# Copyright 2010 Hakan Kjellerstrand hakank@bonetmail.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 model was created by Hakan Kjellerstrand (hakank@bonetmail.com)
Also see my other Google CP Solver models:
http://www.hakank.org/google_or_tools/
"""
from ortools.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)])
collector = solver.AllSolutionCollector(solution)
# collector = solver.FirstSolutionCollector(solution)
# search_log = solver.SearchLog(100, x[0])
solver.Solve(solver.Phase([q[i] for i in range(n)],
solver.INT_VAR_SIMPLE,
solver.ASSIGN_MIN_VALUE),
[collector])
num_solutions = collector.SolutionCount()
print "num_solutions: ", num_solutions
if num_solutions > 0:
for s in range(num_solutions):
qval = [collector.Value(s, q[i]) 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
print
print "num_solutions:", num_solutions
print "failures:", solver.Failures()
print "branches:", solver.Branches()
print "WallTime:", solver.WallTime()
else:
print "No solutions found"
n = 8
if __name__ == "__main__":
main(n)