# Copyright 2010 Hakan Kjellerstrand hakank@gmail.com
#
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#
# Unless required by applicable law or agreed to in writing, software
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and

"""

Magic squares in Google CP Solver.

Magic square problem.

This model was created by Hakan Kjellerstrand (hakank@gmail.com)
"""
import string, sys
from 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.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

#
# solution and search
#
solution = solver.Assignment()

# db: DecisionBuilder
db = solver.Phase(x_flat,
#solver.INT_VAR_DEFAULT,
solver.CHOOSE_FIRST_UNBOUND,
#solver.CHOOSE_MIN_SIZE_LOWEST_MAX,

solver.ASSIGN_CENTER_VALUE
#solver.ASSIGN_MIN_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)