138 lines
4.1 KiB
Python
138 lines
4.1 KiB
Python
# Copyright 2010 Hakan Kjellerstrand hakank@bonetmail.com
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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"""
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Seseman Convent problem in Google CP Solver.
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n is the length of a border
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There are (n-2)^2 "holes", i.e.
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there are n^2 - (n-2)^2 variables to find out.
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The simplest problem, n = 3 (n x n matrix)
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which is represented by the following matrix:
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a b c
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d e
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f g h
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Where the following constraints must hold:
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a + b + c = border_sum
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a + d + f = border_sum
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c + e + h = border_sum
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f + g + h = border_sum
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a + b + c + d + e + f = total_sum
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Compare with the following models:
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* Tailor/Essence': http://hakank.org/tailor/seseman.eprime
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* MiniZinc: http://hakank.org/minizinc/seseman.mzn
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* SICStus: http://hakank.org/sicstus/seseman.pl
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* Zinc: http://hakank.org/minizinc/seseman.zinc
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* Choco: http://hakank.org/choco/Seseman.java
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* Comet: http://hakank.org/comet/seseman.co
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* ECLiPSe: http://hakank.org/eclipse/seseman.ecl
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* Gecode: http://hakank.org/gecode/seseman.cpp
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* Gecode/R: http://hakank.org/gecode_r/seseman.rb
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* JaCoP: http://hakank.org/JaCoP/Seseman.java
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This model was created by Hakan Kjellerstrand (hakank@bonetmail.com)
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Also see my other Google CP Solver models: http://www.hakank.org/google_or_tools/
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"""
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from constraint_solver import pywrapcp
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def main(unused_argv):
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# Create the solver.
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solver = pywrapcp.Solver('Seseman Convent problem')
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# data
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n = 3
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border_sum = n*n
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# declare variables
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total_sum = solver.IntVar(1,n*n*n*n, 'total_sum')
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# x[0..n-1,0..n-1]
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x = {}
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for i in range(n):
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for j in range(n):
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x[(i,j)] = solver.IntVar(0,n*n, 'x %i %i' % (i, j))
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#
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# constraints
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#
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# zero all middle cells
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for i in range(1,n-1):
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for j in range(1,n-1):
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solver.Add(x[(i,j)] == 0)
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# all borders must be >= 1
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for i in range(n):
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for j in range(n):
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if i == 0 or j == 0 or i == n-1 or j == n-1:
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solver.Add(x[(i,j)] >= 1)
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# sum the borders (border_sum)
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solver.Add(solver.Sum([x[(i,0)] for i in range(n)]) == border_sum)
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solver.Add(solver.Sum([x[(i,n-1)] for i in range(n)]) == border_sum)
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solver.Add(solver.Sum([x[(0,i)] for i in range(n)]) == border_sum)
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solver.Add(solver.Sum([x[(n-1,i)] for i in range(n)]) == border_sum)
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# total
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solver.Add(solver.Sum([x[(i,j)] for i in range(n) for j in range(n)]) == total_sum)
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#
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# solution and search
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#
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solution = solver.Assignment()
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solution.Add([x[(i,j)] for i in range(n) for j in range(n)])
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solution.Add(total_sum)
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# all solutions
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collector = solver.AllSolutionCollector(solution)
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# search_log = solver.SearchLog(100, total_sum)
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solver.Solve(solver.Phase([x[(i,j)] for i in range(n) for j in range(n)],
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solver.CHOOSE_PATH,
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solver.ASSIGN_MIN_VALUE),
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[collector])
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#[collector, search_log])
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num_solutions = collector.SolutionCount()
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# print "x:", x
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print "num_solutions:", num_solutions
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print
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for s in range(num_solutions):
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# print [collector.Value(s, x[(i,j)])
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# for i in range(n) for j in range(n)]
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print "total_sum:", collector.Value(s, total_sum)
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for i in range(n):
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for j in range(n):
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print collector.Value(s, x[(i,j)]),
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print
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print
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print "failures:", solver.Failures()
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print "branches:", solver.Branches()
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print "WallTime:", solver.WallTime()
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print "num_solutions:", num_solutions
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if __name__ == '__main__':
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main("cp sample")
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