking 15 and 9 with renovation length 211.0.\nChoose corridor linking 16 and 10 with renovation length 206.0.\nChoose corridor linking 16 and 18 with renovation length 588.0.\nChoose corridor linking 1 and 2 with renovation length 233.0.\nChoose corridor linking 1 and 3 with renovation length 342.0.\nChoose corridor linking 2 and 3 with renovation length 269.0.\nChoose corridor linking 21 and 19 with renovation length 2047.0.\nChoose corridor linking 21 and 8 with renovation length 1709.0.\nChoose corridor linking 4 and 5 with renovation length 102.0.\nChoose corridor linking 4 and 6 with renovation length 460.0.\nChoose corridor linking 4 and 9 with renovation length 365.0.\nChoose corridor linking 17 and 18 with renovation length 1342.0.\nChoose corridor linking 17 and 7 with renovation length 1991.0.\nChoose corridor linking 5 and 10 with renovation length 365.0.\nChoose corridor linking 18 and 20 with renovation length 199.0.\nChoose corridor linking 9 and 10 with renovation length 81.0.\nChoose corridor linking 20 and 7 with renovation length 1707.0.\nChoose corridor linking 7 and 0 with renovation length 5032.0.\nThe selected corridors must join all 0 2 4 6 8 9 12 13 15 18 21 into one accessible corridor system and no corridor may be counted more than once.\n\nAlso, when you send back the set of corridors to renovate, please follow this simple JSON layout so I can read it automatically:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nIn plain terms: \"solution\" is just a list of corridor links to include. Each pair like [u1, v1] means \"take the hallway (or connection) between node u1 and node v1\" — think of those u/v tokens as the room or junction IDs on the building map. This JSON is only a sketch of the shape I need, not the actual answer.\n\nPlease use the exact identifiers from 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\", or a capital letter followed by digits like \"A1\" or \"X7\".", "instance": { "problem_type": "STP", "num_nodes": 22, "num_edges": 28, "edges": [ { "u": 12, "v": 20, "w": 429.0 }, { "u": 13, "v": 4, "w": 448.0 }, { "u": 13, "v": 16, "w": 1279.0 }, { "u": 13, "v": 21, "w": 1646.0 }, { "u": 14, "v": 20, "w": 3110.0 }, { "u": 14, "v": 3, "w": 453.0 }, { "u": 14, "v": 7, "w": 1444.0 }, { "u": 15, "v": 7, "w": 123.0 }, { "u": 15, "v": 6, "w": 465.0 }, { "u": 16, "v": 17, "w": 70.0 }, { "u": 16, "v": 10, "w": 211.0 }, { "u": 17, "v": 11, "w": 206.0 }, { "u": 17, "v": 19, "w": 588.0 }, { "u": 2, "v": 3, "w": 233.0 }, { "u": 2, "v": 4, "w": 342.0 }, { "u": 3, "v": 4, "w": 269.0 }, { "u": 22, "v": 20, "w": 2047.0 }, { "u": 22, "v": 9, "w": 1709.0 }, { "u": 5, "v": 6, "w": 102.0 }, { "u": 5, "v": 7, "w": 460.0 }, { "u": 5, "v": 10, "w": 365.0 }, { "u": 18, "v": 19, "w": 1342.0 }, { "u": 18, "v": 8, "w": 1991.0 }, { "u": 6, "v": 11, "w": 365.0 }, { "u": 19, "v": 21, "w": 199.0 }, { "u": 10, "v": 11, "w": 81.0 }, { "u": 21, "v": 8, "w": 1707.0 }, { "u": 8, "v": 1, "w": 5032.0 } ], "terminals": [ 1, 3, 5, 7, 9, 10, 13, 14, 16, 19, 22 ], "source_file": "I012.stp", "density": 0.12121212121212122, "viz_instance": "generated_data/STP/viz/STP_L/instance_0027.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0027.png" }, "solution": [ [ 4, 13 ], [ 13, 16 ], [ 14, 20 ], [ 3, 14 ], [ 16, 17 ], [ 10, 16 ], [ 17, 19 ], [ 3, 4 ], [ 20, 22 ], [ 9, 22 ], [ 5, 7 ], [ 5, 10 ], [ 19, 21 ], [ 8, 21 ], [ 1, 8 ] ], "obj": 17947.0, "instance_variant": { "problem_type": "STP", "num_nodes": 22, "num_edges": 28, "edges": [ { "u": 11, "v": 19, "w": 429.0 }, { "u": 12, "v": 3, "w": 448.0 }, { "u": 12, "v": 15, "w": 1279.0 }, { "u": 12, "v": 20, "w": 1646.0 }, { "u": 13, "v": 19, "w": 3110.0 }, { "u": 13, "v": 2, "w": 453.0 }, { "u": 13, "v": 6, "w": 1444.0 }, { "u": 14, "v": 6, "w": 123.0 }, { "u": 14, "v": 5, "w": 465.0 }, { "u": 15, "v": 16, "w": 70.0 }, { "u": 15, "v": 9, "w": 211.0 }, { "u": 16, "v": 10, "w": 206.0 }, { "u": 16, "v": 18, "w": 588.0 }, { "u": 1, "v": 2, "w": 233.0 }, { "u": 1, "v": 3, "w": 342.0 }, { "u": 2, "v": 3, "w": 269.0 }, { "u": 21, "v": 19, "w": 2047.0 }, { "u": 21, "v": 8, "w": 1709.0 }, { "u": 4, "v": 5, "w": 102.0 }, { "u": 4, "v": 6, "w": 460.0 }, { "u": 4, "v": 9, "w": 365.0 }, { "u": 17, "v": 18, "w": 1342.0 }, { "u": 17, "v": 7, "w": 1991.0 }, { "u": 5, "v": 10, "w": 365.0 }, { "u": 18, "v": 20, "w": 199.0 }, { "u": 9, "v": 10, "w": 81.0 }, { "u": 20, "v": 7, "w": 1707.0 }, { "u": 7, "v": 0, "w": 5032.0 } ], "density": 0.12121212121212122, "source_file": "I012.stp", "terminals": [ 0, 2, 4, 6, 8, 9, 12, 13, 15, 18, 21 ] }, "solution_variant": [ [ 3, 12 ], [ 12, 15 ], [ 13, 19 ], [ 2, 13 ], [ 15, 16 ], [ 9, 15 ], [ 16, 18 ], [ 2, 3 ], [ 19, 21 ], [ 8, 21 ], [ 4, 6 ], [ 4, 9 ], [ 18, 20 ], [ 7, 20 ], [ 0, 7 ] ], "context_index": 28, "input_format": "nl", "input_index_base": 0 }, { "task_name": "STP", "problem_type": "STP", "instruction": "We’ve been asked by the block association to decide how to hook up lamppost circuits so every community square shares one continuous lighting system. The decision is simply which connections to make; a better plan is the one with the smallest total amount of cable used, which you figure out by summing the lengths of all selected connections. It’s okay to route power through other poles or junctions that aren’t squares to save wire, but every square must be part of the single network and no duplicate runs or missing squares are allowed. The specific layout and measurements appear below.\n\n{\n \"number_of_poles_and_junctions\": 24,\n \"number_of_possible_connection_segments\": 30,\n \"edges\": [\n {\n \"pole_u\": 16,\n \"pole_v\": 17,\n \"cable_length\": 448.0\n },\n {\n \"pole_u\": 16,\n \"pole_v\": 0,\n \"cable_length\": 27.0\n },\n {\n \"pole_u\": 16,\n \"pole_v\": 8,\n \"cable_length\": 342.0\n },\n {\n \"pole_u\": 17,\n \"pole_v\": 20,\n \"cable_length\": 40.0\n },\n {\n \"pole_u\": 17,\n \"pole_v\": 6,\n \"cable_length\": 343.0\n },\n {\n \"pole_u\": 12,\n \"pole_v\": 23,\n \"cable_length\": 519.0\n },\n {\n \"pole_u\": 19,\n \"pole_v\": 5,\n \"cable_length\": 316.0\n },\n {\n \"pole_u\": 19,\n \"pole_v\": 21,\n \"cable_length\": 77.0\n },\n {\n \"pole_u\": 19,\n \"pole_v\": 4,\n \"cable_length\": 620.0\n },\n {\n \"pole_u\": 20,\n \"pole_v\": 0,\n \"cable_length\": 447.0\n },\n {\n \"pole_u\": 20,\n \"pole_v\": 1,\n \"cable_length\": 391.0\n },\n {\n \"pole_u\": 21,\n \"pole_v\": 11,\n \"cable_length\": 127.0\n },\n {\n \"pole_u\": 21,\n \"pole_v\": 10,\n \"cable_length\": 387.0\n },\n {\n \"pole_u\": 13,\n \"pole_v\": 14,\n \"cable_length\": 659.0\n },\n {\n \"pole_u\": 13,\n \"pole_v\": 4,\n \"cable_length\": 1565.0\n },\n {\n \"pole_u\": 22,\n \"pole_v\": 7,\n \"cable_length\": 517.0\n },\n {\n \"pole_u\": 22,\n \"pole_v\": 23,\n \"cable_length\": 1064.0\n },\n {\n \"pole_u\": 22,\n \"pole_v\": 10,\n \"cable_length\": 454.0\n },\n {\n \"pole_u\": 1,\n \"pole_v\": 11,\n \"cable_length\": 20.0\n },\n {\n \"pole_u\": 1,\n \"pole_v\": 2,\n \"cable_length\": 468.0\n },\n {\n \"pole_u\": 2,\n \"pole_v\": 5,\n \"cable_length\": 72.0\n },\n {\n \"pole_u\": 2,\n \"pole_v\": 15,\n \"cable_length\": 356.0\n },\n {\n \"pole_u\": 2,\n \"pole_v\": 18,\n \"cable_length\": 356.0\n },\n {\n \"pole_u\": 3,\n \"pole_v\": 4,\n \"cable_length\": 322.0\n },\n {\n \"pole_u\": 3,\n \"pole_v\": 5,\n \"cable_length\": 624.0\n },\n {\n \"pole_u\": 6,\n \"pole_v\": 7,\n \"cable_length\": 454.0\n },\n {\n \"pole_u\": 6,\n \"pole_v\": 8,\n \"cable_length\": 458.0\n },\n {\n \"pole_u\": 9,\n \"pole_v\": 10,\n \"cable_length\": 115.0\n },\n {\n \"pole_u\": 9,\n \"pole_v\": 11,\n \"cable_length\": 384.0\n },\n {\n \"pole_u\": 15,\n \"pole_v\": 18,\n \"cable_length\": 90.0\n }\n ],\n \"squares_to_connect\": [\n 2,\n 4,\n 5,\n 6,\n 11,\n 18,\n 20\n ]\n}\n\nAlso, when you send the actual plan back, please stick to a tiny JSON shape like this so it’s easy to read and plug in:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nThink of it like a little form: \"solution\" is the list of cable runs you want to make, and each pair [u1, v1] is one direct connection between two poles or junctions. This block is just a sketch of the shape I need, not the final wiring list — fill it with the actual pairs from the instance when you reply.\n\nPlease make sure to use the exact identifiers given in the instance input — don’t rename them or invent new ones. \n- 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 24, "num_edges": 30, "edges": [ { "u": 17, "v": 18, "w": 448.0 }, { "u": 17, "v": 1, "w": 27.0 }, { "u": 17, "v": 9, "w": 342.0 }, { "u": 18, "v": 21, "w": 40.0 }, { "u": 18, "v": 7, "w": 343.0 }, { "u": 13, "v": 24, "w": 519.0 }, { "u": 20, "v": 6, "w": 316.0 }, { "u": 20, "v": 22, "w": 77.0 }, { "u": 20, "v": 5, "w": 620.0 }, { "u": 21, "v": 1, "w": 447.0 }, { "u": 21, "v": 2, "w": 391.0 }, { "u": 22, "v": 12, "w": 127.0 }, { "u": 22, "v": 11, "w": 387.0 }, { "u": 14, "v": 15, "w": 659.0 }, { "u": 14, "v": 5, "w": 1565.0 }, { "u": 23, "v": 8, "w": 517.0 }, { "u": 23, "v": 24, "w": 1064.0 }, { "u": 23, "v": 11, "w": 454.0 }, { "u": 2, "v": 12, "w": 20.0 }, { "u": 2, "v": 3, "w": 468.0 }, { "u": 3, "v": 6, "w": 72.0 }, { "u": 3, "v": 16, "w": 356.0 }, { "u": 3, "v": 19, "w": 356.0 }, { "u": 4, "v": 5, "w": 322.0 }, { "u": 4, "v": 6, "w": 624.0 }, { "u": 7, "v": 8, "w": 454.0 }, { "u": 7, "v": 9, "w": 458.0 }, { "u": 10, "v": 11, "w": 115.0 }, { "u": 10, "v": 12, "w": 384.0 }, { "u": 16, "v": 19, "w": 90.0 } ], "terminals": [ 3, 5, 6, 7, 12, 19, 21 ], "source_file": "I042.stp", "density": 0.10869565217391304, "viz_instance": "generated_data/STP/viz/STP_L/instance_0028.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0028.png" }, "solution": [ [ 18, 21 ], [ 7, 18 ], [ 6, 20 ], [ 20, 22 ], [ 5, 20 ], [ 2, 21 ], [ 12, 22 ], [ 2, 12 ], [ 3, 6 ], [ 3, 19 ] ], "obj": 2362.0, "instance_variant": { "problem_type": "STP", "num_nodes": 24, "num_edges": 30, "edges": [ { "u": 16, "v": 17, "w": 448.0 }, { "u": 16, "v": 0, "w": 27.0 }, { "u": 16, "v": 8, "w": 342.0 }, { "u": 17, "v": 20, "w": 40.0 }, { "u": 17, "v": 6, "w": 343.0 }, { "u": 12, "v": 23, "w": 519.0 }, { "u": 19, "v": 5, "w": 316.0 }, { "u": 19, "v": 21, "w": 77.0 }, { "u": 19, "v": 4, "w": 620.0 }, { "u": 20, "v": 0, "w": 447.0 }, { "u": 20, "v": 1, "w": 391.0 }, { "u": 21, "v": 11, "w": 127.0 }, { "u": 21, "v": 10, "w": 387.0 }, { "u": 13, "v": 14, "w": 659.0 }, { "u": 13, "v": 4, "w": 1565.0 }, { "u": 22, "v": 7, "w": 517.0 }, { "u": 22, "v": 23, "w": 1064.0 }, { "u": 22, "v": 10, "w": 454.0 }, { "u": 1, "v": 11, "w": 20.0 }, { "u": 1, "v": 2, "w": 468.0 }, { "u": 2, "v": 5, "w": 72.0 }, { "u": 2, "v": 15, "w": 356.0 }, { "u": 2, "v": 18, "w": 356.0 }, { "u": 3, "v": 4, "w": 322.0 }, { "u": 3, "v": 5, "w": 624.0 }, { "u": 6, "v": 7, "w": 454.0 }, { "u": 6, "v": 8, "w": 458.0 }, { "u": 9, "v": 10, "w": 115.0 }, { "u": 9, "v": 11, "w": 384.0 }, { "u": 15, "v": 18, "w": 90.0 } ], "density": 0.10869565217391304, "source_file": "I042.stp", "terminals": [ 2, 4, 5, 6, 11, 18, 20 ] }, "solution_variant": [ [ 17, 20 ], [ 6, 17 ], [ 5, 19 ], [ 19, 21 ], [ 4, 19 ], [ 1, 20 ], [ 11, 21 ], [ 1, 11 ], [ 2, 5 ], [ 2, 18 ] ], "context_index": 29, "input_format": "json", "input_index_base": 0 }, { "task_name": "STP", "problem_type": "STP", "instruction": "Out in the countryside the planner’s job is to select certain roads so that every pickup location is connected into a single drivable web — adding crossroads to bridge gaps is allowed — while keeping the overall miles of road used to a minimum. The way to compare plans is to total the lengths of the chosen roads; the lower that total, the better the plan. It’s required that no pickup be excluded and the chosen roads together form one continuous network, with each road’s length counted once in the sum. The exact roads and distances are listed below.\n\nBelow are the 26 candidate roads among the 22 map points; the required pickup sites are 1 7 10 11 13 20.\nRoad between 19 and 11 with length 1311.0.\nRoad between 20 and 11 with length 1766.0.\nRoad between 0 and 1 with length 686.0.\nRoad between 0 and 2 with length 1323.0.\nRoad between 0 and 8 with length 272581.0.\nRoad between 1 and 12 with length 1292.0.\nRoad between 1 and 7 with length 522.0.\nRoad between 2 and 11 with length 1042.0.\nRoad between 2 and 12 with length 622.0.\nRoad between 3 and 4 with length 195.0.\nRoad between 3 and 8 with length 272581.0.\nRoad between 3 and 10 with length 382.0.\nRoad between 4 and 14 with length 373.0.\nRoad between 4 and 5 with length 390.0.\nRoad between 5 and 15 with length 404.0.\nRoad between 6 and 7 with length 589.0.\nRoad between 7 and 18 with length 199.0.\nRoad between 21 and 13 with length 244.0.\nRoad between 11 and 9 with length 1964.0.\nRoad between 12 and 17 with length 1394.0.\nRoad between 13 and 9 with length 6.0.\nRoad between 13 and 14 with length 513.0.\nRoad between 14 and 10 with length 115.0.\nRoad between 15 and 16 with length 5.0.\nRoad between 16 and 18 with length 215.0.\nRoad between 9 and 10 with length 526.0.\nThe planner must select a subset of these roads that spans every required pickup site 1 7 10 11 13 20 while minimizing the total miles used.\n\nYou can just send back the chosen roads in a tiny JSON sketch like this — super simple and easy to read:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nHere \"solution\" is just a list of road segments; each pair like [u1, v1] stands for the single road that joins crossroads u1 and v1. Think of it like filling out a short form: one row per chosen road, with the two endpoints listed.\n\nThis is only a sketch of the expected shape, not the actual answer — replace the placeholders with the real node identifiers from the instance.\n\nPlease use the identifiers exactly as they appear in the instance input — no renaming, no invented labels. \n- 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 22, "num_edges": 26, "edges": [ { "u": 20, "v": 12, "w": 1311.0 }, { "u": 21, "v": 12, "w": 1766.0 }, { "u": 1, "v": 2, "w": 686.0 }, { "u": 1, "v": 3, "w": 1323.0 }, { "u": 1, "v": 9, "w": 272581.0 }, { "u": 2, "v": 13, "w": 1292.0 }, { "u": 2, "v": 8, "w": 522.0 }, { "u": 3, "v": 12, "w": 1042.0 }, { "u": 3, "v": 13, "w": 622.0 }, { "u": 4, "v": 5, "w": 195.0 }, { "u": 4, "v": 9, "w": 272581.0 }, { "u": 4, "v": 11, "w": 382.0 }, { "u": 5, "v": 15, "w": 373.0 }, { "u": 5, "v": 6, "w": 390.0 }, { "u": 6, "v": 16, "w": 404.0 }, { "u": 7, "v": 8, "w": 589.0 }, { "u": 8, "v": 19, "w": 199.0 }, { "u": 22, "v": 14, "w": 244.0 }, { "u": 12, "v": 10, "w": 1964.0 }, { "u": 13, "v": 18, "w": 1394.0 }, { "u": 14, "v": 10, "w": 6.0 }, { "u": 14, "v": 15, "w": 513.0 }, { "u": 15, "v": 11, "w": 115.0 }, { "u": 16, "v": 17, "w": 5.0 }, { "u": 17, "v": 19, "w": 215.0 }, { "u": 10, "v": 11, "w": 526.0 } ], "terminals": [ 2, 8, 11, 12, 14, 21 ], "source_file": "I037.stp", "density": 0.11255411255411256, "viz_instance": "generated_data/STP/viz/STP_L/instance_0029.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0029.png" }, "solution": [ [ 12, 21 ], [ 2, 8 ], [ 5, 15 ], [ 5, 6 ], [ 6, 16 ], [ 8, 19 ], [ 10, 12 ], [ 10, 14 ], [ 14, 15 ], [ 11, 15 ], [ 16, 17 ], [ 17, 19 ] ], "obj": 6472.0, "instance_variant": { "problem_type": "STP", "num_nodes": 22, "num_edges": 26, "edges": [ { "u": 19, "v": 11, "w": 1311.0 }, { "u": 20, "v": 11, "w": 1766.0 }, { "u": 0, "v": 1, "w": 686.0 }, { "u": 0, "v": 2, "w": 1323.0 }, { "u": 0, "v": 8, "w": 272581.0 }, { "u": 1, "v": 12, "w": 1292.0 }, { "u": 1, "v": 7, "w": 522.0 }, { "u": 2, "v": 11, "w": 1042.0 }, { "u": 2, "v": 12, "w": 622.0 }, { "u": 3, "v": 4, "w": 195.0 }, { "u": 3, "v": 8, "w": 272581.0 }, { "u": 3, "v": 10, "w": 382.0 }, { "u": 4, "v": 14, "w": 373.0 }, { "u": 4, "v": 5, "w": 390.0 }, { "u": 5, "v": 15, "w": 404.0 }, { "u": 6, "v": 7, "w": 589.0 }, { "u": 7, "v": 18, "w": 199.0 }, { "u": 21, "v": 13, "w": 244.0 }, { "u": 11, "v": 9, "w": 1964.0 }, { "u": 12, "v": 17, "w": 1394.0 }, { "u": 13, "v": 9, "w": 6.0 }, { "u": 13, "v": 14, "w": 513.0 }, { "u": 14, "v": 10, "w": 115.0 }, { "u": 15, "v": 16, "w": 5.0 }, { "u": 16, "v": 18, "w": 215.0 }, { "u": 9, "v": 10, "w": 526.0 } ], "density": 0.11255411255411256, "source_file": "I037.stp", "terminals": [ 1, 7, 10, 11, 13, 20 ] }, "solution_variant": [ [ 11, 20 ], [ 1, 7 ], [ 4, 14 ], [ 4, 5 ], [ 5, 15 ], [ 7, 18 ], [ 9, 11 ], [ 9, 13 ], [ 13, 14 ], [ 10, 14 ], [ 15, 16 ], [ 16, 18 ] ], "context_index": 30, "input_format": "nl", "input_index_base": 0 }, { "task_name": "STP", "problem_type": "STP", "instruction": "Recently the maintenance team was asked to design a duct layout that connects every required room into one continuous ventilation route, and they had to pick which duct segments to put in. A few non-room spaces can act as shortcuts, so the decision comes down to selecting the segments that join everything up. The better layout is the one that reaches every required room with a single connected system and keeps the overall duct footage minimal — you measure that by adding up the lengths of the ducts you plan to install. No required room can be skipped, and the system must be one connected network, not split apart. The concrete map and numbers are shown below.