# 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.

"""

  Seseman Convent problem in Google CP Solver.


  n is the length of a border
  There are (n-2)^2 "holes", i.e.
  there are n^2 - (n-2)^2 variables to find out.

  The simplest problem, n = 3 (n x n matrix)
  which is represented by the following matrix:

   a b c
   d   e
   f g h

  Where the following constraints must hold:

    a + b + c = border_sum
    a + d + f = border_sum
    c + e + h = border_sum
    f + g + h = border_sum
    a + b + c + d + e + f = total_sum


  Compare with the following models:
  * Tailor/Essence': http://hakank.org/tailor/seseman.eprime
  * MiniZinc: http://hakank.org/minizinc/seseman.mzn
  * SICStus: http://hakank.org/sicstus/seseman.pl
  * Zinc: http://hakank.org/minizinc/seseman.zinc
  * Choco: http://hakank.org/choco/Seseman.java
  * Comet: http://hakank.org/comet/seseman.co
  * ECLiPSe: http://hakank.org/eclipse/seseman.ecl
  * Gecode: http://hakank.org/gecode/seseman.cpp
  * Gecode/R: http://hakank.org/gecode_r/seseman.rb
  * JaCoP: http://hakank.org/JaCoP/Seseman.java


  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 constraint_solver import pywrapcp

def main(unused_argv):
    # Create the solver.
    solver = pywrapcp.Solver('Seseman Convent problem')

    # data
    n = 3
    border_sum = n*n

    # declare variables
    total_sum = solver.IntVar(1,n*n*n*n, 'total_sum')
    # x[0..n-1,0..n-1]
    x = {}
    for i in range(n):
        for j in range(n):
            x[(i,j)] = solver.IntVar(0,n*n, 'x %i %i' % (i, j))


    #
    # constraints
    #
    # zero all middle cells
    for i in range(1,n-1):
        for j in range(1,n-1):
            solver.Add(x[(i,j)] == 0)

    # all borders must be >= 1
    for i in range(n):
        for j in range(n):
            if i == 0 or j == 0 or i == n-1 or j == n-1:
                solver.Add(x[(i,j)] >= 1)


    # sum the borders (border_sum)
    solver.Add(solver.Sum([x[(i,0)]   for i in range(n)]) == border_sum)
    solver.Add(solver.Sum([x[(i,n-1)] for i in range(n)]) == border_sum)
    solver.Add(solver.Sum([x[(0,i)]   for i in range(n)]) == border_sum)
    solver.Add(solver.Sum([x[(n-1,i)] for i in range(n)]) == border_sum)

    # total
    solver.Add(solver.Sum([x[(i,j)] for i in range(n) for j in range(n)]) == total_sum)

    #
    # solution and search
    #
    solution = solver.Assignment()
    solution.Add([x[(i,j)] for i in range(n) for j in range(n)])
    solution.Add(total_sum)

    # all solutions
    collector = solver.AllSolutionCollector(solution)
    # search_log = solver.SearchLog(100, total_sum)
    solver.Solve(solver.Phase([x[(i,j)] for i in range(n) for j in range(n)],
                              solver.CHOOSE_PATH,
                              solver.ASSIGN_MIN_VALUE),
                              [collector])
                              #[collector, search_log])

    num_solutions = collector.SolutionCount()
    # print "x:", x
    print "num_solutions:", num_solutions
    print
    for s in range(num_solutions):
        # print [collector.Value(s, x[(i,j)])
        #        for i in range(n) for j in range(n)]
        print "total_sum:", collector.Value(s, total_sum)
        for i in range(n):
            for j in range(n):
                print collector.Value(s, x[(i,j)]),
            print
        print

    print "failures:", solver.Failures()
    print "branches:", solver.Branches()
    print "WallTime:", solver.WallTime()
    print "num_solutions:", num_solutions


if __name__ == '__main__':
    main("cp sample")