019: Magic Squares and Sequences

# 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.

"""

  Magic squares in Google CP Solver.

  Magic square problem.

  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 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.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_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)