\n\nThe concrete map and numbers are shown below: it lists 22 distinct locations, 26 possible duct segments, and required rooms 0 1 2 4 10 13 17 18.\nA candidate duct segment connects 11 and 12 and is 2013.0 feet long.\nA candidate duct segment connects 11 and 13 and is 651.0 feet long.\nA candidate duct segment connects 12 and 14 and is 398.0 feet long.\nA candidate duct segment connects 12 and 16 and is 189.0 feet long.\nA candidate duct segment connects 18 and 19 and is 1066.0 feet long.\nA candidate duct segment connects 18 and 8 and is 5387.0 feet long.\nA candidate duct segment connects 18 and 6 and is 1509.0 feet long.\nA candidate duct segment connects 15 and 2 and is 4664.0 feet long.\nA candidate duct segment connects 15 and 21 and is 16809.0 feet long.\nA candidate duct segment connects 15 and 17 and is 4492.0 feet long.\nA candidate duct segment connects 14 and 13 and is 2032.0 feet long.\nA candidate duct segment connects 14 and 1 and is 604.0 feet long.\nA candidate duct segment connects 13 and 7 and is 508.0 feet long.\nA candidate duct segment connects 13 and 0 and is 984.0 feet long.\nA candidate duct segment connects 8 and 9 and is 1794.0 feet long.\nA candidate duct segment connects 9 and 10 and is 1961.0 feet long.\nA candidate duct segment connects 9 and 20 and is 1401.0 feet long.\nA candidate duct segment connects 16 and 10 and is 1132.0 feet long.\nA candidate duct segment connects 16 and 5 and is 576.0 feet long.\nA candidate duct segment connects 17 and 1 and is 608.0 feet long.\nA candidate duct segment connects 17 and 4 and is 2299.0 feet long.\nA candidate duct segment connects 0 and 1 and is 2061.0 feet long.\nA candidate duct segment connects 3 and 4 and is 402.0 feet long.\nA candidate duct segment connects 3 and 5 and is 458.0 feet long.\nA candidate duct segment connects 4 and 6 and is 471.0 feet long.\nA candidate duct segment connects 5 and 6 and is 417.0 feet long.\nThe maintenance team must choose segments that connect every required room into one continuous ventilation network while minimizing the total duct footage.\n\nWhen you send back which duct segments you picked, a tiny JSON snippet like the one below is the easiest way for me to read it automatically. Nothing fancy — just a list of edge pairs.\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nHere \"solution\" is just a list of the duct segments you plan to install. Each segment is written as a short pair [u, v] naming the two endpoints (use the same labels you see on the map). This block is only a sketch of the shape I expect — not the actual answer.\n\nPlease make sure to use the identifiers exactly as they appear in the instance input — do not rename them or invent new labels.\n- 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”.\n\nWhen you're ready, paste the real list of segments in that format and I’ll take a look.", "instance": { "problem_type": "STP", "num_nodes": 22, "num_edges": 26, "edges": [ { "u": 12, "v": 13, "w": 2013.0 }, { "u": 12, "v": 14, "w": 651.0 }, { "u": 13, "v": 15, "w": 398.0 }, { "u": 13, "v": 17, "w": 189.0 }, { "u": 19, "v": 20, "w": 1066.0 }, { "u": 19, "v": 9, "w": 5387.0 }, { "u": 19, "v": 7, "w": 1509.0 }, { "u": 16, "v": 3, "w": 4664.0 }, { "u": 16, "v": 22, "w": 16809.0 }, { "u": 16, "v": 18, "w": 4492.0 }, { "u": 15, "v": 14, "w": 2032.0 }, { "u": 15, "v": 2, "w": 604.0 }, { "u": 14, "v": 8, "w": 508.0 }, { "u": 14, "v": 1, "w": 984.0 }, { "u": 9, "v": 10, "w": 1794.0 }, { "u": 10, "v": 11, "w": 1961.0 }, { "u": 10, "v": 21, "w": 1401.0 }, { "u": 17, "v": 11, "w": 1132.0 }, { "u": 17, "v": 6, "w": 576.0 }, { "u": 18, "v": 2, "w": 608.0 }, { "u": 18, "v": 5, "w": 2299.0 }, { "u": 1, "v": 2, "w": 2061.0 }, { "u": 4, "v": 5, "w": 402.0 }, { "u": 4, "v": 6, "w": 458.0 }, { "u": 5, "v": 7, "w": 471.0 }, { "u": 6, "v": 7, "w": 417.0 } ], "terminals": [ 1, 2, 3, 5, 11, 14, 18, 19 ], "source_file": "I040.stp", "density": 0.11255411255411256, "viz_instance": "generated_data/STP/viz/STP_L/instance_0030.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0030.png" }, "solution": [ [ 13, 15 ], [ 13, 17 ], [ 7, 19 ], [ 3, 16 ], [ 16, 18 ], [ 14, 15 ], [ 2, 15 ], [ 1, 14 ], [ 11, 17 ], [ 6, 17 ], [ 2, 18 ], [ 5, 7 ], [ 6, 7 ] ], "obj": 18076.0, "instance_variant": { "problem_type": "STP", "num_nodes": 22, "num_edges": 26, "edges": [ { "u": 11, "v": 12, "w": 2013.0 }, { "u": 11, "v": 13, "w": 651.0 }, { "u": 12, "v": 14, "w": 398.0 }, { "u": 12, "v": 16, "w": 189.0 }, { "u": 18, "v": 19, "w": 1066.0 }, { "u": 18, "v": 8, "w": 5387.0 }, { "u": 18, "v": 6, "w": 1509.0 }, { "u": 15, "v": 2, "w": 4664.0 }, { "u": 15, "v": 21, "w": 16809.0 }, { "u": 15, "v": 17, "w": 4492.0 }, { "u": 14, "v": 13, "w": 2032.0 }, { "u": 14, "v": 1, "w": 604.0 }, { "u": 13, "v": 7, "w": 508.0 }, { "u": 13, "v": 0, "w": 984.0 }, { "u": 8, "v": 9, "w": 1794.0 }, { "u": 9, "v": 10, "w": 1961.0 }, { "u": 9, "v": 20, "w": 1401.0 }, { "u": 16, "v": 10, "w": 1132.0 }, { "u": 16, "v": 5, "w": 576.0 }, { "u": 17, "v": 1, "w": 608.0 }, { "u": 17, "v": 4, "w": 2299.0 }, { "u": 0, "v": 1, "w": 2061.0 }, { "u": 3, "v": 4, "w": 402.0 }, { "u": 3, "v": 5, "w": 458.0 }, { "u": 4, "v": 6, "w": 471.0 }, { "u": 5, "v": 6, "w": 417.0 } ], "density": 0.11255411255411256, "source_file": "I040.stp", "terminals": [ 0, 1, 2, 4, 10, 13, 17, 18 ] }, "solution_variant": [ [ 12, 14 ], [ 12, 16 ], [ 6, 18 ], [ 2, 15 ], [ 15, 17 ], [ 13, 14 ], [ 1, 14 ], [ 0, 13 ], [ 10, 16 ], [ 5, 16 ], [ 1, 17 ], [ 4, 6 ], [ 5, 6 ] ], "context_index": 31, "input_format": "markdown_table", "input_index_base": 0 }, { "task_name": "STP", "problem_type": "STP", "instruction": "We were briefed by a field biologist who needs a simple map: which corridors should be maintained so all the tracked habitats form one unbroken route for animals. The best plan is the one that joins all monitored sites, possibly routing through intermediate patches, while keeping the total amount of fencing or clearing (measured by adding up the lengths of the chosen corridors) as small as possible. No monitored patch can be left disconnected, and duplicate or double-counted corridors don’t make sense — each link is counted once. The exact patch list and corridor lengths are given below.\n\n{\n \"total_habitat_patches\": 25,\n \"total_possible_corridors\": 32,\n \"edges\": [\n {\n \"patch_endpoint_a\": 16,\n \"patch_endpoint_b\": 23,\n \"corridor_length\": 167.0\n },\n {\n \"patch_endpoint_a\": 16,\n \"patch_endpoint_b\": 13,\n \"corridor_length\": 891.0\n },\n {\n \"patch_endpoint_a\": 16,\n \"patch_endpoint_b\": 22,\n \"corridor_length\": 1452.0\n },\n {\n \"patch_endpoint_a\": 17,\n \"patch_endpoint_b\": 7,\n \"corridor_length\": 893.0\n },\n {\n \"patch_endpoint_a\": 17,\n \"patch_endpoint_b\": 5,\n \"corridor_length\": 980.0\n },\n {\n \"patch_endpoint_a\": 17,\n \"patch_endpoint_b\": 15,\n \"corridor_length\": 1232.0\n },\n {\n \"patch_endpoint_a\": 12,\n \"patch_endpoint_b\": 24,\n \"corridor_length\": 563.0\n },\n {\n \"patch_endpoint_a\": 12,\n \"patch_endpoint_b\": 2,\n \"corridor_length\": 436.0\n },\n {\n \"patch_endpoint_a\": 12,\n \"patch_endpoint_b\": 6,\n \"corridor_length\": 627.0\n },\n {\n \"patch_endpoint_a\": 20,\n \"patch_endpoint_b\": 25,\n \"corridor_length\": 1614.0\n },\n {\n \"patch_endpoint_a\": 20,\n \"patch_endpoint_b\": 21,\n \"corridor_length\": 2133.0\n },\n {\n \"patch_endpoint_a\": 1,\n \"patch_endpoint_b\": 5,\n \"corridor_length\": 887.0\n },\n {\n \"patch_endpoint_a\": 24,\n \"patch_endpoint_b\": 14,\n \"corridor_length\": 552.0\n },\n {\n \"patch_endpoint_a\": 24,\n \"patch_endpoint_b\": 25,\n \"corridor_length\": 500.0\n },\n {\n \"patch_endpoint_a\": 25,\n \"patch_endpoint_b\": 10,\n \"corridor_length\": 167.0\n },\n {\n \"patch_endpoint_a\": 3,\n \"patch_endpoint_b\": 4,\n \"corridor_length\": 626.0\n },\n {\n \"patch_endpoint_a\": 3,\n \"patch_endpoint_b\": 5,\n \"corridor_length\": 1395.0\n },\n {\n \"patch_endpoint_a\": 4,\n \"patch_endpoint_b\": 18,\n \"corridor_length\": 440.0\n },\n {\n \"patch_endpoint_a\": 4,\n \"patch_endpoint_b\": 5,\n \"corridor_length\": 1352.0\n },\n {\n \"patch_endpoint_a\": 15,\n \"patch_endpoint_b\": 19,\n \"corridor_length\": 215.0\n },\n {\n \"patch_endpoint_a\": 15,\n \"patch_endpoint_b\": 14,\n \"corridor_length\": 144.0\n },\n {\n \"patch_endpoint_a\": 6,\n \"patch_endpoint_b\": 14,\n \"corridor_length\": 547.0\n },\n {\n \"patch_endpoint_a\": 6,\n \"patch_endpoint_b\": 7,\n \"corridor_length\": 1394.0\n },\n {\n \"patch_endpoint_a\": 7,\n \"patch_endpoint_b\": 13,\n \"corridor_length\": 1694.0\n },\n {\n \"patch_endpoint_a\": 8,\n \"patch_endpoint_b\": 2,\n \"corridor_length\": 370.0\n },\n {\n \"patch_endpoint_a\": 8,\n \"patch_endpoint_b\": 10,\n \"corridor_length\": 648.0\n },\n {\n \"patch_endpoint_a\": 8,\n \"patch_endpoint_b\": 9,\n \"corridor_length\": 871.0\n },\n {\n \"patch_endpoint_a\": 21,\n \"patch_endpoint_b\": 19,\n \"corridor_length\": 1562.0\n },\n {\n \"patch_endpoint_a\": 9,\n \"patch_endpoint_b\": 11,\n \"corridor_length\": 486.0\n },\n {\n \"patch_endpoint_a\": 9,\n \"patch_endpoint_b\": 13,\n \"corridor_length\": 1350.0\n },\n {\n \"patch_endpoint_a\": 10,\n \"patch_endpoint_b\": 11,\n \"corridor_length\": 670.0\n },\n {\n \"patch_endpoint_a\": 19,\n \"patch_endpoint_b\": 18,\n \"corridor_length\": 361.0\n }\n ],\n \"monitored_patches\": [\n 15,\n 17,\n 18,\n 23,\n 24\n ]\n}\n\nWhen you hand me the final set of corridors, please put it in this simple JSON shape:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nHere \"solution\" is a list of corridor links to keep; each pair [u, v] means the corridor between patch u and patch v. Think of it like ticking boxes on a form — one pair per corridor, no duplicates, order doesn't matter. This JSON is just a sketch of the expected shape, not the actual answer.\n\nPlease use the exact identifiers from the instance input — don't rename patches or invent new labels. \n- 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 25, "num_edges": 32, "edges": [ { "u": 16, "v": 23, "w": 167.0 }, { "u": 16, "v": 13, "w": 891.0 }, { "u": 16, "v": 22, "w": 1452.0 }, { "u": 17, "v": 7, "w": 893.0 }, { "u": 17, "v": 5, "w": 980.0 }, { "u": 17, "v": 15, "w": 1232.0 }, { "u": 12, "v": 24, "w": 563.0 }, { "u": 12, "v": 2, "w": 436.0 }, { "u": 12, "v": 6, "w": 627.0 }, { "u": 20, "v": 25, "w": 1614.0 }, { "u": 20, "v": 21, "w": 2133.0 }, { "u": 1, "v": 5, "w": 887.0 }, { "u": 24, "v": 14, "w": 552.0 }, { "u": 24, "v": 25, "w": 500.0 }, { "u": 25, "v": 10, "w": 167.0 }, { "u": 3, "v": 4, "w": 626.0 }, { "u": 3, "v": 5, "w": 1395.0 }, { "u": 4, "v": 18, "w": 440.0 }, { "u": 4, "v": 5, "w": 1352.0 }, { "u": 15, "v": 19, "w": 215.0 }, { "u": 15, "v": 14, "w": 144.0 }, { "u": 6, "v": 14, "w": 547.0 }, { "u": 6, "v": 7, "w": 1394.0 }, { "u": 7, "v": 13, "w": 1694.0 }, { "u": 8, "v": 2, "w": 370.0 }, { "u": 8, "v": 10, "w": 648.0 }, { "u": 8, "v": 9, "w": 871.0 }, { "u": 21, "v": 19, "w": 1562.0 }, { "u": 9, "v": 11, "w": 486.0 }, { "u": 9, "v": 13, "w": 1350.0 }, { "u": 10, "v": 11, "w": 670.0 }, { "u": 19, "v": 18, "w": 361.0 } ], "terminals": [ 15, 17, 18, 23, 24 ], "source_file": "I049.stp", "density": 0.10666666666666667, "viz_instance": "generated_data/STP/viz/STP_L/instance_0031.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0031.png" }, "solution": [ [ 16, 23 ], [ 13, 16 ], [ 7, 17 ], [ 15, 17 ], [ 14, 24 ], [ 15, 19 ], [ 14, 15 ], [ 7, 13 ], [ 18, 19 ] ], "obj": 6149.0, "instance_variant": { "problem_type": "STP", "num_nodes": 25, "num_edges": 32, "edges": [ { "u": 16, "v": 23, "w": 167.0 }, { "u": 16, "v": 13, "w": 891.0 }, { "u": 16, "v": 22, "w": 1452.0 }, { "u": 17, "v": 7, "w": 893.0 }, { "u": 17, "v": 5, "w": 980.0 }, { "u": 17, "v": 15, "w": 1232.0 }, { "u": 12, "v": 24, "w": 563.0 }, { "u": 12, "v": 2, "w": 436.0 }, { "u": 12, "v": 6, "w": 627.0 }, { "u": 20, "v": 25, "w": 1614.0 }, { "u": 20, "v": 21, "w": 2133.0 }, { "u": 1, "v": 5, "w": 887.0 }, { "u": 24, "v": 14, "w": 552.0 }, { "u": 24, "v": 25, "w": 500.0 }, { "u": 25, "v": 10, "w": 167.0 }, { "u": 3, "v": 4, "w": 626.0 }, { "u": 3, "v": 5, "w": 1395.0 }, { "u": 4, "v": 18, "w": 440.0 }, { "u": 4, "v": 5, "w": 1352.0 }, { "u": 15, "v": 19, "w": 215.0 }, { "u": 15, "v": 14, "w": 144.0 }, { "u": 6, "v": 14, "w": 547.0 }, { "u": 6, "v": 7, "w": 1394.0 }, { "u": 7, "v": 13, "w": 1694.0 }, { "u": 8, "v": 2, "w": 370.0 }, { "u": 8, "v": 10, "w": 648.0 }, { "u": 8, "v": 9, "w": 871.0 }, { "u": 21, "v": 19, "w": 1562.0 }, { "u": 9, "v": 11, "w": 486.0 }, { "u": 9, "v": 13, "w": 1350.0 }, { "u": 10, "v": 11, "w": 670.0 }, { "u": 19, "v": 18, "w": 361.0 } ], "density": 0.10666666666666667, "source_file": "I049.stp", "terminals": [ 15, 17, 18, 23, 24 ] }, "solution_variant": [ [ 16, 23 ], [ 13, 16 ], [ 7, 17 ], [ 15, 17 ], [ 14, 24 ], [ 15, 19 ], [ 14, 15 ], [ 7, 13 ], [ 18, 19 ] ], "context_index": 32, "input_format": "json", "input_index_base": 1 }, { "task_name": "STP", "problem_type": "STP", "instruction": "Recently the operations team asked for a quick layout: which backroom paths should be opened so all the specified areas sit on one continuous service circuit. The choice is which corridors to include, and it’s fine to thread the route through spare storage rooms to make connections. A better layout is one that includes every required area in the same connected path (nothing missing or split off) and has the smallest possible total length when you add up the lengths of the opened passages. The exact diagram and lengths are shown below.\n\nThe store layout instance contains 26 backroom zones, 31 candidate passages, and the required service areas are A B C D E G I K P S T V X.\nCandidate corridor between H and S with length 2102.0.\nCandidate corridor between H and G with length 2641.0.\nCandidate corridor between H and I with length 1639.0.\nCandidate corridor between I and M with length 2433.0.\nCandidate corridor between I and V with length 2192.0.\nCandidate corridor between Z and D with length 751.0.\nCandidate corridor between Z and W with length 463.0.\nCandidate corridor between Z and U with length 363.0.\nCandidate corridor between J and E with length 119.0.\nCandidate corridor between J and K with length 147.0.\nCandidate corridor between J and L with length 1073.0.\nCandidate corridor between K and B with length 967.0.\nCandidate corridor between K and U with length 1355.0.\nCandidate corridor between L and F with length 156.0.\nCandidate corridor between L and O with length 450.0.\nCandidate corridor between M and A with length 166.0.\nCandidate corridor between M and V with length 2612.0.\nCandidate corridor between E and F with length 1104.0.\nCandidate corridor between E and D with length 467.0.\nCandidate corridor between F and C with length 477.0.\nCandidate corridor between N and A with length 1189.0.\nCandidate corridor between N and Q with length 2736.0.\nCandidate corridor between P and T with length 2999.0.\nCandidate corridor between P and A with length 2811.0.\nCandidate corridor between B and V with length 985.0.\nCandidate corridor between W and Y with length 3609.0.\nCandidate corridor between U and G with length 2380.0.\nCandidate corridor between R and S with length 4253.0.\nCandidate corridor between C and D with length 1203.0.\nCandidate corridor between X and Y with length 1017.0.\nCandidate corridor between X and G with length 1651.0.\nSelect corridors that join all A B C D E G I K P S T V X into one continuous service circuit while minimizing the total opened passage length.\n\nAlso, when you send back which passages to open, please use this simple JSON shape so I can read it straight away:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nThis just means \"solution\" holds a list of pairs; each pair is an edge (a passage) between two room/node identifiers. It's just a sketch of the expected shape — not the actual answer — so fill in the real node IDs from the instance when you reply.\n\nPlease use the identifiers exactly as they appear in the instance input — do not rename them and do not invent new labels. \n- 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 26, "num_edges": 31, "edges": [ { "u": 8, "v": 19, "w": 2102.0 }, { "u": 8, "v": 7, "w": 2641.0 }, { "u": 8, "v": 9, "w": 1639.0 }, { "u": 9, "v": 13, "w": 2433.0 }, { "u": 9, "v": 22, "w": 2192.0 }, { "u": 26, "v": 4, "w": 751.0 }, { "u": 26, "v": 23, "w": 463.0 }, { "u": 26, "v": 21, "w": 363.0 }, { "u": 10, "v": 5, "w": 119.0 }, { "u": 10, "v": 11, "w": 147.0 }, { "u": 10, "v": 12, "w": 1073.0 }, { "u": 11, "v": 2, "w": 967.0 }, { "u": 11, "v": 21, "w": 1355.0 }, { "u": 12, "v": 6, "w": 156.0 }, { "u": 12, "v": 15, "w": 450.0 }, { "u": 13, "v": 1, "w": 166.0 }, { "u": 13, "v": 22, "w": 2612.0 }, { "u": 5, "v": 6, "w": 1104.0 }, { "u": 5, "v": 4, "w": 467.0 }, { "u": 6, "v": 3, "w": 477.0 }, { "u": 14, "v": 1, "w": 1189.0 }, { "u": 14, "v": 17, "w": 2736.0 }, { "u": 16, "v": 20, "w": 2999.0 }, { "u": 16, "v": 1, "w": 2811.0 }, { "u": 2, "v": 22, "w": 985.0 }, { "u": 23, "v": 25, "w": 3609.0 }, { "u": 21, "v": 7, "w": 2380.0 }, { "u": 18, "v": 19, "w": 4253.0 }, { "u": 3, "v": 4, "w": 1203.0 }, { "u": 24, "v": 25, "w": 1017.0 }, { "u": 24, "v": 7, "w": 1651.0 } ], "terminals": [ 1, 2, 3, 4, 5, 7, 9, 11, 16, 19, 20, 22, 24 ], "source_file": "I019.stp", "density": 0.09538461538461539, "viz_instance": "generated_data/STP/viz/STP_L/instance_0032.