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# 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.
"""

  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@gmail.com)
  Also see my other Google CP Solver models:
  http://www.hakank.org/google_or_tools/
"""
from __future__ import print_function
from ortools.constraint_solver import pywrapcp


# 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)]), end=" ")
    print()
  print()

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