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.

  Faster than the previous versions:
  - http://www.hakank.org/gogle_cp_solver/nqueens.py
  - http://www.hakank.org/gogle_cp_solver/nqueens2.py


  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, num_sol=0, print_sol=1):
    # Create the solver.
    solver = pywrapcp.Solver('n-queens')

    #
    # data
    #
    print "n:", n
    print "num_sol:", num_sol
    print "print_sol:", print_sol

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

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


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


    #
    # search
    #

    db = solver.Phase(q,
                      solver.CHOOSE_MIN_SIZE_LOWEST_MAX,
                      solver.ASSIGN_CENTER_VALUE)

    solver.NewSearch(db)
    num_solutions = 0
    while solver.NextSolution():
        if print_sol:
            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
        if num_sol > 0 and num_solutions >= num_sol:
            break

    solver.EndSearch()

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


n = 8
num_sol = 0
print_sol = 1
if __name__ == '__main__':
    if len(sys.argv) > 1:
        n = int(sys.argv[1])
    if len(sys.argv) > 2:
        num_sol = int(sys.argv[2])
    if len(sys.argv) > 3:
        print_sol = int(sys.argv[3])


    main(n, num_sol, print_sol)

    # print_sol = False
    # show_all = False
    # for n in range(1000,1001):
    #     print
    #     main(n, num_sol, print_sol)