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0032.png" }, "solution": [ [ 8, 19 ], [ 7, 8 ], [ 8, 9 ], [ 9, 13 ], [ 9, 22 ], [ 5, 10 ], [ 10, 11 ], [ 2, 11 ], [ 1, 13 ], [ 4, 5 ], [ 16, 20 ], [ 1, 16 ], [ 2, 22 ], [ 3, 4 ], [ 7, 24 ] ], "obj": 22522.0, "instance_variant": { "problem_type": "STP", "num_nodes": 26, "num_edges": 31, "edges": [ { "u": "H", "v": "S", "w": 2102.0 }, { "u": "H", "v": "G", "w": 2641.0 }, { "u": "H", "v": "I", "w": 1639.0 }, { "u": "I", "v": "M", "w": 2433.0 }, { "u": "I", "v": "V", "w": 2192.0 }, { "u": "Z", "v": "D", "w": 751.0 }, { "u": "Z", "v": "W", "w": 463.0 }, { "u": "Z", "v": "U", "w": 363.0 }, { "u": "J", "v": "E", "w": 119.0 }, { "u": "J", "v": "K", "w": 147.0 }, { "u": "J", "v": "L", "w": 1073.0 }, { "u": "K", "v": "B", "w": 967.0 }, { "u": "K", "v": "U", "w": 1355.0 }, { "u": "L", "v": "F", "w": 156.0 }, { "u": "L", "v": "O", "w": 450.0 }, { "u": "M", "v": "A", "w": 166.0 }, { "u": "M", "v": "V", "w": 2612.0 }, { "u": "E", "v": "F", "w": 1104.0 }, { "u": "E", "v": "D", "w": 467.0 }, { "u": "F", "v": "C", "w": 477.0 }, { "u": "N", "v": "A", "w": 1189.0 }, { "u": "N", "v": "Q", "w": 2736.0 }, { "u": "P", "v": "T", "w": 2999.0 }, { "u": "P", "v": "A", "w": 2811.0 }, { "u": "B", "v": "V", "w": 985.0 }, { "u": "W", "v": "Y", "w": 3609.0 }, { "u": "U", "v": "G", "w": 2380.0 }, { "u": "R", "v": "S", "w": 4253.0 }, { "u": "C", "v": "D", "w": 1203.0 }, { "u": "X", "v": "Y", "w": 1017.0 }, { "u": "X", "v": "G", "w": 1651.0 } ], "density": 0.09538461538461539, "source_file": "I019.stp", "terminals": [ "A", "B", "C", "D", "E", "G", "I", "K", "P", "S", "T", "V", "X" ] }, "solution_variant": [ [ "H", "S" ], [ "G", "H" ], [ "H", "I" ], [ "I", "M" ], [ "I", "V" ], [ "E", "J" ], [ "J", "K" ], [ "B", "K" ], [ "A", "M" ], [ "D", "E" ], [ "P", "T" ], [ "A", "P" ], [ "B", "V" ], [ "C", "D" ], [ "G", "X" ] ], "context_index": 33, "input_format": "nl", "input_index_base": "names" }, { "task_name": "STP", "problem_type": "STP", "instruction": "A venue manager wants a tidy backstage: several stage areas must be joined into one connected setup using platform connectors, and the trick is picking which runs to build — running through other backstage spots is allowed if it shortens the job. One plan is preferable when the total length of installed connectors is smaller; simply sum the lengths of every connector in the plan to get that total. Every staging zone needs to be part of the network, and installing unnecessary duplicate connectors should be avoided. The exact layout and connector lengths are provided below.\n\nThere are 24 backstage locations, 28 possible connector runs, and the required staging zones are H M O X.\nPotential connector run between U and F with length 997.0.\nPotential connector run between U and Q with length 1659.0.\nPotential connector run between U and V with length 708.0.\nPotential connector run between V and W with length 833.0.\nPotential connector run between V and J with length 3223.0.\nPotential connector run between M and L with length 1012.0.\nPotential connector run between M and S with length 105.0.\nPotential connector run between M and G with length 1366.0.\nPotential connector run between A and B with length 992.0.\nPotential connector run between B and I with length 10.0.\nPotential connector run between C and D with length 509.0.\nPotential connector run between C and E with length 497.0.\nPotential connector run between D and E with length 124.0.\nPotential connector run between D and W with length 2048.0.\nPotential connector run between E and G with length 589.0.\nPotential connector run between S and T with length 1261.0.\nPotential connector run between N and O with length 1683.0.\nPotential connector run between N and R with length 1781.0.\nPotential connector run between O and Q with length 1230.0.\nPotential connector run between P and Q with length 399.0.\nPotential connector run between P and R with length 2075.0.\nPotential connector run between P and T with length 682.0.\nPotential connector run between X and K with length 292.0.\nPotential connector run between X and J with length 4333.0.\nPotential connector run between H and I with length 428.0.\nPotential connector run between F and G with length 1050.0.\nPotential connector run between F and T with length 345.0.\nPotential connector run between I and J with length 1278.0.\nThe manager should choose runs that join all required staging zones with minimum total connector length and no unnecessary duplicates.\n\nWhen you send back your chosen plan, please use this simple JSON shape so it's easy to read and check:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nThis just sketches the format: \"solution\" holds a list of connector pairs, and each pair [X, Y] is one connector joining staging area X to staging area Y. Think of it as a short form list of which runs to build — that's all it needs to show.\n\nThis JSON is only a template for the expected shape, not the actual answer.\n\nPlease make sure to use the exact identifiers from the instance input — do not rename them or invent new ones.\n- 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 24, "num_edges": 28, "edges": [ { "u": 21, "v": 6, "w": 997.0 }, { "u": 21, "v": 17, "w": 1659.0 }, { "u": 21, "v": 22, "w": 708.0 }, { "u": 22, "v": 23, "w": 833.0 }, { "u": 22, "v": 10, "w": 3223.0 }, { "u": 13, "v": 12, "w": 1012.0 }, { "u": 13, "v": 19, "w": 105.0 }, { "u": 13, "v": 7, "w": 1366.0 }, { "u": 1, "v": 2, "w": 992.0 }, { "u": 2, "v": 9, "w": 10.0 }, { "u": 3, "v": 4, "w": 509.0 }, { "u": 3, "v": 5, "w": 497.0 }, { "u": 4, "v": 5, "w": 124.0 }, { "u": 4, "v": 23, "w": 2048.0 }, { "u": 5, "v": 7, "w": 589.0 }, { "u": 19, "v": 20, "w": 1261.0 }, { "u": 14, "v": 15, "w": 1683.0 }, { "u": 14, "v": 18, "w": 1781.0 }, { "u": 15, "v": 17, "w": 1230.0 }, { "u": 16, "v": 17, "w": 399.0 }, { "u": 16, "v": 18, "w": 2075.0 }, { "u": 16, "v": 20, "w": 682.0 }, { "u": 24, "v": 11, "w": 292.0 }, { "u": 24, "v": 10, "w": 4333.0 }, { "u": 8, "v": 9, "w": 428.0 }, { "u": 6, "v": 7, "w": 1050.0 }, { "u": 6, "v": 20, "w": 345.0 }, { "u": 9, "v": 10, "w": 1278.0 } ], "terminals": [ 8, 13, 15, 24 ], "source_file": "I020.stp", "density": 0.10144927536231885, "viz_instance": "generated_data/STP/viz/STP_L/instance_0033.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0033.png" }, "solution": [ [ 6, 21 ], [ 21, 22 ], [ 10, 22 ], [ 13, 19 ], [ 19, 20 ], [ 15, 17 ], [ 16, 17 ], [ 16, 20 ], [ 10, 24 ], [ 8, 9 ], [ 6, 20 ], [ 9, 10 ] ], "obj": 14989.0, "instance_variant": { "problem_type": "STP", "num_nodes": 24, "num_edges": 28, "edges": [ { "u": "U", "v": "F", "w": 997.0 }, { "u": "U", "v": "Q", "w": 1659.0 }, { "u": "U", "v": "V", "w": 708.0 }, { "u": "V", "v": "W", "w": 833.0 }, { "u": "V", "v": "J", "w": 3223.0 }, { "u": "M", "v": "L", "w": 1012.0 }, { "u": "M", "v": "S", "w": 105.0 }, { "u": "M", "v": "G", "w": 1366.0 }, { "u": "A", "v": "B", "w": 992.0 }, { "u": "B", "v": "I", "w": 10.0 }, { "u": "C", "v": "D", "w": 509.0 }, { "u": "C", "v": "E", "w": 497.0 }, { "u": "D", "v": "E", "w": 124.0 }, { "u": "D", "v": "W", "w": 2048.0 }, { "u": "E", "v": "G", "w": 589.0 }, { "u": "S", "v": "T", "w": 1261.0 }, { "u": "N", "v": "O", "w": 1683.0 }, { "u": "N", "v": "R", "w": 1781.0 }, { "u": "O", "v": "Q", "w": 1230.0 }, { "u": "P", "v": "Q", "w": 399.0 }, { "u": "P", "v": "R", "w": 2075.0 }, { "u": "P", "v": "T", "w": 682.0 }, { "u": "X", "v": "K", "w": 292.0 }, { "u": "X", "v": "J", "w": 4333.0 }, { "u": "H", "v": "I", "w": 428.0 }, { "u": "F", "v": "G", "w": 1050.0 }, { "u": "F", "v": "T", "w": 345.0 }, { "u": "I", "v": "J", "w": 1278.0 } ], "density": 0.10144927536231885, "source_file": "I020.stp", "terminals": [ "H", "M", "O", "X" ] }, "solution_variant": [ [ "F", "U" ], [ "U", "V" ], [ "J", "V" ], [ "M", "S" ], [ "S", "T" ], [ "O", "Q" ], [ "P", "Q" ], [ "P", "T" ], [ "J", "X" ], [ "H", "I" ], [ "F", "T" ], [ "I", "J" ] ], "context_index": 34, "input_format": "nl", "input_index_base": "names" }, { "task_name": "STP", "problem_type": "STP", "instruction": "Someone from the parks team wants a simple plan: choose benches and the short paths between them so all picnic groves are joined into one uninterrupted promenade. The choice is about which connections to use — clearings can act as intermediate tie-ins if that helps — and the winner is the layout with the smallest overall path length. The overall length gets computed by adding up the lengths of each chosen connection. Requirements are straightforward: don’t leave any grove out, make sure everything is connected into a single route, and don’t double-count or build redundant pieces. The exact layout and distances are shown below.\n\nThere are 22 marked locations and 25 candidate short paths; the picnic groves to span are 1 2 4 6 7 10 11 14 15 19 20.\nCandidate short path between 8 and 1 with length 1368.0.\nCandidate short path between 8 and 6 with length 2585.0.\nCandidate short path between 8 and 12 with length 780654.0.\nCandidate short path between 9 and 7 with length 1632.0.\nCandidate short path between 9 and 12 with length 784131.0.\nCandidate short path between 9 and 20 with length 2288.0.\nCandidate short path between 21 and 15 with length 2151.0.\nCandidate short path between 18 and 3 with length 503.0.\nCandidate short path between 19 and 3 with length 924.0.\nCandidate short path between 14 and 16 with length 3201.0.\nCandidate short path between 14 and 4 with length 834.0.\nCandidate short path between 2 and 3 with length 2303.0.\nCandidate short path between 2 and 17 with length 1969.0.\nCandidate short path between 2 and 7 with length 2588.0.\nCandidate short path between 2 and 5 with length 1886.0.\nCandidate short path between 4 and 0 with length 3597.0.\nCandidate short path between 10 and 1 with length 935.0.\nCandidate short path between 11 and 20 with length 534.0.\nCandidate short path between 0 and 1 with length 3153.0.\nCandidate short path between 6 and 17 with length 489.0.\nCandidate short path between 6 and 13 with length 525240.0.\nCandidate short path between 7 and 13 with length 525451.0.\nCandidate short path between 15 and 5 with length 431.0.\nCandidate short path between 15 and 16 with length 334.0.\nCandidate short path between 16 and 17 with length 1528.0.\nChoose a subset of these connections that spans 1 2 4 6 7 10 11 14 15 19 20 into one uninterrupted promenade with minimum total path length, without leaving any grove out or adding redundant pieces.\n\nAlso, to keep things machine-friendly, I'll show the shape I expect the answer to take in a tiny JSON sketch — just a relaxed heads-up so you know what to fill in.\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nThis just means: \"solution\" is a list of chosen connections, and each inner pair [u, v] is a short path you’d build between bench (or clearing) u and bench v. Think of it like a simple checklist of which links to include in the promenade. The block above is only a sketch of the shape I want — not the final, filled-in plan.\n\nPlease make sure to use the exact identifiers from the instance input when you give the real selection — don’t rename them or invent new labels. \n- 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 22, "num_edges": 25, "edges": [ { "u": 9, "v": 2, "w": 1368.0 }, { "u": 9, "v": 7, "w": 2585.0 }, { "u": 9, "v": 13, "w": 780654.0 }, { "u": 10, "v": 8, "w": 1632.0 }, { "u": 10, "v": 13, "w": 784131.0 }, { "u": 10, "v": 21, "w": 2288.0 }, { "u": 22, "v": 16, "w": 2151.0 }, { "u": 19, "v": 4, "w": 503.0 }, { "u": 20, "v": 4, "w": 924.0 }, { "u": 15, "v": 17, "w": 3201.0 }, { "u": 15, "v": 5, "w": 834.0 }, { "u": 3, "v": 4, "w": 2303.0 }, { "u": 3, "v": 18, "w": 1969.0 }, { "u": 3, "v": 8, "w": 2588.0 }, { "u": 3, "v": 6, "w": 1886.0 }, { "u": 5, "v": 1, "w": 3597.0 }, { "u": 11, "v": 2, "w": 935.0 }, { "u": 12, "v": 21, "w": 534.0 }, { "u": 1, "v": 2, "w": 3153.0 }, { "u": 7, "v": 18, "w": 489.0 }, { "u": 7, "v": 14, "w": 525240.0 }, { "u": 8, "v": 14, "w": 525451.0 }, { "u": 16, "v": 6, "w": 431.0 }, { "u": 16, "v": 17, "w": 334.0 }, { "u": 17, "v": 18, "w": 1528.0 } ], "terminals": [ 2, 3, 5, 7, 8, 11, 12, 15, 16, 20, 21 ], "source_file": "I050.stp", "density": 0.10822510822510822, "viz_instance": "generated_data/STP/viz/STP_L/instance_0034.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0034.png" }, "solution": [ [ 2, 9 ], [ 7, 9 ], [ 8, 10 ], [ 10, 21 ], [ 4, 20 ], [ 15, 17 ], [ 5, 15 ], [ 3, 4 ], [ 3, 18 ], [ 3, 8 ], [ 2, 11 ], [ 12, 21 ], [ 7, 18 ], [ 16, 17 ], [ 17, 18 ] ], "obj": 23512.0, "instance_variant": { "problem_type": "STP", "num_nodes": 22, "num_edges": 25, "edges": [ { "u": 8, "v": 1, "w": 1368.0 }, { "u": 8, "v": 6, "w": 2585.0 }, { "u": 8, "v": 12, "w": 780654.0 }, { "u": 9, "v": 7, "w": 1632.0 }, { "u": 9, "v": 12, "w": 784131.0 }, { "u": 9, "v": 20, "w": 2288.0 }, { "u": 21, "v": 15, "w": 2151.0 }, { "u": 18, "v": 3, "w": 503.0 }, { "u": 19, "v": 3, "w": 924.0 }, { "u": 14, "v": 16, "w": 3201.0 }, { "u": 14, "v": 4, "w": 834.0 }, { "u": 2, "v": 3, "w": 2303.0 }, { "u": 2, "v": 17, "w": 1969.0 }, { "u": 2, "v": 7, "w": 2588.0 }, { "u": 2, "v": 5, "w": 1886.0 }, { "u": 4, "v": 0, "w": 3597.0 }, { "u": 10, "v": 1, "w": 935.0 }, { "u": 11, "v": 20, "w": 534.0 }, { "u": 0, "v": 1, "w": 3153.0 }, { "u": 6, "v": 17, "w": 489.0 }, { "u": 6, "v": 13, "w": 525240.0 }, { "u": 7, "v": 13, "w": 525451.0 }, { "u": 15, "v": 5, "w": 431.0 }, { "u": 15, "v": 16, "w": 334.0 }, { "u": 16, "v": 17, "w": 1528.0 } ], "density": 0.10822510822510822, "source_file": "I050.stp", "terminals": [ 1, 2, 4, 6, 7, 10, 11, 14, 15, 19, 20 ] }, "solution_variant": [ [ 1, 8 ], [ 6, 8 ], [ 7, 9 ], [ 9, 20 ], [ 3, 19 ], [ 14, 16 ], [ 4, 14 ], [ 2, 3 ], [ 2, 17 ], [ 2, 7 ], [ 1, 10 ], [ 11, 20 ], [ 6, 17 ], [ 15, 16 ], [ 16, 17 ] ], "context_index": 35, "input_format": "markdown_table", "input_index_base": 0 }, { "task_name": "STP", "problem_type": "STP", "instruction": "Many people on the ops crew are trying to work out which fiber lines to put into service so all of the important racks end up reachable through one contiguous fabric. The decision is picking a subset of trunk links to activate; it’s fine to route traffic through other racks or patch points if that reduces cabling. The best selection is the one that ties together every critical rack while producing the lowest total active fiber length — obtained by adding up the lengths of the activated trunks. Every critical rack must be included, trunks are simply on or off (no duplicate counting), and the full layout and lengths come next.\n\nBelow is the layout: 23 nodes, 28 candidate trunks, critical racks C E F G H K M T W.\nCandidate trunk between P and T with length 1008.0.\nCandidate trunk between P and A with length 2883.0.\nCandidate trunk between P and V with length 2342.0.\nCandidate trunk between A and M with length 907.0.\nCandidate trunk between A and R with length 902.0.\nCandidate trunk between A and D with length 1877.0.\nCandidate trunk between Q and U with length 1188.0.\nCandidate trunk between Q and V with length 2160.0.\nCandidate trunk between Q and F with length 15755.0.\nCandidate trunk between R and S with length 899.0.\nCandidate trunk between D and O with length 364.0.\nCandidate trunk between D and E with length 430.0.\nCandidate trunk between E and O with length 104.0.\nCandidate trunk between W and L with length 1275.0.\nCandidate trunk between W and V with length 326.0.\nCandidate trunk between W and U with length 718.0.\nCandidate trunk between I and M with length 1789.0.\nCandidate trunk between J and K with length 240.0.\nCandidate trunk between J and G with length 102.0.\nCandidate trunk between K and H with length 99.0.\nCandidate trunk between K and T with length 220.0.\nCandidate trunk between G and H with length 242.0.\nCandidate trunk between G and B with length 199.0.\nCandidate trunk between H and N with length 350.0.\nCandidate trunk between L and C with length 939.0.\nCandidate trunk between T and N with length 231.0.\nCandidate trunk between N and C with length 65.0.\nCandidate trunk between B and C with length 463.0.\nActivate a subset of the listed trunks so all C E F G H K M T W are spanned while minimizing the total active trunk length.\n\nOh — and when you send the answer back, just use this simple JSON layout so I can read it automatically:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nThis \"solution\" list is just a plain list of trunks to activate. Each inner pair [u, v] denotes a single trunk between node u and node v that you want turned on so the important racks end up connected. Think of it like filling out a short checklist of links rather than a big report.