054: N-Queens

# Copyright 2010 Hakan Kjellerstrand hakank@gmail.com
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

"""

  n-queens problem in Google CP Solver.

  N queens problem.

  This version use NewSearch()/NextSolution() for looping through
  the solutions.

  This model was created by Hakan Kjellerstrand (hakank@gmail.com)
  Also see my other Google CP Solver models: http://www.hakank.org/google_or_tools/
"""
import sys, string
from constraint_solver import pywrapcp


def main(n=8):
    # Create the solver.
    solver = pywrapcp.Solver('n-queens')

    #
    # data
    #
    # n = 8 # size of board (n x n)

    # declare variables
    q = [solver.IntVar(0,n-1, 'x%i' % i) for i in range(n)]

    #
    # constraints
    #
    solver.Add(solver.AllDifferent(q))
    for i in range(n):
        for j in range(i):
            solver.Add(q[i] != q[j])
            solver.Add(q[i] + i != q[j] + j)
            solver.Add(q[i] - i != q[j] - j)

    # for i in range(n):
    #     for j in range(i):
    #         solver.Add(abs(q[i]-q[j]) != abs(i-j))

    # symmetry breaking
    # solver.Add(q[0] == 0)


    #
    # solution and search
    #
    solution = solver.Assignment()
    solution.Add([q[i] for i in range(n)])


    # db: DecisionBuilder
    db = solver.Phase([q[i] for i in range(n)],
                      # solver.CHOOSE_FIRST_UNBOUND,
                      solver.CHOOSE_MIN_SIZE_LOWEST_MAX,
                      solver.ASSIGN_CENTER_VALUE)

    solver.NewSearch(db)
    num_solutions = 0
    while solver.NextSolution():
        qval = [q[i].Value() for i in range(n)]
        print "q:", qval
        for i in range(n):
            for j in range(n):
                if qval[i] == j:
                    print "Q",
                else:
                    print "_",
            print
        print
        num_solutions += 1
    solver.EndSearch()

    print
    print "num_solutions:", num_solutions
    print "failures:", solver.Failures()
    print "branches:", solver.Branches()
    print "WallTime:", solver.WallTime()


n = 8
if __name__ == '__main__':
    if len(sys.argv) > 1:
        n = string.atoi(sys.argv[1])
    main(n)