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

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

    parameters = pywrapcp.DefaultPhaseParameters()

    # parameters.heuristic_num_failures_limit = 1000
    
    parameters.heuristic_period = n*n*n

    # parameters.var_selection_schema = parameters.CHOOSE_MAX_SUM_IMPACT
    parameters.var_selection_schema = parameters.CHOOSE_MAX_AVERAGE_IMPACT
    # parameters.var_selection_schema = parameters.CHOOSE_MAX_VALUE_IMPACT
    
    # parameters.value_selection_schema = parameters.SELECT_MIN_IMPACT
    # parameters.value_selection_schema = parameters.SELECT_MAX_IMPACT
    
    # parameters.initialization_splits = 10
    # parameters.initialization_splits = 20

    
    # parameters.random_seed = 0


    db = solver.DefaultPhase(q, parameters)

    
    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 "wall_time:", solver.wall_time()


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)