\n\nThis JSON is only a sketch of the shape I expect — not the actual set of links. Please use the exact node identifiers from the instance input; do not rename them or invent new labels. \n\nfor 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”.", "instance": { "problem_type": "STP", "num_nodes": 23, "num_edges": 28, "edges": [ { "u": 16, "v": 20, "w": 1008.0 }, { "u": 16, "v": 1, "w": 2883.0 }, { "u": 16, "v": 22, "w": 2342.0 }, { "u": 1, "v": 13, "w": 907.0 }, { "u": 1, "v": 18, "w": 902.0 }, { "u": 1, "v": 4, "w": 1877.0 }, { "u": 17, "v": 21, "w": 1188.0 }, { "u": 17, "v": 22, "w": 2160.0 }, { "u": 17, "v": 6, "w": 15755.0 }, { "u": 18, "v": 19, "w": 899.0 }, { "u": 4, "v": 15, "w": 364.0 }, { "u": 4, "v": 5, "w": 430.0 }, { "u": 5, "v": 15, "w": 104.0 }, { "u": 23, "v": 12, "w": 1275.0 }, { "u": 23, "v": 22, "w": 326.0 }, { "u": 23, "v": 21, "w": 718.0 }, { "u": 9, "v": 13, "w": 1789.0 }, { "u": 10, "v": 11, "w": 240.0 }, { "u": 10, "v": 7, "w": 102.0 }, { "u": 11, "v": 8, "w": 99.0 }, { "u": 11, "v": 20, "w": 220.0 }, { "u": 7, "v": 8, "w": 242.0 }, { "u": 7, "v": 2, "w": 199.0 }, { "u": 8, "v": 14, "w": 350.0 }, { "u": 12, "v": 3, "w": 939.0 }, { "u": 20, "v": 14, "w": 231.0 }, { "u": 14, "v": 3, "w": 65.0 }, { "u": 2, "v": 3, "w": 463.0 } ], "terminals": [ 3, 5, 6, 7, 8, 11, 13, 20, 23 ], "source_file": "I006.stp", "density": 0.11067193675889328, "viz_instance": "generated_data/STP/viz/STP_L/instance_0035.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0035.png" }, "solution": [ [ 16, 20 ], [ 1, 16 ], [ 1, 13 ], [ 1, 4 ], [ 17, 21 ], [ 6, 17 ], [ 4, 5 ], [ 12, 23 ], [ 21, 23 ], [ 8, 11 ], [ 11, 20 ], [ 7, 8 ], [ 3, 12 ], [ 14, 20 ], [ 3, 14 ] ], "obj": 27837.0, "instance_variant": { "problem_type": "STP", "num_nodes": 23, "num_edges": 28, "edges": [ { "u": "P", "v": "T", "w": 1008.0 }, { "u": "P", "v": "A", "w": 2883.0 }, { "u": "P", "v": "V", "w": 2342.0 }, { "u": "A", "v": "M", "w": 907.0 }, { "u": "A", "v": "R", "w": 902.0 }, { "u": "A", "v": "D", "w": 1877.0 }, { "u": "Q", "v": "U", "w": 1188.0 }, { "u": "Q", "v": "V", "w": 2160.0 }, { "u": "Q", "v": "F", "w": 15755.0 }, { "u": "R", "v": "S", "w": 899.0 }, { "u": "D", "v": "O", "w": 364.0 }, { "u": "D", "v": "E", "w": 430.0 }, { "u": "E", "v": "O", "w": 104.0 }, { "u": "W", "v": "L", "w": 1275.0 }, { "u": "W", "v": "V", "w": 326.0 }, { "u": "W", "v": "U", "w": 718.0 }, { "u": "I", "v": "M", "w": 1789.0 }, { "u": "J", "v": "K", "w": 240.0 }, { "u": "J", "v": "G", "w": 102.0 }, { "u": "K", "v": "H", "w": 99.0 }, { "u": "K", "v": "T", "w": 220.0 }, { "u": "G", "v": "H", "w": 242.0 }, { "u": "G", "v": "B", "w": 199.0 }, { "u": "H", "v": "N", "w": 350.0 }, { "u": "L", "v": "C", "w": 939.0 }, { "u": "T", "v": "N", "w": 231.0 }, { "u": "N", "v": "C", "w": 65.0 }, { "u": "B", "v": "C", "w": 463.0 } ], "density": 0.11067193675889328, "source_file": "I006.stp", "terminals": [ "C", "E", "F", "G", "H", "K", "M", "T", "W" ] }, "solution_variant": [ [ "P", "T" ], [ "A", "P" ], [ "A", "M" ], [ "A", "D" ], [ "Q", "U" ], [ "F", "Q" ], [ "D", "E" ], [ "L", "W" ], [ "U", "W" ], [ "H", "K" ], [ "K", "T" ], [ "G", "H" ], [ "C", "L" ], [ "N", "T" ], [ "C", "N" ] ], "context_index": 36, "input_format": "nl", "input_index_base": "names" }, { "task_name": "STP", "problem_type": "STP", "instruction": "Picture this: the safety office wants a single, continuous pedestrian route that touches every emergency shelter, and the job is to choose which sidewalks, side streets, and plazas to clear to make that happen. What makes one selection better than another is the total length of pavement that ends up cleared — add up the lengths of the chosen sidewalks to get that total, and smaller is better. The chosen stretches must form one unbroken network hitting every shelter (nothing left out and no disconnected pieces), and cleared segments are counted only once; the concrete map and lengths follow below.\n\n# total_intersections_and_plazas=24\n# total_sidewalk_and_street_segments=30\n# shelter_node_ids=C X\nsegment_endpoint_node_u,segment_endpoint_node_v,segment_length_meters\nA,B,678.0\nA,C,639.0\nX,U,1377.0\nX,O,505.0\nX,N,3391.0\nB,M,199.0\nB,D,439.0\nC,M,310.0\nD,T,1083.0\nS,V,109.0\nT,J,345.0\nT,I,793.0\nM,N,1476.0\nE,F,772.0\nE,G,911.0\nF,W,911.0\nG,K,221.0\nG,W,771.0\nH,I,603.0\nH,J,935.0\nI,L,662.0\nJ,U,1106.0\nK,V,609.0\nK,L,772.0\nL,V,167.0\nU,P,240.0\nW,P,1903.0\nQ,P,1001.0\nQ,O,1877.0\nN,R,114.0\n\nIf you want to hand me the set of cleared stretches in a machine-friendly way, just use a tiny JSON snippet like this:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nThink of \"solution\" as the checklist of sidewalk segments to clear. Each little pair [u, v] is one segment connecting location u to location v — just list the segments you pick. This block is only a sketch of the shape I expect, not the actual answer.\n\nPlease make sure to use the exact identifiers that appear in the instance input — don't rename them or invent new labels. \n- 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 24, "num_edges": 30, "edges": [ { "u": 1, "v": 2, "w": 678.0 }, { "u": 1, "v": 3, "w": 639.0 }, { "u": 24, "v": 21, "w": 1377.0 }, { "u": 24, "v": 15, "w": 505.0 }, { "u": 24, "v": 14, "w": 3391.0 }, { "u": 2, "v": 13, "w": 199.0 }, { "u": 2, "v": 4, "w": 439.0 }, { "u": 3, "v": 13, "w": 310.0 }, { "u": 4, "v": 20, "w": 1083.0 }, { "u": 19, "v": 22, "w": 109.0 }, { "u": 20, "v": 10, "w": 345.0 }, { "u": 20, "v": 9, "w": 793.0 }, { "u": 13, "v": 14, "w": 1476.0 }, { "u": 5, "v": 6, "w": 772.0 }, { "u": 5, "v": 7, "w": 911.0 }, { "u": 6, "v": 23, "w": 911.0 }, { "u": 7, "v": 11, "w": 221.0 }, { "u": 7, "v": 23, "w": 771.0 }, { "u": 8, "v": 9, "w": 603.0 }, { "u": 8, "v": 10, "w": 935.0 }, { "u": 9, "v": 12, "w": 662.0 }, { "u": 10, "v": 21, "w": 1106.0 }, { "u": 11, "v": 22, "w": 609.0 }, { "u": 11, "v": 12, "w": 772.0 }, { "u": 12, "v": 22, "w": 167.0 }, { "u": 21, "v": 16, "w": 240.0 }, { "u": 23, "v": 16, "w": 1903.0 }, { "u": 17, "v": 16, "w": 1001.0 }, { "u": 17, "v": 15, "w": 1877.0 }, { "u": 14, "v": 18, "w": 114.0 } ], "terminals": [ 3, 24 ], "source_file": "I019.stp", "density": 0.10869565217391304, "viz_instance": "generated_data/STP/viz/STP_L/instance_0036.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0036.png" }, "solution": [ [ 21, 24 ], [ 2, 13 ], [ 2, 4 ], [ 3, 13 ], [ 4, 20 ], [ 10, 20 ], [ 10, 21 ] ], "obj": 4859.0, "instance_variant": { "problem_type": "STP", "num_nodes": 24, "num_edges": 30, "edges": [ { "u": "A", "v": "B", "w": 678.0 }, { "u": "A", "v": "C", "w": 639.0 }, { "u": "X", "v": "U", "w": 1377.0 }, { "u": "X", "v": "O", "w": 505.0 }, { "u": "X", "v": "N", "w": 3391.0 }, { "u": "B", "v": "M", "w": 199.0 }, { "u": "B", "v": "D", "w": 439.0 }, { "u": "C", "v": "M", "w": 310.0 }, { "u": "D", "v": "T", "w": 1083.0 }, { "u": "S", "v": "V", "w": 109.0 }, { "u": "T", "v": "J", "w": 345.0 }, { "u": "T", "v": "I", "w": 793.0 }, { "u": "M", "v": "N", "w": 1476.0 }, { "u": "E", "v": "F", "w": 772.0 }, { "u": "E", "v": "G", "w": 911.0 }, { "u": "F", "v": "W", "w": 911.0 }, { "u": "G", "v": "K", "w": 221.0 }, { "u": "G", "v": "W", "w": 771.0 }, { "u": "H", "v": "I", "w": 603.0 }, { "u": "H", "v": "J", "w": 935.0 }, { "u": "I", "v": "L", "w": 662.0 }, { "u": "J", "v": "U", "w": 1106.0 }, { "u": "K", "v": "V", "w": 609.0 }, { "u": "K", "v": "L", "w": 772.0 }, { "u": "L", "v": "V", "w": 167.0 }, { "u": "U", "v": "P", "w": 240.0 }, { "u": "W", "v": "P", "w": 1903.0 }, { "u": "Q", "v": "P", "w": 1001.0 }, { "u": "Q", "v": "O", "w": 1877.0 }, { "u": "N", "v": "R", "w": 114.0 } ], "density": 0.10869565217391304, "source_file": "I019.stp", "terminals": [ "C", "X" ] }, "solution_variant": [ [ "U", "X" ], [ "B", "M" ], [ "B", "D" ], [ "C", "M" ], [ "D", "T" ], [ "J", "T" ], [ "J", "U" ] ], "context_index": 37, "input_format": "csv", "input_index_base": "names" }, { "task_name": "STP", "problem_type": "STP", "instruction": "We’re planning the wiring of a new gallery and need to choose which display links to install so every interactive point is part of a single tour loop. It’s okay to run lines through other rooms to join things up, but the goal is to keep the total length of installed connectors as small as possible; the score for any layout is simply the sum of the lengths of the connectors used. Every interactive station must be connected into that one circuit, and no connector should be counted twice. The exact layout and measurements are listed below.\n\n{\n \"total_gallery_nodes\": 28,\n \"total_possible_connectors\": 36,\n \"edges\": [\n {\n \"endpoint_node_a\": 16,\n \"endpoint_node_b\": 13,\n \"connector_length\": 369.0\n },\n {\n \"endpoint_node_a\": 16,\n \"endpoint_node_b\": 17,\n \"connector_length\": 1275.0\n },\n {\n \"endpoint_node_a\": 16,\n \"endpoint_node_b\": 1,\n \"connector_length\": 10172.0\n },\n {\n \"endpoint_node_a\": 28,\n \"endpoint_node_b\": 12,\n \"connector_length\": 396.0\n },\n {\n \"endpoint_node_a\": 28,\n \"endpoint_node_b\": 4,\n \"connector_length\": 388.0\n },\n {\n \"endpoint_node_a\": 28,\n \"endpoint_node_b\": 17,\n \"connector_length\": 946.0\n },\n {\n \"endpoint_node_a\": 18,\n \"endpoint_node_b\": 19,\n \"connector_length\": 779.0\n },\n {\n \"endpoint_node_a\": 18,\n \"endpoint_node_b\": 25,\n \"connector_length\": 723.0\n },\n {\n \"endpoint_node_a\": 18,\n \"endpoint_node_b\": 24,\n \"connector_length\": 1692.0\n },\n {\n \"endpoint_node_a\": 19,\n \"endpoint_node_b\": 26,\n \"connector_length\": 1053.0\n },\n {\n \"endpoint_node_a\": 14,\n \"endpoint_node_b\": 15,\n \"connector_length\": 843.0\n },\n {\n \"endpoint_node_a\": 14,\n \"endpoint_node_b\": 12,\n \"connector_length\": 287.0\n },\n {\n \"endpoint_node_a\": 15,\n \"endpoint_node_b\": 13,\n \"connector_length\": 232.0\n },\n {\n \"endpoint_node_a\": 20,\n \"endpoint_node_b\": 21,\n \"connector_length\": 4617.0\n },\n {\n \"endpoint_node_a\": 20,\n \"endpoint_node_b\": 22,\n \"connector_length\": 668.0\n },\n {\n \"endpoint_node_a\": 21,\n \"endpoint_node_b\": 23,\n \"connector_length\": 1287.0\n },\n {\n \"endpoint_node_a\": 17,\n \"endpoint_node_b\": 5,\n \"connector_length\": 447.0\n },\n {\n \"endpoint_node_a\": 2,\n \"endpoint_node_b\": 3,\n \"connector_length\": 460.0\n },\n {\n \"endpoint_node_a\": 2,\n \"endpoint_node_b\": 7,\n \"connector_length\": 2333.0\n },\n {\n \"endpoint_node_a\": 2,\n \"endpoint_node_b\": 27,\n \"connector_length\": 11308.0\n },\n {\n \"endpoint_node_a\": 3,\n \"endpoint_node_b\": 6,\n \"connector_length\": 2333.0\n },\n {\n \"endpoint_node_a\": 3,\n \"endpoint_node_b\": 26,\n \"connector_length\": 6670.0\n },\n {\n \"endpoint_node_a\": 4,\n \"endpoint_node_b\": 5,\n \"connector_length\": 581.0\n },\n {\n \"endpoint_node_a\": 4,\n \"endpoint_node_b\": 26,\n \"connector_length\": 7949.0\n },\n {\n \"endpoint_node_a\": 5,\n \"endpoint_node_b\": 27,\n \"connector_length\": 2061.0\n },\n {\n \"endpoint_node_a\": 6,\n \"endpoint_node_b\": 7,\n \"connector_length\": 457.0\n },\n {\n \"endpoint_node_a\": 6,\n \"endpoint_node_b\": 24,\n \"connector_length\": 4405.0\n },\n {\n \"endpoint_node_a\": 6,\n \"endpoint_node_b\": 22,\n \"connector_length\": 4349.0\n },\n {\n \"endpoint_node_a\": 7,\n \"endpoint_node_b\": 9,\n \"connector_length\": 14628.0\n },\n {\n \"endpoint_node_a\": 8,\n \"endpoint_node_b\": 9,\n \"connector_length\": 496.0\n },\n {\n \"endpoint_node_a\": 8,\n \"endpoint_node_b\": 11,\n \"connector_length\": 4043.0\n },\n {\n \"endpoint_node_a\": 9,\n \"endpoint_node_b\": 10,\n \"connector_length\": 4004.0\n },\n {\n \"endpoint_node_a\": 22,\n \"endpoint_node_b\": 23,\n \"connector_length\": 4147.0\n },\n {\n \"endpoint_node_a\": 23,\n \"endpoint_node_b\": 24,\n \"connector_length\": 3612.0\n },\n {\n \"endpoint_node_a\": 10,\n \"endpoint_node_b\": 11,\n \"connector_length\": 475.0\n },\n {\n \"endpoint_node_a\": 12,\n \"endpoint_node_b\": 13,\n \"connector_length\": 752.0\n }\n ],\n \"interactive_stations\": [\n 5,\n 7,\n 8,\n 15,\n 20\n ]\n}\n\nOh — when you reply, please stick to this simple JSON shape so I can read your layout easily:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nThe \"solution\" entry should be a list of connector pairs. Each pair [u1, v1] means \"run a connector between station u1 and station v1\" — so you're just listing which links to install. This block is just a sketch of the expected shape, not the actual wiring plan.\n\nPlease make sure to use the exact identifiers from the instance input — do not rename them or invent new labels.\n- 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 28, "num_edges": 36, "edges": [ { "u": 16, "v": 13, "w": 369.0 }, { "u": 16, "v": 17, "w": 1275.0 }, { "u": 16, "v": 1, "w": 10172.0 }, { "u": 28, "v": 12, "w": 396.0 }, { "u": 28, "v": 4, "w": 388.0 }, { "u": 28, "v": 17, "w": 946.0 }, { "u": 18, "v": 19, "w": 779.0 }, { "u": 18, "v": 25, "w": 723.0 }, { "u": 18, "v": 24, "w": 1692.0 }, { "u": 19, "v": 26, "w": 1053.0 }, { "u": 14, "v": 15, "w": 843.0 }, { "u": 14, "v": 12, "w": 287.0 }, { "u": 15, "v": 13, "w": 232.0 }, { "u": 20, "v": 21, "w": 4617.0 }, { "u": 20, "v": 22, "w": 668.0 }, { "u": 21, "v": 23, "w": 1287.0 }, { "u": 17, "v": 5, "w": 447.0 }, { "u": 2, "v": 3, "w": 460.0 }, { "u": 2, "v": 7, "w": 2333.0 }, { "u": 2, "v": 27, "w": 11308.0 }, { "u": 3, "v": 6, "w": 2333.0 }, { "u": 3, "v": 26, "w": 6670.0 }, { "u": 4, "v": 5, "w": 581.0 }, { "u": 4, "v": 26, "w": 7949.0 }, { "u": 5, "v": 27, "w": 2061.0 }, { "u": 6, "v": 7, "w": 457.0 }, { "u": 6, "v": 24, "w": 4405.0 }, { "u": 6, "v": 22, "w": 4349.0 }, { "u": 7, "v": 9, "w": 14628.0 }, { "u": 8, "v": 9, "w": 496.0 }, { "u": 8, "v": 11, "w": 4043.0 }, { "u": 9, "v": 10, "w": 4004.0 }, { "u": 22, "v": 23, "w": 4147.0 }, { "u": 23, "v": 24, "w": 3612.0 }, { "u": 10, "v": 11, "w": 475.0 }, { "u": 12, "v": 13, "w": 752.0 } ], "terminals": [ 5, 7, 8, 15, 20 ], "source_file": "I040.stp", "density": 0.09523809523809523, "viz_instance": "generated_data/STP/viz/STP_L/instance_0037.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0037.png" }, "solution": [ [ 13, 16 ], [ 16, 17 ], [ 13, 15 ], [ 20, 22 ], [ 5, 17 ], [ 2, 7 ], [ 2, 27 ], [ 5, 27 ], [ 6, 7 ], [ 6, 22 ], [ 7, 9 ], [ 8, 9 ] ], "obj": 38623.0, "instance_variant": { "problem_type": "STP", "num_nodes": 28, "num_edges": 36, "edges": [ { "u": 16, "v": 13, "w": 369.0 }, { "u": 16, "v": 17, "w": 1275.0 }, { "u": 16, "v": 1, "w": 10172.0 }, { "u": 28, "v": 12, "w": 396.0 }, { "u": 28, "v": 4, "w": 388.0 }, { "u": 28, "v": 17, "w": 946.0 }, { "u": 18, "v": 19, "w": 779.0 }, { "u": 18, "v": 25, "w": 723.0 }, { "u": 18, "v": 24, "w": 1692.0 }, { "u": 19, "v": 26, "w": 1053.0 }, { "u": 14, "v": 15, "w": 843.0 }, { "u": 14, "v": 12, "w": 287.0 }, { "u": 15, "v": 13, "w": 232.0 }, { "u": 20, "v": 21, "w": 4617.0 }, { "u": 20, "v": 22, "w": 668.0 }, { "u": 21, "v": 23, "w": 1287.0 }, { "u": 17, "v": 5, "w": 447.0 }, { "u": 2, "v": 3, "w": 460.0 }, { "u": 2, "v": 7, "w": 2333.0 }, { "u": 2, "v": 27, "w": 11308.0 }, { "u": 3, "v": 6, "w": 2333.0 }, { "u": 3, "v": 26, "w": 6670.0 }, { "u": 4, "v": 5, "w": 581.0 }, { "u": 4, "v": 26, "w": 7949.0 }, { "u": 5, "v": 27, "w": 2061.0 }, { "u": 6, "v": 7, "w": 457.0 }, { "u": 6, "v": 24, "w": 4405.0 }, { "u": 6, "v": 22, "w": 4349.0 }, { "u": 7, "v": 9, "w": 14628.0 }, { "u": 8, "v": 9, "w": 496.0 }, { "u": 8, "v": 11, "w": 4043.0 }, { "u": 9, "v": 10, "w": 4004.0 }, { "u": 22, "v": 23, "w": 4147.0 }, { "u": 23, "v": 24, "w": 3612.0 }, { "u": 10, "v": 11, "w": 475.0 }, { "u": 12, "v": 13, "w": 752.0 } ], "density": 0.09523809523809523, "source_file": "I040.stp", "terminals": [ 5, 7, 8, 15, 20 ] }, "solution_variant": [ [ 13, 16 ], [ 16, 17 ], [ 13, 15 ], [ 20, 22 ], [ 5, 17 ], [ 2, 7 ], [ 2, 27 ], [ 5, 27 ], [ 6, 7 ], [ 6, 22 ], [ 7, 9 ], [ 8, 9 ] ], "context_index": 38, "input_format": "json", "input_index_base": 1 }, { "task_name": "STP", "problem_type": "STP", "instruction": "I’m imagining a city planner staring at a map, deciding which streets to pave so every neighborhood hub ends up linked by one continuous paved route. The idea is to pick a set of streets that reaches all the hubs, letting other intersections be used as little junctions where helpful, and then check the plan by adding up the lengths of the streets chosen — the smaller that total sum, the better the plan. Every hub must be on the paved network, each selected street only counts once when totaling length, and the specific streets and their lengths are shown below.\n\nI’m looking at 25 intersections and 30 candidate streets; the neighborhood hubs I must link are B C D E F G H P S V W Y.\nI can pave the street between U and Y, which would add 858.0 to the total.\nI can pave the street between U and K, which would add 19.0 to the total.\nI can pave the street between V and W, which would add 423.0 to the total.\nI can pave the street between V and S, which would add 63.0 to the total.\nI can pave the street between W and T, which would add 2763.0 to the total.\nI can pave the street between E and F, which would add 16.0 to the total.\nI can pave the street between E and H, which would add 800.0 to the total.\nI can pave the street between F and G, which would add 1376.0 to the total.\nI can pave the street between F and D, which would add 437.0 to the total.\nI can pave the street between X and Y, which would add 18.0 to the total.\nI can pave the street between X and K, which would add 862.0 to the total.\nI can pave the street between X and T, which would add 559.0 to the total.\nI can pave the street between A and J, which would add 4193.0 to the total.