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nqueens_cp

<table align="left"> <td> <a href="https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/constraint_solver/nqueens_cp.ipynb">Run in Google Colab</a> </td> <td> <a href="https://github.com/google/or-tools/blob/main/ortools/constraint_solver/samples/nqueens_cp.py">View source on GitHub</a> </td> </table>

First, you must install ortools package in this colab.

python

%pip install ortools

OR-Tools solution to the N-queens problem.

python

import sys
from ortools.constraint_solver import pywrapcp


def main(board_size):
    # Creates the solver.
    solver = pywrapcp.Solver("n-queens")

    # Creates the variables.
    # The array index is the column, and the value is the row.
    queens = [solver.IntVar(0, board_size - 1, f"x{i}") for i in range(board_size)]

    # Creates the constraints.
    # All rows must be different.
    solver.Add(solver.AllDifferent(queens))

    # No two queens can be on the same diagonal.
    solver.Add(solver.AllDifferent([queens[i] + i for i in range(board_size)]))
    solver.Add(solver.AllDifferent([queens[i] - i for i in range(board_size)]))

    db = solver.Phase(queens, solver.CHOOSE_FIRST_UNBOUND, solver.ASSIGN_MIN_VALUE)

    # Iterates through the solutions, displaying each.
    num_solutions = 0
    solver.NewSearch(db)
    while solver.NextSolution():
        # Displays the solution just computed.
        for i in range(board_size):
            for j in range(board_size):
                if queens[j].Value() == i:
                    # There is a queen in column j, row i.
                    print("Q", end=" ")
                else:
                    print("_", end=" ")
            print()
        print()
        num_solutions += 1
    solver.EndSearch()

    # Statistics.
    print("\nStatistics")
    print(f"  failures: {solver.Failures()}")
    print(f"  branches: {solver.Branches()}")
    print(f"  wall time: {solver.WallTime()} ms")
    print(f"  Solutions found: {num_solutions}")


# By default, solve the 8x8 problem.
size = 8
if len(sys.argv) > 1:
    size = int(sys.argv[1])
main(size)