054: N-Queens

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# Fast constraint solving in Python  - https://github.com/yangeorget/nucs
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# Copyright 2024 - Yan Georget
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import argparse
from typing import List

from nucs.problems.problem import Problem
from nucs.propagators.propagators import ALG_ALLDIFFERENT
from nucs.solvers.backtrack_solver import BacktrackSolver
from nucs.statistics import get_statistics


class QueensProblem(Problem):
    """
    A simple model for the n-queens problem.

    CSPLIB problem #54 - https://www.csplib.org/Problems/prob054/
    """

    def __init__(self, n: int):
        super().__init__(
            [(0, n - 1)] * n,
            list(range(n)) * 3,
            [0] * n + list(range(n)) + list(range(0, -n, -1)),
        )
        self.add_propagator((list(range(n)), ALG_ALLDIFFERENT, []))
        self.add_propagator((list(range(n, 2 * n)), ALG_ALLDIFFERENT, []))
        self.add_propagator((list(range(2 * n, 3 * n)), ALG_ALLDIFFERENT, []))

    def solution_as_matrix(self, solution: List[int]) -> List[List[str]]:
        n = len(solution)
        return [([" "] * i + ["X"] + [" "] * (n - i - 1)) for i in range(n)]


# Run with the following command (the second run is much faster because the code has been compiled):
# NUMBA_CACHE_DIR=.numba/cache python queens_problem.py -n 10
if __name__ == "__main__":
    parser = argparse.ArgumentParser()
    parser.add_argument("-n", type=int, default=10)
    args = parser.parse_args()
    problem = QueensProblem(args.n)
    solver = BacktrackSolver(problem)
    solver.solve_all()
    print(get_statistics(solver.statistics))