\nI can pave the street between A and S, which would add 2318.0 to the total.\nI can pave the street between D and H, which would add 1193.0 to the total.\nI can pave the street between H and C, which would add 742.0 to the total.\nI can pave the street between K and L, which would add 1312.0 to the total.\nI can pave the street between L and M, which would add 500.0 to the total.\nI can pave the street between L and T, which would add 884.0 to the total.\nI can pave the street between M and N, which would add 2930.0 to the total.\nI can pave the street between M and J, which would add 828.0 to the total.\nI can pave the street between N and G, which would add 1001.0 to the total.\nI can pave the street between B and I, which would add 1735.0 to the total.\nI can pave the street between B and O, which would add 3224.0 to the total.\nI can pave the street between I and R, which would add 18.0 to the total.\nI can pave the street between I and G, which would add 1412.0 to the total.\nI can pave the street between O and P, which would add 1403.0 to the total.\nI can pave the street between P and Q, which would add 282.0 to the total.\nI can pave the street between Q and R, which would add 512.0 to the total.\nI can pave the street between S and J, which would add 2844.0 to the total.\nI will judge any paving plan by the total length of streets chosen and prefer the plan with the smallest sum.\n\nIf you want to hand me the final plan in a machine-friendly way, just follow this simple shape:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nThis \"solution\" list is just a list of streets to pave, each street given as a pair of endpoint identifiers. Think of each [u, v] as \"pave the street between intersection u and intersection v.\" This is only a sketch of the expected shape — not the actual answer itself.\n\nPlease make sure to use the exact identifiers from the instance input — don't rename them or invent new labels.\n- 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 25, "num_edges": 30, "edges": [ { "u": 21, "v": 25, "w": 858.0 }, { "u": 21, "v": 11, "w": 19.0 }, { "u": 22, "v": 23, "w": 423.0 }, { "u": 22, "v": 19, "w": 63.0 }, { "u": 23, "v": 20, "w": 2763.0 }, { "u": 5, "v": 6, "w": 16.0 }, { "u": 5, "v": 8, "w": 800.0 }, { "u": 6, "v": 7, "w": 1376.0 }, { "u": 6, "v": 4, "w": 437.0 }, { "u": 24, "v": 25, "w": 18.0 }, { "u": 24, "v": 11, "w": 862.0 }, { "u": 24, "v": 20, "w": 559.0 }, { "u": 1, "v": 10, "w": 4193.0 }, { "u": 1, "v": 19, "w": 2318.0 }, { "u": 4, "v": 8, "w": 1193.0 }, { "u": 8, "v": 3, "w": 742.0 }, { "u": 11, "v": 12, "w": 1312.0 }, { "u": 12, "v": 13, "w": 500.0 }, { "u": 12, "v": 20, "w": 884.0 }, { "u": 13, "v": 14, "w": 2930.0 }, { "u": 13, "v": 10, "w": 828.0 }, { "u": 14, "v": 7, "w": 1001.0 }, { "u": 2, "v": 9, "w": 1735.0 }, { "u": 2, "v": 15, "w": 3224.0 }, { "u": 9, "v": 18, "w": 18.0 }, { "u": 9, "v": 7, "w": 1412.0 }, { "u": 15, "v": 16, "w": 1403.0 }, { "u": 16, "v": 17, "w": 282.0 }, { "u": 17, "v": 18, "w": 512.0 }, { "u": 19, "v": 10, "w": 2844.0 } ], "terminals": [ 2, 3, 4, 5, 6, 7, 8, 16, 19, 22, 23, 25 ], "source_file": "I002.stp", "density": 0.1, "viz_instance": "generated_data/STP/viz/STP_L/instance_0038.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0038.png" }, "solution": [ [ 22, 23 ], [ 19, 22 ], [ 20, 23 ], [ 5, 6 ], [ 5, 8 ], [ 6, 7 ], [ 4, 6 ], [ 24, 25 ], [ 20, 24 ], [ 3, 8 ], [ 12, 13 ], [ 12, 20 ], [ 13, 14 ], [ 7, 14 ], [ 2, 9 ], [ 9, 18 ], [ 7, 9 ], [ 16, 17 ], [ 17, 18 ] ], "obj": 16471.0, "instance_variant": { "problem_type": "STP", "num_nodes": 25, "num_edges": 30, "edges": [ { "u": "U", "v": "Y", "w": 858.0 }, { "u": "U", "v": "K", "w": 19.0 }, { "u": "V", "v": "W", "w": 423.0 }, { "u": "V", "v": "S", "w": 63.0 }, { "u": "W", "v": "T", "w": 2763.0 }, { "u": "E", "v": "F", "w": 16.0 }, { "u": "E", "v": "H", "w": 800.0 }, { "u": "F", "v": "G", "w": 1376.0 }, { "u": "F", "v": "D", "w": 437.0 }, { "u": "X", "v": "Y", "w": 18.0 }, { "u": "X", "v": "K", "w": 862.0 }, { "u": "X", "v": "T", "w": 559.0 }, { "u": "A", "v": "J", "w": 4193.0 }, { "u": "A", "v": "S", "w": 2318.0 }, { "u": "D", "v": "H", "w": 1193.0 }, { "u": "H", "v": "C", "w": 742.0 }, { "u": "K", "v": "L", "w": 1312.0 }, { "u": "L", "v": "M", "w": 500.0 }, { "u": "L", "v": "T", "w": 884.0 }, { "u": "M", "v": "N", "w": 2930.0 }, { "u": "M", "v": "J", "w": 828.0 }, { "u": "N", "v": "G", "w": 1001.0 }, { "u": "B", "v": "I", "w": 1735.0 }, { "u": "B", "v": "O", "w": 3224.0 }, { "u": "I", "v": "R", "w": 18.0 }, { "u": "I", "v": "G", "w": 1412.0 }, { "u": "O", "v": "P", "w": 1403.0 }, { "u": "P", "v": "Q", "w": 282.0 }, { "u": "Q", "v": "R", "w": 512.0 }, { "u": "S", "v": "J", "w": 2844.0 } ], "density": 0.1, "source_file": "I002.stp", "terminals": [ "B", "C", "D", "E", "F", "G", "H", "P", "S", "V", "W", "Y" ] }, "solution_variant": [ [ "V", "W" ], [ "S", "V" ], [ "T", "W" ], [ "E", "F" ], [ "E", "H" ], [ "F", "G" ], [ "D", "F" ], [ "X", "Y" ], [ "T", "X" ], [ "C", "H" ], [ "L", "M" ], [ "L", "T" ], [ "M", "N" ], [ "G", "N" ], [ "B", "I" ], [ "I", "R" ], [ "G", "I" ], [ "P", "Q" ], [ "Q", "R" ] ], "context_index": 39, "input_format": "markdown_table", "input_index_base": "names" }, { "task_name": "STP", "problem_type": "STP", "instruction": "A last-minute rethink meant choosing a set of walkways that would join every stage and vendor area into one neat network, with the option to add a few temporary link points where they save money. The question was which exact paths to construct; a better plan is the one that connects all required spots and ends up costing the least overall — tally the construction costs of the selected walkways and prefer the plan with the smallest sum. All stages and vendors must be included in the network, and the same connection can’t be counted twice to game the total. The exact map and cost breakdown are down below.\n\n{\n \"total_locations\": 29,\n \"candidate_walkways_count\": 38,\n \"edges\": [\n {\n \"endpoint_a\": 27,\n \"endpoint_b\": 1,\n \"construction_cost\": 3052.0\n },\n {\n \"endpoint_a\": 27,\n \"endpoint_b\": 23,\n \"construction_cost\": 2505.0\n },\n {\n \"endpoint_a\": 29,\n \"endpoint_b\": 20,\n \"construction_cost\": 19406.0\n },\n {\n \"endpoint_a\": 29,\n \"endpoint_b\": 26,\n \"construction_cost\": 3260.0\n },\n {\n \"endpoint_a\": 29,\n \"endpoint_b\": 24,\n \"construction_cost\": 5219.0\n },\n {\n \"endpoint_a\": 22,\n \"endpoint_b\": 13,\n \"construction_cost\": 874.0\n },\n {\n \"endpoint_a\": 22,\n \"endpoint_b\": 25,\n \"construction_cost\": 1127.0\n },\n {\n \"endpoint_a\": 22,\n \"endpoint_b\": 4,\n \"construction_cost\": 3059.0\n },\n {\n \"endpoint_a\": 23,\n \"endpoint_b\": 14,\n \"construction_cost\": 557.0\n },\n {\n \"endpoint_a\": 23,\n \"endpoint_b\": 13,\n \"construction_cost\": 3225.0\n },\n {\n \"endpoint_a\": 21,\n \"endpoint_b\": 28,\n \"construction_cost\": 1423.0\n },\n {\n \"endpoint_a\": 21,\n \"endpoint_b\": 24,\n \"construction_cost\": 5184.0\n },\n {\n \"endpoint_a\": 28,\n \"endpoint_b\": 24,\n \"construction_cost\": 4167.0\n },\n {\n \"endpoint_a\": 3,\n \"endpoint_b\": 25,\n \"construction_cost\": 1413.0\n },\n {\n \"endpoint_a\": 3,\n \"endpoint_b\": 16,\n \"construction_cost\": 293.0\n },\n {\n \"endpoint_a\": 4,\n \"endpoint_b\": 18,\n \"construction_cost\": 229.0\n },\n {\n \"endpoint_a\": 4,\n \"endpoint_b\": 11,\n \"construction_cost\": 270749.0\n },\n {\n \"endpoint_a\": 5,\n \"endpoint_b\": 6,\n \"construction_cost\": 509.0\n },\n {\n \"endpoint_a\": 5,\n \"endpoint_b\": 7,\n \"construction_cost\": 929.0\n },\n {\n \"endpoint_a\": 5,\n \"endpoint_b\": 11,\n \"construction_cost\": 270566.0\n },\n {\n \"endpoint_a\": 6,\n \"endpoint_b\": 15,\n \"construction_cost\": 929.0\n },\n {\n \"endpoint_a\": 6,\n \"endpoint_b\": 18,\n \"construction_cost\": 1087.0\n },\n {\n \"endpoint_a\": 7,\n \"endpoint_b\": 15,\n \"construction_cost\": 509.0\n },\n {\n \"endpoint_a\": 7,\n \"endpoint_b\": 24,\n \"construction_cost\": 2485.0\n },\n {\n \"endpoint_a\": 8,\n \"endpoint_b\": 9,\n \"construction_cost\": 795.0\n },\n {\n \"endpoint_a\": 8,\n \"endpoint_b\": 10,\n \"construction_cost\": 870.0\n },\n {\n \"endpoint_a\": 9,\n \"endpoint_b\": 17,\n \"construction_cost\": 381.0\n },\n {\n \"endpoint_a\": 9,\n \"endpoint_b\": 26,\n \"construction_cost\": 2688.0\n },\n {\n \"endpoint_a\": 10,\n \"endpoint_b\": 17,\n \"construction_cost\": 144.0\n },\n {\n \"endpoint_a\": 12,\n \"endpoint_b\": 25,\n \"construction_cost\": 10.0\n },\n {\n \"endpoint_a\": 12,\n \"endpoint_b\": 2,\n \"construction_cost\": 44.0\n },\n {\n \"endpoint_a\": 12,\n \"endpoint_b\": 14,\n \"construction_cost\": 816.0\n },\n {\n \"endpoint_a\": 24,\n \"endpoint_b\": 13,\n \"construction_cost\": 1701.0\n },\n {\n \"endpoint_a\": 26,\n \"endpoint_b\": 18,\n \"construction_cost\": 3369.0\n },\n {\n \"endpoint_a\": 26,\n \"endpoint_b\": 15,\n \"construction_cost\": 1412.0\n },\n {\n \"endpoint_a\": 14,\n \"endpoint_b\": 1,\n \"construction_cost\": 58.0\n },\n {\n \"endpoint_a\": 19,\n \"endpoint_b\": 20,\n \"construction_cost\": 1767.0\n },\n {\n \"endpoint_a\": 1,\n \"endpoint_b\": 2,\n \"construction_cost\": 720.0\n }\n ],\n \"required_spots\": [\n 13,\n 14\n ]\n}\n\nWhen you’re ready to send the chosen set of walkways, just follow this simple JSON layout so it’s easy to read and check:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nThink of \"solution\" as a list of edge pairs — each [u, v] is a walkway joining node u and node v. Fill that list with the pairs you picked for the event map. It’s just a sketch of the expected shape, not the actual answer itself.\n\nPlease use the node identifiers exactly as they appear in the instance input — don’t rename them or invent new labels.\n- 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 29, "num_edges": 38, "edges": [ { "u": 27, "v": 1, "w": 3052.0 }, { "u": 27, "v": 23, "w": 2505.0 }, { "u": 29, "v": 20, "w": 19406.0 }, { "u": 29, "v": 26, "w": 3260.0 }, { "u": 29, "v": 24, "w": 5219.0 }, { "u": 22, "v": 13, "w": 874.0 }, { "u": 22, "v": 25, "w": 1127.0 }, { "u": 22, "v": 4, "w": 3059.0 }, { "u": 23, "v": 14, "w": 557.0 }, { "u": 23, "v": 13, "w": 3225.0 }, { "u": 21, "v": 28, "w": 1423.0 }, { "u": 21, "v": 24, "w": 5184.0 }, { "u": 28, "v": 24, "w": 4167.0 }, { "u": 3, "v": 25, "w": 1413.0 }, { "u": 3, "v": 16, "w": 293.0 }, { "u": 4, "v": 18, "w": 229.0 }, { "u": 4, "v": 11, "w": 270749.0 }, { "u": 5, "v": 6, "w": 509.0 }, { "u": 5, "v": 7, "w": 929.0 }, { "u": 5, "v": 11, "w": 270566.0 }, { "u": 6, "v": 15, "w": 929.0 }, { "u": 6, "v": 18, "w": 1087.0 }, { "u": 7, "v": 15, "w": 509.0 }, { "u": 7, "v": 24, "w": 2485.0 }, { "u": 8, "v": 9, "w": 795.0 }, { "u": 8, "v": 10, "w": 870.0 }, { "u": 9, "v": 17, "w": 381.0 }, { "u": 9, "v": 26, "w": 2688.0 }, { "u": 10, "v": 17, "w": 144.0 }, { "u": 12, "v": 25, "w": 10.0 }, { "u": 12, "v": 2, "w": 44.0 }, { "u": 12, "v": 14, "w": 816.0 }, { "u": 24, "v": 13, "w": 1701.0 }, { "u": 26, "v": 18, "w": 3369.0 }, { "u": 26, "v": 15, "w": 1412.0 }, { "u": 14, "v": 1, "w": 58.0 }, { "u": 19, "v": 20, "w": 1767.0 }, { "u": 1, "v": 2, "w": 720.0 } ], "terminals": [ 13, 14 ], "source_file": "I025.stp", "density": 0.09359605911330049, "viz_instance": "generated_data/STP/viz/STP_L/instance_0039.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0039.png" }, "solution": [ [ 13, 22 ], [ 22, 25 ], [ 12, 25 ], [ 12, 14 ] ], "obj": 2827.0, "instance_variant": { "problem_type": "STP", "num_nodes": 29, "num_edges": 38, "edges": [ { "u": 27, "v": 1, "w": 3052.0 }, { "u": 27, "v": 23, "w": 2505.0 }, { "u": 29, "v": 20, "w": 19406.0 }, { "u": 29, "v": 26, "w": 3260.0 }, { "u": 29, "v": 24, "w": 5219.0 }, { "u": 22, "v": 13, "w": 874.0 }, { "u": 22, "v": 25, "w": 1127.0 }, { "u": 22, "v": 4, "w": 3059.0 }, { "u": 23, "v": 14, "w": 557.0 }, { "u": 23, "v": 13, "w": 3225.0 }, { "u": 21, "v": 28, "w": 1423.0 }, { "u": 21, "v": 24, "w": 5184.0 }, { "u": 28, "v": 24, "w": 4167.0 }, { "u": 3, "v": 25, "w": 1413.0 }, { "u": 3, "v": 16, "w": 293.0 }, { "u": 4, "v": 18, "w": 229.0 }, { "u": 4, "v": 11, "w": 270749.0 }, { "u": 5, "v": 6, "w": 509.0 }, { "u": 5, "v": 7, "w": 929.0 }, { "u": 5, "v": 11, "w": 270566.0 }, { "u": 6, "v": 15, "w": 929.0 }, { "u": 6, "v": 18, "w": 1087.0 }, { "u": 7, "v": 15, "w": 509.0 }, { "u": 7, "v": 24, "w": 2485.0 }, { "u": 8, "v": 9, "w": 795.0 }, { "u": 8, "v": 10, "w": 870.0 }, { "u": 9, "v": 17, "w": 381.0 }, { "u": 9, "v": 26, "w": 2688.0 }, { "u": 10, "v": 17, "w": 144.0 }, { "u": 12, "v": 25, "w": 10.0 }, { "u": 12, "v": 2, "w": 44.0 }, { "u": 12, "v": 14, "w": 816.0 }, { "u": 24, "v": 13, "w": 1701.0 }, { "u": 26, "v": 18, "w": 3369.0 }, { "u": 26, "v": 15, "w": 1412.0 }, { "u": 14, "v": 1, "w": 58.0 }, { "u": 19, "v": 20, "w": 1767.0 }, { "u": 1, "v": 2, "w": 720.0 } ], "density": 0.09359605911330049, "source_file": "I025.stp", "terminals": [ 13, 14 ] }, "solution_variant": [ [ 13, 22 ], [ 22, 25 ], [ 12, 25 ], [ 12, 14 ] ], "context_index": 40, "input_format": "json", "input_index_base": 1 }, { "task_name": "STP", "problem_type": "STP", "instruction": "I’m looking at a building map and the goal is to activate certain fiber runs so that all the listed offices are connected into a single, continuous network while keeping the sum of cable lengths as low as possible. To compare layouts, just total the lengths of the activated runs; the lowest total is preferable. Intermediate closets or junctions can be used to make links shorter, but every required office must be connected and nothing can be left out or split off. The full layout and measurements are provided below.\n\nI count 26 distinct locations, 33 candidate cable runs, and the offices that must be connected are 2 4 5 7 8 10 15 17 19 25.\nI see a cable run between 6 and 1 with length 975.0.\nI see a cable run between 6 and 10 with length 4091.0.\nI see a cable run between 6 and 11 with length 13212.0.\nI see a cable run between 21 and 22 with length 7803.0.\nI see a cable run between 22 and 24 with length 880.0.\nI see a cable run between 22 and 25 with length 2884.0.\nI see a cable run between 23 and 12 with length 10023.0.\nI see a cable run between 7 and 12 with length 4169.0.\nI see a cable run between 8 and 13 with length 12013.0.\nI see a cable run between 8 and 0 with length 4349.0.\nI see a cable run between 8 and 3 with length 5787.0.\nI see a cable run between 9 and 3 with length 4424.0.\nI see a cable run between 9 and 2 with length 2757.0.\nI see a cable run between 9 and 25 with length 20776.0.\nI see a cable run between 10 and 2 with length 544.0.\nI see a cable run between 10 and 11 with length 9234.0.\nI see a cable run between 0 and 5 with length 231627.0.\nI see a cable run between 0 and 17 with length 10952.0.\nI see a cable run between 1 and 2 with length 4499.0.\nI see a cable run between 1 and 3 with length 4312.0.\nI see a cable run between 1 and 5 with length 227517.0.\nI see a cable run between 11 and 19 with length 8831.0.\nI see a cable run between 12 and 17 with length 7186.0.\nI see a cable run between 16 and 18 with length 1779.0.\nI see a cable run between 16 and 19 with length 6381.0.\nI see a cable run between 16 and 20 with length 33605.0.\nI see a cable run between 4 and 18 with length 7447.0.\nI see a cable run between 19 and 17 with length 20537.0.\nI see a cable run between 24 and 25 with length 2195.0.\nI see a cable run between 24 and 15 with length 20495.0.\nI see a cable run between 13 and 15 with length 12265.0.\nI see a cable run between 13 and 14 with length 14850.0.\nI see a cable run between 14 and 15 with length 14081.0.\nI'll total activated run lengths to compare layouts and choose the lowest-sum solution.\n\nAlso, when you send the chosen layout back, a nice compact way to list the activated runs is with a little JSON sketch like this:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nThis just means \"solution\" is a list of cable runs to switch on; each pair like [u1, v1] is the run between endpoint u1 and endpoint v1. Treat the u1, v1 entries above as placeholders — the real reply should replace those placeholders with the actual endpoint labels from the map.\n\nThis JSON is only a sketch of the shape I want, not the actual answer. Please use the exact identifiers from the instance input — do not rename them or invent new labels. \n- 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 26, "num_edges": 33, "edges": [ { "u": 7, "v": 2, "w": 975.0 }, { "u": 7, "v": 11, "w": 4091.0 }, { "u": 7, "v": 12, "w": 13212.0 }, { "u": 22, "v": 23, "w": 7803.0 }, { "u": 23, "v": 25, "w": 880.0 }, { "u": 23, "v": 26, "w": 2884.0 }, { "u": 24, "v": 13, "w": 10023.0 }, { "u": 8, "v": 13, "w": 4169.0 }, { "u": 9, "v": 14, "w": 12013.0 }, { "u": 9, "v": 1, "w": 4349.0 }, { "u": 9, "v": 4, "w": 5787.0 }, { "u": 10, "v": 4, "w": 4424.0 }, { "u": 10, "v": 3, "w": 2757.0 }, { "u": 10, "v": 26, "w": 20776.0 }, { "u": 11, "v": 3, "w": 544.0 }, { "u": 11, "v": 12, "w": 9234.0 }, { "u": 1, "v": 6, "w": 231627.0 }, { "u": 1, "v": 18, "w": 10952.0 }, { "u": 2, "v": 3, "w": 4499.0 }, { "u": 2, "v": 4, "w": 4312.0 }, { "u": 2, "v": 6, "w": 227517.0 }, { "u": 12, "v": 20, "w": 8831.0 }, { "u": 13, "v": 18, "w": 7186.0 }, { "u": 17, "v": 19, "w": 1779.0 }, { "u": 17, "v": 20, "w": 6381.0 }, { "u": 17, "v": 21, "w": 33605.0 }, { "u": 5, "v": 19, "w": 7447.0 }, { "u": 20, "v": 18, "w": 20537.0 }, { "u": 25, "v": 26, "w": 2195.0 }, { "u": 25, "v": 16, "w": 20495.0 }, { "u": 14, "v": 16, "w": 12265.0 }, { "u": 14, "v": 15, "w": 14850.0 }, { "u": 15, "v": 16, "w": 14081.0 } ], "terminals": [ 3, 5, 6, 8, 9, 11, 16, 18, 20, 26 ], "source_file": "I060.stp", "density": 0.10153846153846154, "viz_instance": "generated_data/STP/viz/STP_L/instance_0040.