{
  "name": "costas_array_n13__v2_h",
  "problem_type": "costas_array",
  "params": {
    "n": 13
  },
  "prompt": "Find a Costas array of order 13: place 13 marks on an 13x13 grid, one per row and one per column, such that all 13*(12)/2 displacement vectors (dr, dc) between pairs of marks (with dc > 0) are pairwise distinct.\n\nReturn x as a list of 13 integers in 0..12, where x[c] is the row of the mark in column c (permutation), or state \"UNSATISFIABLE\" if no such array exists.\n\nPartial assignment (fixed values that must be respected):\n- x[4]=3, x[9]=1\nReturn a complete solution consistent with these fixed assignments.",
  "satisfiable": true,
  "solution": {
    "x": [
      8,
      7,
      5,
      10,
      3,
      0,
      4,
      12,
      6,
      1,
      2,
      9,
      11
    ]
  },
  "difficulty": {
    "solve_time_ms": 1330.0,
    "search_space": 6227020800,
    "num_variables": 13,
    "num_constraints": 14,
    "num_edges": -1,
    "backend": "pycsp",
    "solve_tier": "hard",
    "solve_pct_global": 82.52,
    "solve_pct_type": 94.44
  },
  "partial_assignment": {
    "x": {
      "4": 3,
      "9": 1
    }
  }
}