# 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 version use a better way of looping through all solutions.
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 ortools.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)
db = solver.Phase([x[(i, j)] for i in range(n) for j in range(n)],
solver.CHOOSE_PATH,
solver.ASSIGN_MIN_VALUE)
solver.NewSearch(db)
num_solutions = 0
while solver.NextSolution():
num_solutions += 1
print "total_sum:", total_sum.Value()
for i in range(n):
for j in range(n):
print x[(i, j)].Value(),
print
print
print "num_solutions:", num_solutions
print "failures:", solver.Failures()
print "branches:", solver.Branches()
print "WallTime:", solver.WallTime()
if __name__ == "__main__":
main("cp sample")