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0040.png" }, "solution": [ [ 8, 13 ], [ 1, 9 ], [ 4, 9 ], [ 4, 10 ], [ 3, 10 ], [ 10, 26 ], [ 3, 11 ], [ 11, 12 ], [ 1, 6 ], [ 1, 18 ], [ 12, 20 ], [ 13, 18 ], [ 17, 19 ], [ 17, 20 ], [ 5, 19 ], [ 25, 26 ], [ 16, 25 ] ], "obj": 348933.0, "instance_variant": { "problem_type": "STP", "num_nodes": 26, "num_edges": 33, "edges": [ { "u": 6, "v": 1, "w": 975.0 }, { "u": 6, "v": 10, "w": 4091.0 }, { "u": 6, "v": 11, "w": 13212.0 }, { "u": 21, "v": 22, "w": 7803.0 }, { "u": 22, "v": 24, "w": 880.0 }, { "u": 22, "v": 25, "w": 2884.0 }, { "u": 23, "v": 12, "w": 10023.0 }, { "u": 7, "v": 12, "w": 4169.0 }, { "u": 8, "v": 13, "w": 12013.0 }, { "u": 8, "v": 0, "w": 4349.0 }, { "u": 8, "v": 3, "w": 5787.0 }, { "u": 9, "v": 3, "w": 4424.0 }, { "u": 9, "v": 2, "w": 2757.0 }, { "u": 9, "v": 25, "w": 20776.0 }, { "u": 10, "v": 2, "w": 544.0 }, { "u": 10, "v": 11, "w": 9234.0 }, { "u": 0, "v": 5, "w": 231627.0 }, { "u": 0, "v": 17, "w": 10952.0 }, { "u": 1, "v": 2, "w": 4499.0 }, { "u": 1, "v": 3, "w": 4312.0 }, { "u": 1, "v": 5, "w": 227517.0 }, { "u": 11, "v": 19, "w": 8831.0 }, { "u": 12, "v": 17, "w": 7186.0 }, { "u": 16, "v": 18, "w": 1779.0 }, { "u": 16, "v": 19, "w": 6381.0 }, { "u": 16, "v": 20, "w": 33605.0 }, { "u": 4, "v": 18, "w": 7447.0 }, { "u": 19, "v": 17, "w": 20537.0 }, { "u": 24, "v": 25, "w": 2195.0 }, { "u": 24, "v": 15, "w": 20495.0 }, { "u": 13, "v": 15, "w": 12265.0 }, { "u": 13, "v": 14, "w": 14850.0 }, { "u": 14, "v": 15, "w": 14081.0 } ], "density": 0.10153846153846154, "source_file": "I060.stp", "terminals": [ 2, 4, 5, 7, 8, 10, 15, 17, 19, 25 ] }, "solution_variant": [ [ 7, 12 ], [ 0, 8 ], [ 3, 8 ], [ 3, 9 ], [ 2, 9 ], [ 9, 25 ], [ 2, 10 ], [ 10, 11 ], [ 0, 5 ], [ 0, 17 ], [ 11, 19 ], [ 12, 17 ], [ 16, 18 ], [ 16, 19 ], [ 4, 18 ], [ 24, 25 ], [ 15, 24 ] ], "context_index": 41, "input_format": "markdown_table", "input_index_base": 0 }, { "task_name": "STP", "problem_type": "STP", "instruction": "In one planning job the engineers have to pick microwave link hops that will join all required cell sites into a single operational backbone, and there are optional relay towers available to route around expensive direct links. The plan must include every required site in that one connected structure — nothing omitted — and using those extra towers is allowed if it reduces the expenses. To rank different plans, sum the cost of each activated hop to get the total cost; the plan with the smallest total cost is preferred, and duplicate selections of the same hop don’t change the cost. The concrete network and costs are shown below.\n\nIt comprises 24 distinct towers, 31 candidate hops, and the required cell sites are 10 11 17 18.\nA candidate microwave hop connects 4 and 3 with activation cost 26866.0.\nA candidate microwave hop connects 9 and 10 with activation cost 688.0.\nA candidate microwave hop connects 9 and 11 with activation cost 16.0.\nA candidate microwave hop connects 10 and 23 with activation cost 389.0.\nA candidate microwave hop connects 16 and 17 with activation cost 54.0.\nA candidate microwave hop connects 16 and 19 with activation cost 3004.0.\nA candidate microwave hop connects 16 and 3 with activation cost 46393.0.\nA candidate microwave hop connects 17 and 14 with activation cost 2894.0.\nA candidate microwave hop connects 17 and 5 with activation cost 3156.0.\nA candidate microwave hop connects 20 and 8 with activation cost 542.0.\nA candidate microwave hop connects 20 and 19 with activation cost 1056.0.\nA candidate microwave hop connects 20 and 15 with activation cost 40249.0.\nA candidate microwave hop connects 12 and 22 with activation cost 442.0.\nA candidate microwave hop connects 12 and 11 with activation cost 1094.0.\nA candidate microwave hop connects 12 and 0 with activation cost 5507.0.\nA candidate microwave hop connects 13 and 5 with activation cost 545.0.\nA candidate microwave hop connects 13 and 14 with activation cost 2155.0.\nA candidate microwave hop connects 13 and 21 with activation cost 3759.0.\nA candidate microwave hop connects 14 and 7 with activation cost 843.0.\nA candidate microwave hop connects 11 and 18 with activation cost 3201.0.\nA candidate microwave hop connects 15 and 1 with activation cost 13481.0.\nA candidate microwave hop connects 15 and 3 with activation cost 8093.0.\nA candidate microwave hop connects 21 and 7 with activation cost 2759.0.\nA candidate microwave hop connects 21 and 22 with activation cost 210.0.\nA candidate microwave hop connects 19 and 6 with activation cost 456.0.\nA candidate microwave hop connects 2 and 1 with activation cost 1028.0.\nA candidate microwave hop connects 2 and 3 with activation cost 18164.0.\nA candidate microwave hop connects 22 and 23 with activation cost 1404.0.\nA candidate microwave hop connects 23 and 8 with activation cost 2344.0.\nA candidate microwave hop connects 6 and 7 with activation cost 312.0.\nA candidate microwave hop connects 6 and 8 with activation cost 762.0.\nThe engineers will assemble these hops into one connected backbone that includes every 10 11 17 18 and minimizes the total activated hop cost.\n\nAlso, when you send the actual plan back, please stick to this simple JSON layout so whatever reads it knows where to look. Here's the shape I expect:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nThis just means \"solution\" is a list of hops to activate; each inner pair is one link between two sites (the order in a pair doesn't matter). Think of it like filling out a short form: list each chosen hop as its two endpoint identifiers. This block is just a sketch of the shape I want — not the real answer.\n\nPlease use the exact identifiers from the instance input with no renaming and no new labels. \n- 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 24, "num_edges": 31, "edges": [ { "u": 5, "v": 4, "w": 26866.0 }, { "u": 10, "v": 11, "w": 688.0 }, { "u": 10, "v": 12, "w": 16.0 }, { "u": 11, "v": 24, "w": 389.0 }, { "u": 17, "v": 18, "w": 54.0 }, { "u": 17, "v": 20, "w": 3004.0 }, { "u": 17, "v": 4, "w": 46393.0 }, { "u": 18, "v": 15, "w": 2894.0 }, { "u": 18, "v": 6, "w": 3156.0 }, { "u": 21, "v": 9, "w": 542.0 }, { "u": 21, "v": 20, "w": 1056.0 }, { "u": 21, "v": 16, "w": 40249.0 }, { "u": 13, "v": 23, "w": 442.0 }, { "u": 13, "v": 12, "w": 1094.0 }, { "u": 13, "v": 1, "w": 5507.0 }, { "u": 14, "v": 6, "w": 545.0 }, { "u": 14, "v": 15, "w": 2155.0 }, { "u": 14, "v": 22, "w": 3759.0 }, { "u": 15, "v": 8, "w": 843.0 }, { "u": 12, "v": 19, "w": 3201.0 }, { "u": 16, "v": 2, "w": 13481.0 }, { "u": 16, "v": 4, "w": 8093.0 }, { "u": 22, "v": 8, "w": 2759.0 }, { "u": 22, "v": 23, "w": 210.0 }, { "u": 20, "v": 7, "w": 456.0 }, { "u": 3, "v": 2, "w": 1028.0 }, { "u": 3, "v": 4, "w": 18164.0 }, { "u": 23, "v": 24, "w": 1404.0 }, { "u": 24, "v": 9, "w": 2344.0 }, { "u": 7, "v": 8, "w": 312.0 }, { "u": 7, "v": 9, "w": 762.0 } ], "terminals": [ 11, 12, 18, 19 ], "source_file": "I031.stp", "density": 0.11231884057971014, "viz_instance": "generated_data/STP/viz/STP_L/instance_0041.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0041.png" }, "solution": [ [ 10, 11 ], [ 10, 12 ], [ 11, 24 ], [ 17, 18 ], [ 17, 20 ], [ 12, 19 ], [ 7, 20 ], [ 9, 24 ], [ 7, 9 ] ], "obj": 10914.0, "instance_variant": { "problem_type": "STP", "num_nodes": 24, "num_edges": 31, "edges": [ { "u": 4, "v": 3, "w": 26866.0 }, { "u": 9, "v": 10, "w": 688.0 }, { "u": 9, "v": 11, "w": 16.0 }, { "u": 10, "v": 23, "w": 389.0 }, { "u": 16, "v": 17, "w": 54.0 }, { "u": 16, "v": 19, "w": 3004.0 }, { "u": 16, "v": 3, "w": 46393.0 }, { "u": 17, "v": 14, "w": 2894.0 }, { "u": 17, "v": 5, "w": 3156.0 }, { "u": 20, "v": 8, "w": 542.0 }, { "u": 20, "v": 19, "w": 1056.0 }, { "u": 20, "v": 15, "w": 40249.0 }, { "u": 12, "v": 22, "w": 442.0 }, { "u": 12, "v": 11, "w": 1094.0 }, { "u": 12, "v": 0, "w": 5507.0 }, { "u": 13, "v": 5, "w": 545.0 }, { "u": 13, "v": 14, "w": 2155.0 }, { "u": 13, "v": 21, "w": 3759.0 }, { "u": 14, "v": 7, "w": 843.0 }, { "u": 11, "v": 18, "w": 3201.0 }, { "u": 15, "v": 1, "w": 13481.0 }, { "u": 15, "v": 3, "w": 8093.0 }, { "u": 21, "v": 7, "w": 2759.0 }, { "u": 21, "v": 22, "w": 210.0 }, { "u": 19, "v": 6, "w": 456.0 }, { "u": 2, "v": 1, "w": 1028.0 }, { "u": 2, "v": 3, "w": 18164.0 }, { "u": 22, "v": 23, "w": 1404.0 }, { "u": 23, "v": 8, "w": 2344.0 }, { "u": 6, "v": 7, "w": 312.0 }, { "u": 6, "v": 8, "w": 762.0 } ], "density": 0.11231884057971014, "source_file": "I031.stp", "terminals": [ 10, 11, 17, 18 ] }, "solution_variant": [ [ 9, 10 ], [ 9, 11 ], [ 10, 23 ], [ 16, 17 ], [ 16, 19 ], [ 11, 18 ], [ 6, 19 ], [ 8, 23 ], [ 6, 8 ] ], "context_index": 42, "input_format": "markdown_table", "input_index_base": 0 }, { "task_name": "STP", "problem_type": "STP", "instruction": "Recently the curator had to figure out which doors and passages to open so visitors can stroll through all the exhibit halls without gaps. The approach allows linking halls directly or via foyers, and the simplest, most efficient setup is the one with the lowest sum of corridor lengths opened. The total is calculated by summing every opened corridor’s length, and every hall must be connected into that single network with no repeats. The actual map and lengths are shown below.\n\nOn this map there are 25 distinct locations, 31 candidate corridors, and the exhibit halls that must be connected are 7 13.\nCorridor option between 20 and 21 has length 300.0.\nCorridor option between 20 and 16 has length 1408.0.\nCorridor option between 20 and 25 has length 1166.0.\nCorridor option between 21 and 12 has length 2810.0.\nCorridor option between 15 and 16 has length 126.0.\nCorridor option between 15 and 19 has length 1420.0.\nCorridor option between 15 and 23 has length 201.0.\nCorridor option between 16 and 17 has length 1473.0.\nCorridor option between 17 and 2 has length 1038.0.\nCorridor option between 17 and 22 has length 1397.0.\nCorridor option between 18 and 13 has length 895.0.\nCorridor option between 18 and 24 has length 52.0.\nCorridor option between 18 and 2 has length 554.0.\nCorridor option between 9 and 12 has length 2044.0.\nCorridor option between 19 and 14 has length 202.0.\nCorridor option between 19 and 23 has length 1536.0.\nCorridor option between 13 and 10 has length 788.0.\nCorridor option between 13 and 11 has length 2640.0.\nCorridor option between 14 and 10 has length 1934.0.\nCorridor option between 14 and 11 has length 1671.0.\nCorridor option between 23 and 12 has length 1830.0.\nCorridor option between 1 and 2 has length 531.0.\nCorridor option between 1 and 3 has length 607.0.\nCorridor option between 3 and 7 has length 262.0.\nCorridor option between 3 and 4 has length 327.0.\nCorridor option between 5 and 6 has length 269.0.\nCorridor option between 5 and 7 has length 493.0.\nCorridor option between 5 and 8 has length 1162.0.\nCorridor option between 6 and 24 has length 493.0.\nCorridor option between 6 and 8 has length 1202.0.\nCorridor option between 7 and 24 has length 269.0.\nThe curator will select the set of corridors with the smallest total length that connects all 7 13.\n\nAlso, to keep things tidy, please give the chosen corridors in a simple JSON layout like this:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nThink of this as a little form: \"solution\" is the list, and each pair [u, v] is a corridor to open between hall u and hall v. This is just the shape I want — a sketch of the expected format, not the actual set of corridors.\n\nPlease use the exact identifiers from 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\".", "instance": { "problem_type": "STP", "num_nodes": 25, "num_edges": 31, "edges": [ { "u": 20, "v": 21, "w": 300.0 }, { "u": 20, "v": 16, "w": 1408.0 }, { "u": 20, "v": 25, "w": 1166.0 }, { "u": 21, "v": 12, "w": 2810.0 }, { "u": 15, "v": 16, "w": 126.0 }, { "u": 15, "v": 19, "w": 1420.0 }, { "u": 15, "v": 23, "w": 201.0 }, { "u": 16, "v": 17, "w": 1473.0 }, { "u": 17, "v": 2, "w": 1038.0 }, { "u": 17, "v": 22, "w": 1397.0 }, { "u": 18, "v": 13, "w": 895.0 }, { "u": 18, "v": 24, "w": 52.0 }, { "u": 18, "v": 2, "w": 554.0 }, { "u": 9, "v": 12, "w": 2044.0 }, { "u": 19, "v": 14, "w": 202.0 }, { "u": 19, "v": 23, "w": 1536.0 }, { "u": 13, "v": 10, "w": 788.0 }, { "u": 13, "v": 11, "w": 2640.0 }, { "u": 14, "v": 10, "w": 1934.0 }, { "u": 14, "v": 11, "w": 1671.0 }, { "u": 23, "v": 12, "w": 1830.0 }, { "u": 1, "v": 2, "w": 531.0 }, { "u": 1, "v": 3, "w": 607.0 }, { "u": 3, "v": 7, "w": 262.0 }, { "u": 3, "v": 4, "w": 327.0 }, { "u": 5, "v": 6, "w": 269.0 }, { "u": 5, "v": 7, "w": 493.0 }, { "u": 5, "v": 8, "w": 1162.0 }, { "u": 6, "v": 24, "w": 493.0 }, { "u": 6, "v": 8, "w": 1202.0 }, { "u": 7, "v": 24, "w": 269.0 } ], "terminals": [ 7, 13 ], "source_file": "I032.stp", "density": 0.10333333333333333, "viz_instance": "generated_data/STP/viz/STP_L/instance_0042.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0042.png" }, "solution": [ [ 13, 18 ], [ 18, 24 ], [ 7, 24 ] ], "obj": 1216.0, "instance_variant": { "problem_type": "STP", "num_nodes": 25, "num_edges": 31, "edges": [ { "u": 20, "v": 21, "w": 300.0 }, { "u": 20, "v": 16, "w": 1408.0 }, { "u": 20, "v": 25, "w": 1166.0 }, { "u": 21, "v": 12, "w": 2810.0 }, { "u": 15, "v": 16, "w": 126.0 }, { "u": 15, "v": 19, "w": 1420.0 }, { "u": 15, "v": 23, "w": 201.0 }, { "u": 16, "v": 17, "w": 1473.0 }, { "u": 17, "v": 2, "w": 1038.0 }, { "u": 17, "v": 22, "w": 1397.0 }, { "u": 18, "v": 13, "w": 895.0 }, { "u": 18, "v": 24, "w": 52.0 }, { "u": 18, "v": 2, "w": 554.0 }, { "u": 9, "v": 12, "w": 2044.0 }, { "u": 19, "v": 14, "w": 202.0 }, { "u": 19, "v": 23, "w": 1536.0 }, { "u": 13, "v": 10, "w": 788.0 }, { "u": 13, "v": 11, "w": 2640.0 }, { "u": 14, "v": 10, "w": 1934.0 }, { "u": 14, "v": 11, "w": 1671.0 }, { "u": 23, "v": 12, "w": 1830.0 }, { "u": 1, "v": 2, "w": 531.0 }, { "u": 1, "v": 3, "w": 607.0 }, { "u": 3, "v": 7, "w": 262.0 }, { "u": 3, "v": 4, "w": 327.0 }, { "u": 5, "v": 6, "w": 269.0 }, { "u": 5, "v": 7, "w": 493.0 }, { "u": 5, "v": 8, "w": 1162.0 }, { "u": 6, "v": 24, "w": 493.0 }, { "u": 6, "v": 8, "w": 1202.0 }, { "u": 7, "v": 24, "w": 269.0 } ], "density": 0.10333333333333333, "source_file": "I032.stp", "terminals": [ 7, 13 ] }, "solution_variant": [ [ 13, 18 ], [ 18, 24 ], [ 7, 24 ] ], "context_index": 43, "input_format": "nl", "input_index_base": 1 }, { "task_name": "STP", "problem_type": "STP", "instruction": "Imagine laying out a network of footpaths and bridges that connects every lecture hall and lab so students can walk from any building to any other. The choice comes down to which connections to build; the best option keeps the total length of new walkways as low as possible — compute that by summing the lengths of the chosen bridges and paths. Plazas can act as extra connection points to save length, and every academic building needs to be part of the network with no unnecessary repeats. The exact campus diagram and distances are shown below.\n\n{\n \"total_sites\": 24,\n \"total_candidate_paths\": 28,\n \"edges\": [\n {\n \"endpoint_a\": 14,\n \"endpoint_b\": 15,\n \"path_length_meters\": 1083.0\n },\n {\n \"endpoint_a\": 14,\n \"endpoint_b\": 1,\n \"path_length_meters\": 273.0\n },\n {\n \"endpoint_a\": 14,\n \"endpoint_b\": 11,\n \"path_length_meters\": 2562.0\n },\n {\n \"endpoint_a\": 15,\n \"endpoint_b\": 9,\n \"path_length_meters\": 1.0\n },\n {\n \"endpoint_a\": 15,\n \"endpoint_b\": 8,\n \"path_length_meters\": 1170.0\n },\n {\n \"endpoint_a\": 4,\n \"endpoint_b\": 23,\n \"path_length_meters\": 709.0\n },\n {\n \"endpoint_a\": 5,\n \"endpoint_b\": 23,\n \"path_length_meters\": 2071.0\n },\n {\n \"endpoint_a\": 16,\n \"endpoint_b\": 17,\n \"path_length_meters\": 243.0\n },\n {\n \"endpoint_a\": 16,\n \"endpoint_b\": 18,\n \"path_length_meters\": 21.0\n },\n {\n \"endpoint_a\": 16,\n \"endpoint_b\": 9,\n \"path_length_meters\": 519.0\n },\n {\n \"endpoint_a\": 17,\n \"endpoint_b\": 19,\n \"path_length_meters\": 21.0\n },\n {\n \"endpoint_a\": 17,\n \"endpoint_b\": 23,\n \"path_length_meters\": 1477.0\n },\n {\n \"endpoint_a\": 18,\n \"endpoint_b\": 19,\n \"path_length_meters\": 243.0\n },\n {\n \"endpoint_a\": 18,\n \"endpoint_b\": 9,\n \"path_length_meters\": 499.0\n },\n {\n \"endpoint_a\": 19,\n \"endpoint_b\": 24,\n \"path_length_meters\": 2101.0\n },\n {\n \"endpoint_a\": 22,\n \"endpoint_b\": 1,\n \"path_length_meters\": 742.0\n },\n {\n \"endpoint_a\": 22,\n \"endpoint_b\": 12,\n \"path_length_meters\": 176.0\n },\n {\n \"endpoint_a\": 6,\n \"endpoint_b\": 12,\n \"path_length_meters\": 1000.0\n },\n {\n \"endpoint_a\": 20,\n \"endpoint_b\": 21,\n \"path_length_meters\": 1496.0\n },\n {\n \"endpoint_a\": 20,\n \"endpoint_b\": 24,\n \"path_length_meters\": 205.0\n },\n {\n \"endpoint_a\": 7,\n \"endpoint_b\": 8,\n \"path_length_meters\": 742.0\n },\n {\n \"endpoint_a\": 7,\n \"endpoint_b\": 12,\n \"path_length_meters\": 5.0\n },\n {\n \"endpoint_a\": 8,\n \"endpoint_b\": 13,\n \"path_length_meters\": 5.0\n },\n {\n \"endpoint_a\": 10,\n \"endpoint_b\": 11,\n \"path_length_meters\": 194.0\n },\n {\n \"endpoint_a\": 24,\n \"endpoint_b\": 3,\n \"path_length_meters\": 222.0\n },\n {\n \"endpoint_a\": 12,\n \"endpoint_b\": 13,\n \"path_length_meters\": 742.0\n },\n {\n \"endpoint_a\": 13,\n \"endpoint_b\": 1,\n \"path_length_meters\": 176.0\n },\n {\n \"endpoint_a\": 1,\n \"endpoint_b\": 2,\n \"path_length_meters\": 1296.0\n }\n ],\n \"required_academic_buildings\": [\n 5,\n 8\n ]\n}\n\nAlso, when you send back the set of connections, it's easiest for me (and any tools reading this) if you pack them into a tiny JSON object with one field called \"solution\". Here's the shape I expect:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nThink of that as a simple form: \"solution\" is the list, and each pair like [u1, v1] is one path or bridge linking two buildings or plazas. It's just a sketch of the format — not the real answer — so replace those placeholders with the actual pairs for your layout.