# 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.
"""
Magic squares in Google CP Solver.
Magic square 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/
"""
import string
import sys
from ortools.constraint_solver import pywrapcp
def main(n=4):
# Create the solver.
solver = pywrapcp.Solver("n-queens")
#
# data
#
#
# declare variables
#
x = {}
for i in range(n):
for j in range(n):
x[(i, j)] = solver.IntVar(1, n * n, "x(%i,%i)" % (i, j))
x_flat = [x[(i, j)] for i in range(n) for j in range(n)]
# the sum
# s = ( n * (n*n + 1)) / 2
s = solver.IntVar(1, n * n * n, "s")
#
# constraints
#
# solver.Add(s == ( n * (n*n + 1)) / 2)
solver.Add(solver.AllDifferent(x_flat))
[solver.Add(solver.Sum([x[(i, j)] for j in range(n)]) == s) for i in range(n)]
[solver.Add(solver.Sum([x[(i, j)] for i in range(n)]) == s) for j in range(n)]
solver.Add(solver.Sum([x[(i, i)] for i in range(n)]) == s) # diag 1
solver.Add(solver.Sum([x[(i, n - i - 1)] for i in range(n)]) == s) # diag 2
# symmetry breaking
# solver.Add(x[(0,0)] == 1)
#
# solution and search
#
solution = solver.Assignment()
solution.Add(x_flat)
solution.Add(s)
# db: DecisionBuilder
db = solver.Phase(x_flat,
# solver.INT_VAR_DEFAULT,
solver.CHOOSE_FIRST_UNBOUND,
# solver.CHOOSE_MIN_SIZE_LOWEST_MAX,
# solver.ASSIGN_MIN_VALUE
solver.ASSIGN_CENTER_VALUE)
solver.NewSearch(db)
num_solutions = 0
while solver.NextSolution():
print "s:", s.Value()
for i in range(n):
for j in range(n):
print "%2i" % x[(i, j)].Value(),
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 = 4
if __name__ == "__main__":
if len(sys.argv) > 1:
n = string.atoi(sys.argv[1])
main(n)