1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 | package org.jcp.jsr331.hakan;/** * * Set partition problem in JSR-331. * * * Problem formulation from * """ * 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. * * Compare with the following models: * - 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 * - Google CP Solver: http://hakank.org/google_or_tools/set_partition.py * * Model by Hakan Kjellerstrand (hakank@gmail.com) * Also see http://www.hakank.org/jsr_331/ * */// Licenced under CC-BY-4.0 : http://creativecommons.org/licenses/by/4.0/import javax.constraints.*;import java.io.*;import java.util.*;import java.text.*;public class SetPartition { int n; int num_sets = 2; Var[] a_flatten; Problem p = ProblemFactory.newProblem("SetPartition"); // main public static void main(String[] args) { int n_in = 16; if (args.length > 0) { n_in = Integer.parseInt(args[0]); } SetPartition pp = new SetPartition(); pp.define(n_in); pp.solve(); } // Problem definition public void define(int n_in) { n = n_in; System.out.println("n:" + n); Var[][] a = new Var[num_sets][n]; a_flatten = new Var[num_sets*n]; for(int i = 0; i < num_sets; i++) { for(int j = 0; j < n; j++) { a[i][j] = p.variable("a-"+i+"-"+j, 0, 1); a_flatten[i*n+j] = a[i][j]; } } // partition the sets (all different) for(int k = 0; k < n; k++) { p.post(a[0][k], "!=" , a[1][k]); } for(int i = 0; i < num_sets; i++) { for(int j = 0; j < num_sets; j++) { if (i < j) { Var[] s1 = new Var[n]; Var[] s2 = new Var[n]; Var[] sq1 = new Var[n]; Var[] sq2 = new Var[n]; Var[] sqsq1 = new Var[n]; Var[] sqsq2 = new Var[n]; for(int k = 0; k < n; k++) { // same cardinality // m.post(sum(k in 1..n) a[i,k] == sum(k in 1..n) a[j,k]); // s1[k] = new javax.constraints.impl.Var(this,"s1+"+i+"-"+j+"-"+k, 0,1); // s2[k] = new javax.constraints.impl.Var(this,"s2+"+i+"-"+j+"-"+k, 0,1); s1[k] = p.variable("s1+"+i+"-"+j+"-"+k, 0,1); s2[k] = p.variable("s2+"+i+"-"+j+"-"+k, 0,1); s1[k] = a[i][k].plus(1); s2[k] = a[j][k].plus(1); // same sum // m.post(sum(k in 1..n) k*a[i,k] == sum(k in 1..n) k*a[j,k]); // sq1[k] = new javax.constraints.impl.Var(this,"sq1+"+i+"-"+j+"-"+k, 0,1); // sq2[k] = new javax.constraints.impl.Var(this,"sq2+"+i+"-"+j+"-"+k, 0,1); sq1[k] = p.variable("sq1+"+i+"-"+j+"-"+k, 0,1); sq2[k] = p.variable("sq2+"+i+"-"+j+"-"+k, 0,1); sq1[k] = (a[i][k].plus(1)).multiply(k); sq2[k] = (a[j][k].plus(1)).multiply(k); // same sum squared // m.post((sum(k in 1..n) (k*a[i,k])^2) == (sum(k in 1..n) (k*a[j,k])^2)); // sqsq1[k] = new javax.constraints.impl.Var(this,"sq1+"+i+"-"+j+"-"+k, 0,1); // sqsq2[k] = new javax.constraints.impl.Var(this,"sq2+"+i+"-"+j+"-"+k, 0,1); sqsq1[k] = p.variable("sq1+"+i+"-"+j+"-"+k, 0,1); sqsq2[k] = p.variable("sq2+"+i+"-"+j+"-"+k, 0,1); sqsq1[k] = (a[i][k].plus(1)).multiply(k).power(2); sqsq2[k] = (a[j][k].plus(1)).multiply(k).power(2); } p.post(p.sum(s1), "=", p.sum(s2)); p.post(p.sum(sq1), "=", p.sum(sq2)); p.post(p.sum(sqsq1), "=", p.sum(sqsq2)); // symmetry breaking p.post(a[0][0],"=", 1); } } } } public void solve() { // // search // Solver solver = p.getSolver(); SearchStrategy strategy = solver.getSearchStrategy(); strategy.setVars(a_flatten); // strategy.setVarSelectorType(VarSelectorType.INPUT_ORDER); // strategy.setVarSelectorType(VarSelectorType.MIN_VALUE); // strategy.setVarSelectorType(VarSelectorType.MAX_VALUE); // strategy.setVarSelectorType(VarSelectorType.MIN_DOMAIN); // strategy.setVarSelectorType(VarSelectorType.MIN_DOMAIN_MIN_VALUE); // strategy.setVarSelectorType(VarSelectorType.MIN_DOMAIN_RANDOM); // strategy.setVarSelectorType(VarSelectorType.RANDOM); // strategy.setVarSelectorType(VarSelectorType.MIN_DOMAIN_MAX_DEGREE); // strategy.setVarSelectorType(VarSelectorType.MIN_DOMAIN_OVER_DEGREE); // strategy.setVarSelectorType(VarSelectorType.MIN_DOMAIN_OVER_WEIGHTED_DEGREE); // strategy.setVarSelectorType(VarSelectorType.MAX_WEIGHTED_DEGREE); // strategy.setVarSelectorType(VarSelectorType.MAX_IMPACT); strategy.setVarSelectorType(VarSelectorType.MAX_DEGREE); // strategy.setVarSelectorType(VarSelectorType.MAX_REGRET); // strategy.setValueSelectorType(ValueSelectorType.IN_DOMAIN); // strategy.setValueSelectorType(ValueSelectorType.MIN); // strategy.setValueSelectorType(ValueSelectorType.MAX); // strategy.setValueSelectorType(ValueSelectorType.MIN_MAX_ALTERNATE); // strategy.setValueSelectorType(ValueSelectorType.MIDDLE); // strategy.setValueSelectorType(ValueSelectorType.MEDIAN); // strategy.setValueSelectorType(ValueSelectorType.RANDOM); strategy.setValueSelectorType(ValueSelectorType.MIN_IMPACT); // strategy.setValueSelectorType(ValueSelectorType.CUSTOM); // // tracing // // solver.addSearchStrategy(new StrategyLogVariables(solver)); // solver.traceExecution(true); // // solve // int num_sols = 0; SolutionIterator iter = solver.solutionIterator(); while (iter.hasNext()) { num_sols++; Solution s = iter.next(); // s.log(); for(int i = 0; i < num_sets; i++) { int sum = 0; for(int j = 0; j < n; j++) { if (s.getValue("a-"+i+"-"+j) == 1) { System.out.format("%2s ", j+1); sum += j+1; } } System.out.print(" = " + sum); System.out.println(); } System.out.println(); } System.out.println("It was " + num_sols + " solutions.\n"); solver.logStats(); }} |