\n\nPlease make sure to use the exact identifiers from the instance input — don't rename them or invent new labels. \n- 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 24, "num_edges": 28, "edges": [ { "u": 14, "v": 15, "w": 1083.0 }, { "u": 14, "v": 1, "w": 273.0 }, { "u": 14, "v": 11, "w": 2562.0 }, { "u": 15, "v": 9, "w": 1.0 }, { "u": 15, "v": 8, "w": 1170.0 }, { "u": 4, "v": 23, "w": 709.0 }, { "u": 5, "v": 23, "w": 2071.0 }, { "u": 16, "v": 17, "w": 243.0 }, { "u": 16, "v": 18, "w": 21.0 }, { "u": 16, "v": 9, "w": 519.0 }, { "u": 17, "v": 19, "w": 21.0 }, { "u": 17, "v": 23, "w": 1477.0 }, { "u": 18, "v": 19, "w": 243.0 }, { "u": 18, "v": 9, "w": 499.0 }, { "u": 19, "v": 24, "w": 2101.0 }, { "u": 22, "v": 1, "w": 742.0 }, { "u": 22, "v": 12, "w": 176.0 }, { "u": 6, "v": 12, "w": 1000.0 }, { "u": 20, "v": 21, "w": 1496.0 }, { "u": 20, "v": 24, "w": 205.0 }, { "u": 7, "v": 8, "w": 742.0 }, { "u": 7, "v": 12, "w": 5.0 }, { "u": 8, "v": 13, "w": 5.0 }, { "u": 10, "v": 11, "w": 194.0 }, { "u": 24, "v": 3, "w": 222.0 }, { "u": 12, "v": 13, "w": 742.0 }, { "u": 13, "v": 1, "w": 176.0 }, { "u": 1, "v": 2, "w": 1296.0 } ], "terminals": [ 5, 8 ], "source_file": "I027.stp", "density": 0.10144927536231885, "viz_instance": "generated_data/STP/viz/STP_L/instance_0043.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0043.png" }, "solution": [ [ 9, 15 ], [ 8, 15 ], [ 5, 23 ], [ 16, 17 ], [ 9, 16 ], [ 17, 23 ] ], "obj": 5481.0, "instance_variant": { "problem_type": "STP", "num_nodes": 24, "num_edges": 28, "edges": [ { "u": 14, "v": 15, "w": 1083.0 }, { "u": 14, "v": 1, "w": 273.0 }, { "u": 14, "v": 11, "w": 2562.0 }, { "u": 15, "v": 9, "w": 1.0 }, { "u": 15, "v": 8, "w": 1170.0 }, { "u": 4, "v": 23, "w": 709.0 }, { "u": 5, "v": 23, "w": 2071.0 }, { "u": 16, "v": 17, "w": 243.0 }, { "u": 16, "v": 18, "w": 21.0 }, { "u": 16, "v": 9, "w": 519.0 }, { "u": 17, "v": 19, "w": 21.0 }, { "u": 17, "v": 23, "w": 1477.0 }, { "u": 18, "v": 19, "w": 243.0 }, { "u": 18, "v": 9, "w": 499.0 }, { "u": 19, "v": 24, "w": 2101.0 }, { "u": 22, "v": 1, "w": 742.0 }, { "u": 22, "v": 12, "w": 176.0 }, { "u": 6, "v": 12, "w": 1000.0 }, { "u": 20, "v": 21, "w": 1496.0 }, { "u": 20, "v": 24, "w": 205.0 }, { "u": 7, "v": 8, "w": 742.0 }, { "u": 7, "v": 12, "w": 5.0 }, { "u": 8, "v": 13, "w": 5.0 }, { "u": 10, "v": 11, "w": 194.0 }, { "u": 24, "v": 3, "w": 222.0 }, { "u": 12, "v": 13, "w": 742.0 }, { "u": 13, "v": 1, "w": 176.0 }, { "u": 1, "v": 2, "w": 1296.0 } ], "density": 0.10144927536231885, "source_file": "I027.stp", "terminals": [ 5, 8 ] }, "solution_variant": [ [ 9, 15 ], [ 8, 15 ], [ 5, 23 ], [ 16, 17 ], [ 9, 16 ], [ 17, 23 ] ], "context_index": 44, "input_format": "json", "input_index_base": 1 }, { "task_name": "STP", "problem_type": "STP", "instruction": "On a recent survey, the task came down to this: choose which connections to run between parking clusters so they all become part of one connected charging network. Better plans use less cable overall — compute the total by adding up the lengths of the links you decide to install — and you’re free to add intermediate junction boxes to cut overall run length. The requirement is that every cluster is included in the single network, no duplicates in counting cable, and nothing gets left out. The specific layout and distances are shown below.\n\n# total_network_locations=26\n# total_candidate_links=32\n# required_parking_clusters=P Y\nlink_endpoint_a,link_endpoint_b,cable_run_length_or_cost\nH,E,608.0\nH,Q,1082.0\nH,K,270502.0\nP,G,886.0\nP,F,1518.0\nP,O,1556.0\nI,J,970.0\nI,M,364.0\nJ,S,1059.0\nJ,U,354.0\nQ,F,92.0\nQ,S,1069.0\nZ,W,1033.0\nZ,X,312.0\nZ,Y,3604.0\nR,D,1252.0\nR,T,1278.0\nR,L,272011.0\nY,A,900.0\nS,T,3770.0\nT,N,4465.0\nU,V,83.0\nU,M,883.0\nV,N,838.0\nV,B,1306.0\nG,E,1444.0\nG,K,271347.0\nM,N,291.0\nW,B,3976.0\nA,B,987.0\nC,D,701.0\nE,F,751.0\n\nWhen you send the final plan, just drop the chosen links into this simple JSON shape so it's easy to check and add up the cable length — nothing fancy, just the pairs of nodes you want connected. For example:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nHere \"solution\" is the list of links you'll install; each inner pair is a connection between two clusters or junction boxes (use the node labels from the map exactly as given). This little block is just a sketch of the expected shape — not the real answer itself.\n\nAll identifiers must be used exactly as they appear in the instance input — no renaming and no new labels.\n- 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 26, "num_edges": 32, "edges": [ { "u": 8, "v": 5, "w": 608.0 }, { "u": 8, "v": 17, "w": 1082.0 }, { "u": 8, "v": 11, "w": 270502.0 }, { "u": 16, "v": 7, "w": 886.0 }, { "u": 16, "v": 6, "w": 1518.0 }, { "u": 16, "v": 15, "w": 1556.0 }, { "u": 9, "v": 10, "w": 970.0 }, { "u": 9, "v": 13, "w": 364.0 }, { "u": 10, "v": 19, "w": 1059.0 }, { "u": 10, "v": 21, "w": 354.0 }, { "u": 17, "v": 6, "w": 92.0 }, { "u": 17, "v": 19, "w": 1069.0 }, { "u": 26, "v": 23, "w": 1033.0 }, { "u": 26, "v": 24, "w": 312.0 }, { "u": 26, "v": 25, "w": 3604.0 }, { "u": 18, "v": 4, "w": 1252.0 }, { "u": 18, "v": 20, "w": 1278.0 }, { "u": 18, "v": 12, "w": 272011.0 }, { "u": 25, "v": 1, "w": 900.0 }, { "u": 19, "v": 20, "w": 3770.0 }, { "u": 20, "v": 14, "w": 4465.0 }, { "u": 21, "v": 22, "w": 83.0 }, { "u": 21, "v": 13, "w": 883.0 }, { "u": 22, "v": 14, "w": 838.0 }, { "u": 22, "v": 2, "w": 1306.0 }, { "u": 7, "v": 5, "w": 1444.0 }, { "u": 7, "v": 11, "w": 271347.0 }, { "u": 13, "v": 14, "w": 291.0 }, { "u": 23, "v": 2, "w": 3976.0 }, { "u": 1, "v": 2, "w": 987.0 }, { "u": 3, "v": 4, "w": 701.0 }, { "u": 5, "v": 6, "w": 751.0 } ], "terminals": [ 16, 25 ], "source_file": "I035.stp", "density": 0.09846153846153846, "viz_instance": "generated_data/STP/viz/STP_L/instance_0044.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0044.png" }, "solution": [ [ 6, 16 ], [ 10, 19 ], [ 10, 21 ], [ 6, 17 ], [ 17, 19 ], [ 1, 25 ], [ 21, 22 ], [ 2, 22 ], [ 1, 2 ] ], "obj": 7368.0, "instance_variant": { "problem_type": "STP", "num_nodes": 26, "num_edges": 32, "edges": [ { "u": "H", "v": "E", "w": 608.0 }, { "u": "H", "v": "Q", "w": 1082.0 }, { "u": "H", "v": "K", "w": 270502.0 }, { "u": "P", "v": "G", "w": 886.0 }, { "u": "P", "v": "F", "w": 1518.0 }, { "u": "P", "v": "O", "w": 1556.0 }, { "u": "I", "v": "J", "w": 970.0 }, { "u": "I", "v": "M", "w": 364.0 }, { "u": "J", "v": "S", "w": 1059.0 }, { "u": "J", "v": "U", "w": 354.0 }, { "u": "Q", "v": "F", "w": 92.0 }, { "u": "Q", "v": "S", "w": 1069.0 }, { "u": "Z", "v": "W", "w": 1033.0 }, { "u": "Z", "v": "X", "w": 312.0 }, { "u": "Z", "v": "Y", "w": 3604.0 }, { "u": "R", "v": "D", "w": 1252.0 }, { "u": "R", "v": "T", "w": 1278.0 }, { "u": "R", "v": "L", "w": 272011.0 }, { "u": "Y", "v": "A", "w": 900.0 }, { "u": "S", "v": "T", "w": 3770.0 }, { "u": "T", "v": "N", "w": 4465.0 }, { "u": "U", "v": "V", "w": 83.0 }, { "u": "U", "v": "M", "w": 883.0 }, { "u": "V", "v": "N", "w": 838.0 }, { "u": "V", "v": "B", "w": 1306.0 }, { "u": "G", "v": "E", "w": 1444.0 }, { "u": "G", "v": "K", "w": 271347.0 }, { "u": "M", "v": "N", "w": 291.0 }, { "u": "W", "v": "B", "w": 3976.0 }, { "u": "A", "v": "B", "w": 987.0 }, { "u": "C", "v": "D", "w": 701.0 }, { "u": "E", "v": "F", "w": 751.0 } ], "density": 0.09846153846153846, "source_file": "I035.stp", "terminals": [ "P", "Y" ] }, "solution_variant": [ [ "F", "P" ], [ "J", "S" ], [ "J", "U" ], [ "F", "Q" ], [ "Q", "S" ], [ "A", "Y" ], [ "U", "V" ], [ "B", "V" ], [ "A", "B" ] ], "context_index": 45, "input_format": "csv", "input_index_base": "names" }, { "task_name": "STP", "problem_type": "STP", "instruction": "Recently the flooding left several shelters cut off, and the team needed to choose which blocked roads to clear so all shelters were linked together. Clearing through some junctions can make the connections shorter, so the trick is to open just the right combination of streets to minimize how many meters the crews have to clear. Judge any plan by adding up the lengths of the reopened segments — a smaller total is better — and ensure every shelter is part of the network and no redundant segments are cleared. The exact map and distances follow below.\n\n# total_nodes=28\n# total_blocked_road_segments=35\n# shelter_nodes=1 6 11 12 16 20 21 22 25 27 28\nnode_u,node_v,clearing_distance_meters\n25,18,658.0\n25,24,3333.0\n5,6,1695.0\n5,13,331.0\n6,28,2511.0\n22,19,372.0\n22,23,645.0\n23,24,406.0\n24,17,784.0\n14,21,3326.0\n14,15,2394.0\n14,18,9264.0\n15,16,9699.0\n15,8,625.0\n20,7,1850.0\n20,28,9279.0\n20,21,2556.0\n16,17,282.0\n16,19,486.0\n17,18,3269.0\n2,3,865.0\n2,4,515.0\n2,9,345.0\n4,21,1592.0\n13,27,1981.0\n3,9,857.0\n3,8,2919.0\n27,28,1073.0\n10,11,1191.0\n11,12,1721.0\n11,8,7110.0\n19,8,9529.0\n1,26,8960.0\n26,7,7433.0\n7,9,3769.0\n\nWhen you’re ready to send back the road-clearing plan, just follow this simple JSON layout — nothing fancy, just the shape I expect:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nThink of each [uX, vX] pair as one reopened street between two junctions, and the whole \"solution\" list is the set of streets you'll reopen. This is just a sketch of the expected shape, not the actual answer — fill in the real junction IDs from the instance when you reply.\n\nPlease use the exact identifiers from the instance input; don’t rename them or invent new labels. \n- 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 28, "num_edges": 35, "edges": [ { "u": 25, "v": 18, "w": 658.0 }, { "u": 25, "v": 24, "w": 3333.0 }, { "u": 5, "v": 6, "w": 1695.0 }, { "u": 5, "v": 13, "w": 331.0 }, { "u": 6, "v": 28, "w": 2511.0 }, { "u": 22, "v": 19, "w": 372.0 }, { "u": 22, "v": 23, "w": 645.0 }, { "u": 23, "v": 24, "w": 406.0 }, { "u": 24, "v": 17, "w": 784.0 }, { "u": 14, "v": 21, "w": 3326.0 }, { "u": 14, "v": 15, "w": 2394.0 }, { "u": 14, "v": 18, "w": 9264.0 }, { "u": 15, "v": 16, "w": 9699.0 }, { "u": 15, "v": 8, "w": 625.0 }, { "u": 20, "v": 7, "w": 1850.0 }, { "u": 20, "v": 28, "w": 9279.0 }, { "u": 20, "v": 21, "w": 2556.0 }, { "u": 16, "v": 17, "w": 282.0 }, { "u": 16, "v": 19, "w": 486.0 }, { "u": 17, "v": 18, "w": 3269.0 }, { "u": 2, "v": 3, "w": 865.0 }, { "u": 2, "v": 4, "w": 515.0 }, { "u": 2, "v": 9, "w": 345.0 }, { "u": 4, "v": 21, "w": 1592.0 }, { "u": 13, "v": 27, "w": 1981.0 }, { "u": 3, "v": 9, "w": 857.0 }, { "u": 3, "v": 8, "w": 2919.0 }, { "u": 27, "v": 28, "w": 1073.0 }, { "u": 10, "v": 11, "w": 1191.0 }, { "u": 11, "v": 12, "w": 1721.0 }, { "u": 11, "v": 8, "w": 7110.0 }, { "u": 19, "v": 8, "w": 9529.0 }, { "u": 1, "v": 26, "w": 8960.0 }, { "u": 26, "v": 7, "w": 7433.0 }, { "u": 7, "v": 9, "w": 3769.0 } ], "terminals": [ 1, 6, 11, 12, 16, 20, 21, 22, 25, 27, 28 ], "source_file": "I084.stp", "density": 0.09259259259259259, "viz_instance": "generated_data/STP/viz/STP_L/instance_0045.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0045.png" }, "solution": [ [ 18, 25 ], [ 6, 28 ], [ 19, 22 ], [ 7, 20 ], [ 20, 28 ], [ 20, 21 ], [ 16, 17 ], [ 16, 19 ], [ 17, 18 ], [ 2, 3 ], [ 2, 4 ], [ 4, 21 ], [ 3, 8 ], [ 27, 28 ], [ 11, 12 ], [ 8, 11 ], [ 8, 19 ], [ 1, 26 ], [ 7, 26 ] ], "obj": 62980.0, "instance_variant": { "problem_type": "STP", "num_nodes": 28, "num_edges": 35, "edges": [ { "u": 25, "v": 18, "w": 658.0 }, { "u": 25, "v": 24, "w": 3333.0 }, { "u": 5, "v": 6, "w": 1695.0 }, { "u": 5, "v": 13, "w": 331.0 }, { "u": 6, "v": 28, "w": 2511.0 }, { "u": 22, "v": 19, "w": 372.0 }, { "u": 22, "v": 23, "w": 645.0 }, { "u": 23, "v": 24, "w": 406.0 }, { "u": 24, "v": 17, "w": 784.0 }, { "u": 14, "v": 21, "w": 3326.0 }, { "u": 14, "v": 15, "w": 2394.0 }, { "u": 14, "v": 18, "w": 9264.0 }, { "u": 15, "v": 16, "w": 9699.0 }, { "u": 15, "v": 8, "w": 625.0 }, { "u": 20, "v": 7, "w": 1850.0 }, { "u": 20, "v": 28, "w": 9279.0 }, { "u": 20, "v": 21, "w": 2556.0 }, { "u": 16, "v": 17, "w": 282.0 }, { "u": 16, "v": 19, "w": 486.0 }, { "u": 17, "v": 18, "w": 3269.0 }, { "u": 2, "v": 3, "w": 865.0 }, { "u": 2, "v": 4, "w": 515.0 }, { "u": 2, "v": 9, "w": 345.0 }, { "u": 4, "v": 21, "w": 1592.0 }, { "u": 13, "v": 27, "w": 1981.0 }, { "u": 3, "v": 9, "w": 857.0 }, { "u": 3, "v": 8, "w": 2919.0 }, { "u": 27, "v": 28, "w": 1073.0 }, { "u": 10, "v": 11, "w": 1191.0 }, { "u": 11, "v": 12, "w": 1721.0 }, { "u": 11, "v": 8, "w": 7110.0 }, { "u": 19, "v": 8, "w": 9529.0 }, { "u": 1, "v": 26, "w": 8960.0 }, { "u": 26, "v": 7, "w": 7433.0 }, { "u": 7, "v": 9, "w": 3769.0 } ], "density": 0.09259259259259259, "source_file": "I084.stp", "terminals": [ 1, 6, 11, 12, 16, 20, 21, 22, 25, 27, 28 ] }, "solution_variant": [ [ 18, 25 ], [ 6, 28 ], [ 19, 22 ], [ 7, 20 ], [ 20, 28 ], [ 20, 21 ], [ 16, 17 ], [ 16, 19 ], [ 17, 18 ], [ 2, 3 ], [ 2, 4 ], [ 4, 21 ], [ 3, 8 ], [ 27, 28 ], [ 11, 12 ], [ 8, 11 ], [ 8, 19 ], [ 1, 26 ], [ 7, 26 ] ], "context_index": 46, "input_format": "csv", "input_index_base": 1 }, { "task_name": "STP", "problem_type": "STP", "instruction": "Someone has to plan the winter schedule at a resort by switching on a selection of lifts and links so every lodge and slope is reachable from the rest. The sensible plans are the ones that keep the overall operated track length down — just add up the length of every lift and connector that’s in use to see how much running it requires; lower totals win. It’s allowed to use intermediate transfer points to stitch sectors together, and every lodge and slope must be included in that single connected network. The detailed instance — the map and track lengths — is given below.\n\n# num_stations=28\n# num_tracks=37\n# required_sites=1 25\nendpoint_u,endpoint_v,track_length\n7,5,809.0\n7,16,695.0\n7,15,1219.0\n1,0,1177.0\n1,25,3155.0\n1,16,3099.0\n8,9,1559.0\n8,10,1032.0\n8,11,1218.0\n10,6,537.0\n10,17,1751.0\n11,18,1262.0\n11,12,1425.0\n25,19,10.0\n25,26,1062.0\n0,26,3106.0\n0,14,1368.0\n0,27,3172.0\n9,18,803.0\n9,17,1303.0\n2,23,1173.0\n2,24,1422.0\n2,13,2127.0\n26,27,148.0\n27,21,1064.0\n15,24,1919.0\n15,12,735.0\n16,6,769.0\n24,3,2665.0\n17,19,3854.0\n19,20,2919.0\n20,22,2628.0\n18,3,1602.0\n21,22,3624.0\n3,4,2688.0\n3,13,3377.0\n5,6,740.0\n\nWhen you send the actual plan, pop it into this little JSON shape so it's easy to read and check:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nEach pair like [u1, v1] is one lift or connector you plan to run — just the two endpoints of that piece of track. It's just a friendly example of the shape I expect, not the real answer.\n\nPlease be sure to use the exact node labels from the instance input — don't rename or invent new ones. \n- 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 28, "num_edges": 37, "edges": [ { "u": 8, "v": 6, "w": 809.0 }, { "u": 8, "v": 17, "w": 695.0 }, { "u": 8, "v": 16, "w": 1219.0 }, { "u": 2, "v": 1, "w": 1177.0 }, { "u": 2, "v": 26, "w": 3155.0 }, { "u": 2, "v": 17, "w": 3099.0 }, { "u": 9, "v": 10, "w": 1559.0 }, { "u": 9, "v": 11, "w": 1032.0 }, { "u": 9, "v": 12, "w": 1218.0 }, { "u": 11, "v": 7, "w": 537.0 }, { "u": 11, "v": 18, "w": 1751.0 }, { "u": 12, "v": 19, "w": 1262.0 }, { "u": 12, "v": 13, "w": 1425.0 }, { "u": 26, "v": 20, "w": 10.0 }, { "u": 26, "v": 27, "w": 1062.0 }, { "u": 1, "v": 27, "w": 3106.0 }, { "u": 1, "v": 15, "w": 1368.0 }, { "u": 1, "v": 28, "w": 3172.0 }, { "u": 10, "v": 19, "w": 803.0 }, { "u": 10, "v": 18, "w": 1303.0 }, { "u": 3, "v": 24, "w": 1173.0 }, { "u": 3, "v": 25, "w": 1422.0 }, { "u": 3, "v": 14, "w": 2127.0 }, { "u": 27, "v": 28, "w": 148.0 }, { "u": 28, "v": 22, "w": 1064.0 }, { "u": 16, "v": 25, "w": 1919.0 }, { "u": 16, "v": 13, "w": 735.0 }, { "u": 17, "v": 7, "w": 769.0 }, { "u": 25, "v": 4, "w": 2665.0 }, { "u": 18, "v": 20, "w": 3854.0 }, { "u": 20, "v": 21, "w": 2919.0 }, { "u": 21, "v": 23, "w": 2628.0 }, { "u": 19, "v": 4, "w": 1602.0 }, { "u": 22, "v": 23, "w": 3624.0 }, { "u": 4, "v": 5, "w": 2688.0 }, { "u": 4, "v": 14, "w": 3377.0 }, { "u": 6, "v": 7, "w": 740.0 } ], "terminals": [ 2, 26 ], "source_file": "I046.stp", "density": 0.09788359788359788, "viz_instance": "generated_data/STP/viz/STP_L/instance_0046.