1# Copyright 2010 Hakan Kjellerstrand hakank@gmail.com 2# 3# Licensed under the Apache License, Version 2.0 (the "License"); 4# you may not use this file except in compliance with the License. 5# You may obtain a copy of the License at 6# 7# http://www.apache.org/licenses/LICENSE-2.0 8# 9# Unless required by applicable law or agreed to in writing, software 10# distributed under the License is distributed on an "AS IS" BASIS, 11# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 12# See the License for the specific language governing permissions and 13# limitations under the License. 14""" 15 16 Set partition problem in Google CP Solver. 17 18 Problem formulation from 19 http://www.koalog.com/resources/samples/PartitionProblem.java.html 20 ''' 21 This is a partition problem. 22 Given the set S = {1, 2, ..., n}, 23 it consists in finding two sets A and B such that: 24 25 A U B = S, 26 |A| = |B|, 27 sum(A) = sum(B), 28 sum_squares(A) = sum_squares(B) 29 30 ''' 31 32 This model uses a binary matrix to represent the sets. 33 34 35 Also, compare with other models which uses var sets: 36 * MiniZinc: http://www.hakank.org/minizinc/set_partition.mzn 37 * Gecode/R: http://www.hakank.org/gecode_r/set_partition.rb 38 * Comet: http://hakank.org/comet/set_partition.co 39 * Gecode: http://hakank.org/gecode/set_partition.cpp 40 * ECLiPSe: http://hakank.org/eclipse/set_partition.ecl 41 * SICStus: http://hakank.org/sicstus/set_partition.pl 42 43 This model was created by Hakan Kjellerstrand (hakank@gmail.com) 44 Also see my other Google CP Solver models: 45 http://www.hakank.org/google_or_tools/ 46""" 47import sys 48 49from ortools.constraint_solver import pywrapcp 50 51 52# 53# Partition the sets (binary matrix representation). 54# 55def partition_sets(x, num_sets, n): 56 solver = list(x.values())[0].solver() 57 58 for i in range(num_sets): 59 for j in range(num_sets): 60 if i != j: 61 b = solver.Sum([x[i, k] * x[j, k] for k in range(n)]) 62 solver.Add(b == 0) 63 64 # ensure that all integers is in 65 # (exactly) one partition 66 b = [x[i, j] for i in range(num_sets) for j in range(n)] 67 solver.Add(solver.Sum(b) == n) 68 69 70def main(n=16, num_sets=2): 71 72 # Create the solver. 73 solver = pywrapcp.Solver("Set partition") 74 75 # 76 # data 77 # 78 print("n:", n) 79 print("num_sets:", num_sets) 80 print() 81 82 # Check sizes 83 assert n % num_sets == 0, "Equal sets is not possible." 84 85 # 86 # variables 87 # 88 89 # the set 90 a = {} 91 for i in range(num_sets): 92 for j in range(n): 93 a[i, j] = solver.IntVar(0, 1, "a[%i,%i]" % (i, j)) 94 95 a_flat = [a[i, j] for i in range(num_sets) for j in range(n)] 96 97 # 98 # constraints 99 # 100 101 # partition set 102 partition_sets(a, num_sets, n) 103 104 for i in range(num_sets): 105 for j in range(i, num_sets): 106 107 # same cardinality 108 solver.Add( 109 solver.Sum([a[i, k] for k in range(n)]) == solver.Sum( 110 [a[j, k] for k in range(n)])) 111 112 # same sum 113 solver.Add( 114 solver.Sum([k * a[i, k] for k in range(n)]) == solver.Sum( 115 [k * a[j, k] for k in range(n)])) 116 117 # same sum squared 118 solver.Add( 119 solver.Sum([(k * a[i, k]) * (k * a[i, k]) for k in range(n)]) == 120 solver.Sum([(k * a[j, k]) * (k * a[j, k]) for k in range(n)])) 121 122 # symmetry breaking for num_sets == 2 123 if num_sets == 2: 124 solver.Add(a[0, 0] == 1) 125 126 # 127 # search and result 128 # 129 db = solver.Phase(a_flat, solver.INT_VAR_DEFAULT, solver.INT_VALUE_DEFAULT) 130 131 solver.NewSearch(db) 132 133 num_solutions = 0 134 while solver.NextSolution(): 135 a_val = {} 136 for i in range(num_sets): 137 for j in range(n): 138 a_val[i, j] = a[i, j].Value() 139 140 sq = sum([(j + 1) * a_val[0, j] for j in range(n)]) 141 print("sums:", sq) 142 sq2 = sum([((j + 1) * a_val[0, j])**2 for j in range(n)]) 143 print("sums squared:", sq2) 144 145 for i in range(num_sets): 146 if sum([a_val[i, j] for j in range(n)]): 147 print(i + 1, ":", end=" ") 148 for j in range(n): 149 if a_val[i, j] == 1: 150 print(j + 1, end=" ") 151 print() 152 153 print() 154 num_solutions += 1 155 156 solver.EndSearch() 157 158 print() 159 print("num_solutions:", num_solutions) 160 print("failures:", solver.Failures()) 161 print("branches:", solver.Branches()) 162 print("WallTime:", solver.WallTime()) 163 164 165n = 16 166num_sets = 2 167if __name__ == "__main__": 168 if len(sys.argv) > 1: 169 n = int(sys.argv[1]) 170 if len(sys.argv) > 2: 171 num_sets = int(sys.argv[2]) 172 173 main(n, num_sets) 174