# 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.
"""
Set partition problem in Google CP Solver.
Problem formulation from
http://www.koalog.com/resources/samples/PartitionProblem.java.html
'''
This is a partition problem.
Given the set S = {1, 2, ..., n},
it consists in finding two sets A and B such that:
A U B = S,
|A| = |B|,
sum(A) = sum(B),
sum_squares(A) = sum_squares(B)
'''
This model uses a binary matrix to represent the sets.
Also, compare with other models which uses var sets:
* MiniZinc: http://www.hakank.org/minizinc/set_partition.mzn
* Gecode/R: http://www.hakank.org/gecode_r/set_partition.rb
* Comet: http://hakank.org/comet/set_partition.co
* Gecode: http://hakank.org/gecode/set_partition.cpp
* ECLiPSe: http://hakank.org/eclipse/set_partition.ecl
* SICStus: http://hakank.org/sicstus/set_partition.pl
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/
"""
import sys
from ortools.constraint_solver import pywrapcp
#
# Partition the sets (binary matrix representation).
#
def partition_sets(x, num_sets, n):
solver = x.values()[0].solver()
for i in range(num_sets):
for j in range(num_sets):
if i != j:
b = solver.Sum([x[i, k] * x[j, k] for k in range(n)])
solver.Add(b == 0)
# ensure that all integers is in
# (exactly) one partition
b = [x[i, j] for i in range(num_sets) for j in range(n)]
solver.Add(solver.Sum(b) == n)
def main(n=16, num_sets=2):
# Create the solver.
solver = pywrapcp.Solver("Set partition")
#
# data
#
print "n:", n
print "num_sets:", num_sets
print
# Check sizes
assert n % num_sets == 0, "Equal sets is not possible."
#
# variables
#
# the set
a = {}
for i in range(num_sets):
for j in range(n):
a[i, j] = solver.IntVar(0, 1, "a[%i,%i]" % (i, j))
a_flat = [a[i, j] for i in range(num_sets) for j in range(n)]
#
# constraints
#
# partition set
partition_sets(a, num_sets, n)
for i in range(num_sets):
for j in range(i, num_sets):
# same cardinality
solver.Add(solver.Sum([a[i, k] for k in range(n)])
==
solver.Sum([a[j, k] for k in range(n)]))
# same sum
solver.Add(solver.Sum([k * a[i, k] for k in range(n)])
==
solver.Sum([k * a[j, k] for k in range(n)]))
# same sum squared
solver.Add(solver.Sum([(k * a[i, k]) * (k * a[i, k])
for k in range(n)])
==
solver.Sum([(k * a[j, k]) * (k * a[j, k])
for k in range(n)]))
# symmetry breaking for num_sets == 2
if num_sets == 2:
solver.Add(a[0, 0] == 1)
#
# search and result
#
db = solver.Phase(a_flat,
solver.INT_VAR_DEFAULT,
solver.INT_VALUE_DEFAULT)
solver.NewSearch(db)
num_solutions = 0
while solver.NextSolution():
a_val = {}
for i in range(num_sets):
for j in range(n):
a_val[i, j] = a[i, j].Value()
sq = sum([(j + 1) * a_val[0, j] for j in range(n)])
print "sums:", sq
sq2 = sum([((j + 1) * a_val[0, j]) ** 2 for j in range(n)])
print "sums squared:", sq2
for i in range(num_sets):
if sum([a_val[i, j] for j in range(n)]):
print i + 1, ":",
for j in range(n):
if a_val[i, j] == 1:
print j + 1,
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 = 16
num_sets = 2
if __name__ == "__main__":
if len(sys.argv) > 1:
n = int(sys.argv[1])
if len(sys.argv) > 2:
num_sets = int(sys.argv[2])
main(n, num_sets)