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0046.png" }, "solution": [ [ 2, 26 ] ], "obj": 3155.0, "instance_variant": { "problem_type": "STP", "num_nodes": 28, "num_edges": 37, "edges": [ { "u": 7, "v": 5, "w": 809.0 }, { "u": 7, "v": 16, "w": 695.0 }, { "u": 7, "v": 15, "w": 1219.0 }, { "u": 1, "v": 0, "w": 1177.0 }, { "u": 1, "v": 25, "w": 3155.0 }, { "u": 1, "v": 16, "w": 3099.0 }, { "u": 8, "v": 9, "w": 1559.0 }, { "u": 8, "v": 10, "w": 1032.0 }, { "u": 8, "v": 11, "w": 1218.0 }, { "u": 10, "v": 6, "w": 537.0 }, { "u": 10, "v": 17, "w": 1751.0 }, { "u": 11, "v": 18, "w": 1262.0 }, { "u": 11, "v": 12, "w": 1425.0 }, { "u": 25, "v": 19, "w": 10.0 }, { "u": 25, "v": 26, "w": 1062.0 }, { "u": 0, "v": 26, "w": 3106.0 }, { "u": 0, "v": 14, "w": 1368.0 }, { "u": 0, "v": 27, "w": 3172.0 }, { "u": 9, "v": 18, "w": 803.0 }, { "u": 9, "v": 17, "w": 1303.0 }, { "u": 2, "v": 23, "w": 1173.0 }, { "u": 2, "v": 24, "w": 1422.0 }, { "u": 2, "v": 13, "w": 2127.0 }, { "u": 26, "v": 27, "w": 148.0 }, { "u": 27, "v": 21, "w": 1064.0 }, { "u": 15, "v": 24, "w": 1919.0 }, { "u": 15, "v": 12, "w": 735.0 }, { "u": 16, "v": 6, "w": 769.0 }, { "u": 24, "v": 3, "w": 2665.0 }, { "u": 17, "v": 19, "w": 3854.0 }, { "u": 19, "v": 20, "w": 2919.0 }, { "u": 20, "v": 22, "w": 2628.0 }, { "u": 18, "v": 3, "w": 1602.0 }, { "u": 21, "v": 22, "w": 3624.0 }, { "u": 3, "v": 4, "w": 2688.0 }, { "u": 3, "v": 13, "w": 3377.0 }, { "u": 5, "v": 6, "w": 740.0 } ], "density": 0.09788359788359788, "source_file": "I046.stp", "terminals": [ 1, 25 ] }, "solution_variant": [ [ 1, 25 ] ], "context_index": 47, "input_format": "csv", "input_index_base": 0 }, { "task_name": "STP", "problem_type": "STP", "instruction": "We’re laying out a backyard so a cluster of benches and tables are all tied together by a single continuous ribbon of hedges and paths, and the job is picking which links to plant. The decision includes whether to include extra planted junctions or stepping-stone corners to make shorter connections between those spots. The winning layout is the one with the smallest total planting length — simply total the lengths of all chosen hedges and paths — but every seating area must sit on that single connected route and no segment is counted twice. The detailed plan and measurements follow below.\n\n# total_junctions=25\n# total_possible_links=31\n# seating_areas=3 5 6 7 8 11 13 17 19 25\nendpoint_u,endpoint_v,segment_length_m\n25,20,762.0\n25,14,773.0\n21,15,1074.0\n21,16,503.0\n21,12,1423.0\n22,8,1724.0\n22,24,651.0\n22,10,733.0\n15,16,1222.0\n15,10,199.0\n16,14,3896.0\n3,13,1014.0\n3,17,792.0\n4,1,659.0\n4,6,1319.0\n1,10,163.0\n17,18,294.0\n17,9,887.0\n18,13,366.0\n18,7,1086.0\n5,8,1295.0\n5,23,1530.0\n6,24,331.0\n7,8,422.0\n7,2,3975.0\n8,9,833.0\n9,12,729.0\n11,13,5676.0\n11,19,1217.0\n24,23,866.0\n20,14,704.0\n\nWhen you’re ready to hand over the chosen links, just drop them in a tiny JSON block like this so I know the shape of your answer:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nThink of \"solution\" as the whole planting plan. Each pair like [u1, v1] is one chosen link — it says “connect spot u1 to spot v1” (that could be a hedge segment between a bench and a corner, or a path between two junctions). This snippet is just a sketch of the format I’ll expect, not the actual final plan.\n\nPlease use the exact identifiers from the instance input — don’t rename them or invent new ones. \n- 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 25, "num_edges": 31, "edges": [ { "u": 25, "v": 20, "w": 762.0 }, { "u": 25, "v": 14, "w": 773.0 }, { "u": 21, "v": 15, "w": 1074.0 }, { "u": 21, "v": 16, "w": 503.0 }, { "u": 21, "v": 12, "w": 1423.0 }, { "u": 22, "v": 8, "w": 1724.0 }, { "u": 22, "v": 24, "w": 651.0 }, { "u": 22, "v": 10, "w": 733.0 }, { "u": 15, "v": 16, "w": 1222.0 }, { "u": 15, "v": 10, "w": 199.0 }, { "u": 16, "v": 14, "w": 3896.0 }, { "u": 3, "v": 13, "w": 1014.0 }, { "u": 3, "v": 17, "w": 792.0 }, { "u": 4, "v": 1, "w": 659.0 }, { "u": 4, "v": 6, "w": 1319.0 }, { "u": 1, "v": 10, "w": 163.0 }, { "u": 17, "v": 18, "w": 294.0 }, { "u": 17, "v": 9, "w": 887.0 }, { "u": 18, "v": 13, "w": 366.0 }, { "u": 18, "v": 7, "w": 1086.0 }, { "u": 5, "v": 8, "w": 1295.0 }, { "u": 5, "v": 23, "w": 1530.0 }, { "u": 6, "v": 24, "w": 331.0 }, { "u": 7, "v": 8, "w": 422.0 }, { "u": 7, "v": 2, "w": 3975.0 }, { "u": 8, "v": 9, "w": 833.0 }, { "u": 9, "v": 12, "w": 729.0 }, { "u": 11, "v": 13, "w": 5676.0 }, { "u": 11, "v": 19, "w": 1217.0 }, { "u": 24, "v": 23, "w": 866.0 }, { "u": 20, "v": 14, "w": 704.0 } ], "terminals": [ 3, 5, 6, 7, 8, 11, 13, 17, 19, 25 ], "source_file": "I011.stp", "density": 0.10333333333333333, "viz_instance": "generated_data/STP/viz/STP_L/instance_0047.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0047.png" }, "solution": [ [ 14, 25 ], [ 8, 22 ], [ 22, 24 ], [ 10, 22 ], [ 15, 16 ], [ 10, 15 ], [ 14, 16 ], [ 3, 17 ], [ 17, 18 ], [ 13, 18 ], [ 7, 18 ], [ 5, 8 ], [ 6, 24 ], [ 7, 8 ], [ 11, 13 ], [ 11, 19 ] ], "obj": 20677.0, "instance_variant": { "problem_type": "STP", "num_nodes": 25, "num_edges": 31, "edges": [ { "u": 25, "v": 20, "w": 762.0 }, { "u": 25, "v": 14, "w": 773.0 }, { "u": 21, "v": 15, "w": 1074.0 }, { "u": 21, "v": 16, "w": 503.0 }, { "u": 21, "v": 12, "w": 1423.0 }, { "u": 22, "v": 8, "w": 1724.0 }, { "u": 22, "v": 24, "w": 651.0 }, { "u": 22, "v": 10, "w": 733.0 }, { "u": 15, "v": 16, "w": 1222.0 }, { "u": 15, "v": 10, "w": 199.0 }, { "u": 16, "v": 14, "w": 3896.0 }, { "u": 3, "v": 13, "w": 1014.0 }, { "u": 3, "v": 17, "w": 792.0 }, { "u": 4, "v": 1, "w": 659.0 }, { "u": 4, "v": 6, "w": 1319.0 }, { "u": 1, "v": 10, "w": 163.0 }, { "u": 17, "v": 18, "w": 294.0 }, { "u": 17, "v": 9, "w": 887.0 }, { "u": 18, "v": 13, "w": 366.0 }, { "u": 18, "v": 7, "w": 1086.0 }, { "u": 5, "v": 8, "w": 1295.0 }, { "u": 5, "v": 23, "w": 1530.0 }, { "u": 6, "v": 24, "w": 331.0 }, { "u": 7, "v": 8, "w": 422.0 }, { "u": 7, "v": 2, "w": 3975.0 }, { "u": 8, "v": 9, "w": 833.0 }, { "u": 9, "v": 12, "w": 729.0 }, { "u": 11, "v": 13, "w": 5676.0 }, { "u": 11, "v": 19, "w": 1217.0 }, { "u": 24, "v": 23, "w": 866.0 }, { "u": 20, "v": 14, "w": 704.0 } ], "density": 0.10333333333333333, "source_file": "I011.stp", "terminals": [ 3, 5, 6, 7, 8, 11, 13, 17, 19, 25 ] }, "solution_variant": [ [ 14, 25 ], [ 8, 22 ], [ 22, 24 ], [ 10, 22 ], [ 15, 16 ], [ 10, 15 ], [ 14, 16 ], [ 3, 17 ], [ 17, 18 ], [ 13, 18 ], [ 7, 18 ], [ 5, 8 ], [ 6, 24 ], [ 7, 8 ], [ 11, 13 ], [ 11, 19 ] ], "context_index": 48, "input_format": "csv", "input_index_base": 1 }, { "task_name": "STP", "problem_type": "STP", "instruction": "We’ve got a campus map with groups of wireless access points that all need to be hooked together into a single backbone, and the task is to pick which cable segments to install so every group is included and everything is connected. What makes one plan better than another is simply the total cable distance — add the lengths of the segments actually used and the smallest sum wins. It’s okay to run cables via intermediate hardware rooms if that cuts down the distance, but every wireless cluster must be part of the one backbone and there can’t be isolated pieces or redundant parallel cables. The detailed layout and numbers follow below.\n\nWe’ve got 24 locations, 25 available cable segments, and the wireless clusters to span are F S.\nRun a cable from T to I with length 313.0.\nRun a cable from T to X with length 2385.0.\nRun a cable from T to U with length 959.0.\nRun a cable from S to Q with length 756.0.\nRun a cable from S to L with length 59.0.\nRun a cable from S to U with length 1560.0.\nRun a cable from Q to R with length 212.0.\nRun a cable from I to P with length 762.0.\nRun a cable from H to P with length 164.0.\nRun a cable from J to X with length 626.0.\nRun a cable from K to X with length 437.0.\nRun a cable from U to M with length 1081.0.\nRun a cable from V to N with length 370.0.\nRun a cable from V to W with length 4544.0.\nRun a cable from V to M with length 879.0.\nRun a cable from W to O with length 1532.0.\nRun a cable from W to D with length 1039.0.\nRun a cable from A to O with length 336.0.\nRun a cable from B to O with length 1271.0.\nRun a cable from D to E with length 334.0.\nRun a cable from L to G with length 223.0.\nRun a cable from L to C with length 1197.0.\nRun a cable from N to C with length 1404.0.\nRun a cable from N to G with length 1270.0.\nRun a cable from F to G with length 825.0.\nKeep every wireless cluster in F S included in one connected backbone, avoid isolated pieces or redundant parallel cables, and minimize the total cable length.\n\nAlso, when you send back the actual wiring plan, please use this JSON layout so I can read it automatically:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nIn plain terms: \"solution\" should be a list of cable segments, and each [X, Y] pair means \"connect node X to node Y\" (those are the endpoints of the cable). This block is just a sketch of the shape I expect — not the real wiring plan.\n\nPlease make sure to use the exact identifiers from the instance input, with no renaming or 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”.", "instance": { "problem_type": "STP", "num_nodes": 24, "num_edges": 25, "edges": [ { "u": 20, "v": 9, "w": 313.0 }, { "u": 20, "v": 24, "w": 2385.0 }, { "u": 20, "v": 21, "w": 959.0 }, { "u": 19, "v": 17, "w": 756.0 }, { "u": 19, "v": 12, "w": 59.0 }, { "u": 19, "v": 21, "w": 1560.0 }, { "u": 17, "v": 18, "w": 212.0 }, { "u": 9, "v": 16, "w": 762.0 }, { "u": 8, "v": 16, "w": 164.0 }, { "u": 10, "v": 24, "w": 626.0 }, { "u": 11, "v": 24, "w": 437.0 }, { "u": 21, "v": 13, "w": 1081.0 }, { "u": 22, "v": 14, "w": 370.0 }, { "u": 22, "v": 23, "w": 4544.0 }, { "u": 22, "v": 13, "w": 879.0 }, { "u": 23, "v": 15, "w": 1532.0 }, { "u": 23, "v": 4, "w": 1039.0 }, { "u": 1, "v": 15, "w": 336.0 }, { "u": 2, "v": 15, "w": 1271.0 }, { "u": 4, "v": 5, "w": 334.0 }, { "u": 12, "v": 7, "w": 223.0 }, { "u": 12, "v": 3, "w": 1197.0 }, { "u": 14, "v": 3, "w": 1404.0 }, { "u": 14, "v": 7, "w": 1270.0 }, { "u": 6, "v": 7, "w": 825.0 } ], "terminals": [ 6, 19 ], "source_file": "I061.stp", "density": 0.09057971014492754, "viz_instance": "generated_data/STP/viz/STP_L/instance_0048.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0048.png" }, "solution": [ [ 12, 19 ], [ 7, 12 ], [ 6, 7 ] ], "obj": 1107.0, "instance_variant": { "problem_type": "STP", "num_nodes": 24, "num_edges": 25, "edges": [ { "u": "T", "v": "I", "w": 313.0 }, { "u": "T", "v": "X", "w": 2385.0 }, { "u": "T", "v": "U", "w": 959.0 }, { "u": "S", "v": "Q", "w": 756.0 }, { "u": "S", "v": "L", "w": 59.0 }, { "u": "S", "v": "U", "w": 1560.0 }, { "u": "Q", "v": "R", "w": 212.0 }, { "u": "I", "v": "P", "w": 762.0 }, { "u": "H", "v": "P", "w": 164.0 }, { "u": "J", "v": "X", "w": 626.0 }, { "u": "K", "v": "X", "w": 437.0 }, { "u": "U", "v": "M", "w": 1081.0 }, { "u": "V", "v": "N", "w": 370.0 }, { "u": "V", "v": "W", "w": 4544.0 }, { "u": "V", "v": "M", "w": 879.0 }, { "u": "W", "v": "O", "w": 1532.0 }, { "u": "W", "v": "D", "w": 1039.0 }, { "u": "A", "v": "O", "w": 336.0 }, { "u": "B", "v": "O", "w": 1271.0 }, { "u": "D", "v": "E", "w": 334.0 }, { "u": "L", "v": "G", "w": 223.0 }, { "u": "L", "v": "C", "w": 1197.0 }, { "u": "N", "v": "C", "w": 1404.0 }, { "u": "N", "v": "G", "w": 1270.0 }, { "u": "F", "v": "G", "w": 825.0 } ], "density": 0.09057971014492754, "source_file": "I061.stp", "terminals": [ "F", "S" ] }, "solution_variant": [ [ "L", "S" ], [ "G", "L" ], [ "F", "G" ] ], "context_index": 49, "input_format": "nl", "input_index_base": "names" }, { "task_name": "STP", "problem_type": "STP", "instruction": "There’s a small-city puzzle: get every plaza connected into one continuous lighting circuit by deciding which lamp posts to tie in. What makes one plan nicer than another is simply how little wire it needs—total wire length equals the sum of the chosen segments—so shorter total runs win, and using spare lamp posts as stepping stones is allowed to cut corners. All plazas must end up on that one circuit, and every piece of wiring is counted once when totaling length. The full diagram and distances are listed below.\n\n# total_lamp_posts=29\n# total_possible_wiring_segments=35\n# plaza_posts=1 2 5 8 10 13 16 19 20 21 23 26 27 28\nendpoint_post_a,endpoint_post_b,wiring_length\n11,12,4061.0\n11,7,7778.0\n11,8,12271.0\n1,2,502.0\n1,3,1925.0\n1,14,426.0\n17,18,1638.0\n17,22,2231.0\n2,13,2000.0\n2,14,196.0\n3,12,5532.0\n3,13,583.0\n15,12,4919.0\n15,27,10015.0\n15,26,2230.0\n24,20,636.0\n25,26,7536.0\n25,28,10305.0\n26,6,6791.0\n28,29,673.0\n19,22,231.0\n19,21,1652.0\n20,21,3528.0\n20,23,5387.0\n21,18,1814.0\n27,7,4899.0\n27,5,9326.0\n4,5,328758.0\n4,6,331706.0\n5,6,9730.0\n23,10,11362.0\n23,9,3758.0\n8,16,18399.0\n16,10,11645.0\n16,18,3705.0\n\nOh, and when you're ready to hand me the wiring plan, please toss it in this simple JSON shape so I can read it cleanly:\n\n{\n \"solution\": [[u1, v1], [u2, v2], ...]\n}\n\nHere \"solution\" is just a list of the chosen wiring segments, and each little pair like [u1, v1] means \"connect lamp post u1 to lamp post v1\" (order doesn't really matter — it's just the segment between those two). This is only a sketch of the expected shape, not the actual answer — replace those placeholders with the real pairs from the diagram.\n\nOne important thing: use the identifiers exactly as they appear in the instance input — do not rename them or invent new ones.\n- 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”.\"", "instance": { "problem_type": "STP", "num_nodes": 29, "num_edges": 35, "edges": [ { "u": 11, "v": 12, "w": 4061.0 }, { "u": 11, "v": 7, "w": 7778.0 }, { "u": 11, "v": 8, "w": 12271.0 }, { "u": 1, "v": 2, "w": 502.0 }, { "u": 1, "v": 3, "w": 1925.0 }, { "u": 1, "v": 14, "w": 426.0 }, { "u": 17, "v": 18, "w": 1638.0 }, { "u": 17, "v": 22, "w": 2231.0 }, { "u": 2, "v": 13, "w": 2000.0 }, { "u": 2, "v": 14, "w": 196.0 }, { "u": 3, "v": 12, "w": 5532.0 }, { "u": 3, "v": 13, "w": 583.0 }, { "u": 15, "v": 12, "w": 4919.0 }, { "u": 15, "v": 27, "w": 10015.0 }, { "u": 15, "v": 26, "w": 2230.0 }, { "u": 24, "v": 20, "w": 636.0 }, { "u": 25, "v": 26, "w": 7536.0 }, { "u": 25, "v": 28, "w": 10305.0 }, { "u": 26, "v": 6, "w": 6791.0 }, { "u": 28, "v": 29, "w": 673.0 }, { "u": 19, "v": 22, "w": 231.0 }, { "u": 19, "v": 21, "w": 1652.0 }, { "u": 20, "v": 21, "w": 3528.0 }, { "u": 20, "v": 23, "w": 5387.0 }, { "u": 21, "v": 18, "w": 1814.0 }, { "u": 27, "v": 7, "w": 4899.0 }, { "u": 27, "v": 5, "w": 9326.0 }, { "u": 4, "v": 5, "w": 328758.0 }, { "u": 4, "v": 6, "w": 331706.0 }, { "u": 5, "v": 6, "w": 9730.0 }, { "u": 23, "v": 10, "w": 11362.0 }, { "u": 23, "v": 9, "w": 3758.0 }, { "u": 8, "v": 16, "w": 18399.0 }, { "u": 16, "v": 10, "w": 11645.0 }, { "u": 16, "v": 18, "w": 3705.0 } ], "terminals": [ 1, 2, 5, 8, 10, 13, 16, 19, 20, 21, 23, 26, 27, 28 ], "source_file": "I073.stp", "density": 0.08620689655172414, "viz_instance": "generated_data/STP/viz/STP_L/instance_0049.png", "viz_solution": "generated_data/STP/viz/STP_L/solution_0049.png" }, "solution": [ [ 11, 12 ], [ 8, 11 ], [ 1, 2 ], [ 1, 3 ], [ 3, 12 ], [ 3, 13 ], [ 12, 15 ], [ 15, 27 ], [ 15, 26 ], [ 25, 26 ], [ 25, 28 ], [ 19, 21 ], [ 20, 21 ], [ 20, 23 ], [ 18, 21 ], [ 5, 27 ], [ 10, 23 ], [ 8, 16 ], [ 16, 18 ] ], "obj": 115052.0, "instance_variant": { "problem_type": "STP", "num_nodes": 29, "num_edges": 35, "edges": [ { "u": 11, "v": 12, "w": 4061.0 }, { "u": 11, "v": 7, "w": 7778.0 }, { "u": 11, "v": 8, "w": 12271.0 }, { "u": 1, "v": 2, "w": 502.0 }, { "u": 1, "v": 3, "w": 1925.0 }, { "u": 1, "v": 14, "w": 426.0 }, { "u": 17, "v": 18, "w": 1638.0 }, { "u": 17, "v": 22, "w": 2231.0 }, { "u": 2, "v": 13, "w": 2000.0 }, { "u": 2, "v": 14, "w": 196.0 }, { "u": 3, "v": 12, "w": 5532.0 }, { "u": 3, "v": 13, "w": 583.0 }, { "u": 15, "v": 12, "w": 4919.0 }, { "u": 15, "v": 27, "w": 10015.0 }, { "u": 15, "v": 26, "w": 2230.0 }, { "u": 24, "v": 20, "w": 636.0 }, { "u": 25, "v": 26, "w": 7536.0 }, { "u": 25, "v": 28, "w": 10305.0 }, { "u": 26, "v": 6, "w": 6791.0 }, { "u": 28, "v": 29, "w": 673.0 }, { "u": 19, "v": 22, "w": 231.0 }, { "u": 19, "v": 21, "w": 1652.0 }, { "u": 20, "v": 21, "w": 3528.0 }, { "u": 20, "v": 23, "w": 5387.0 }, { "u": 21, "v": 18, "w": 1814.0 }, { "u": 27, "v": 7, "w": 4899.0 }, { "u": 27, "v": 5, "w": 9326.0 }, { "u": 4, "v": 5, "w": 328758.0 }, { "u": 4, "v": 6, "w": 331706.0 }, { "u": 5, "v": 6, "w": 9730.0 }, { "u": 23, "v": 10, "w": 11362.0 }, { "u": 23, "v": 9, "w": 3758.0 }, { "u": 8, "v": 16, "w": 18399.0 }, { "u": 16, "v": 10, "w": 11645.0 }, { "u": 16, "v": 18, "w": 3705.0 } ], "density": 0.08620689655172414, "source_file": "I073.stp", "terminals": [ 1, 2, 5, 8, 10, 13, 16, 19, 20, 21, 23, 26, 27, 28 ] }, "solution_variant": [ [ 11, 12 ], [ 8, 11 ], [ 1, 2 ], [ 1, 3 ], [ 3, 12 ], [ 3, 13 ], [ 12, 15 ], [ 15, 27 ], [ 15, 26 ], [ 25, 26 ], [ 25, 28 ], [ 19, 21 ], [ 20, 21 ], [ 20, 23 ], [ 18, 21 ], [ 5, 27 ], [ 10, 23 ], [ 8, 16 ], [ 16, 18 ] ], "context_index": 50, "input_format": "csv", "input_index_base": 1 } ]