/** * * Einav puzzle in Choco3 * * * From * "A programming puzzle from Einav" * http://gcanyon.wordpress.com/2009/10/28/a-programming-puzzle-from-einav/ * """ * My friend Einav gave me this programming puzzle to work on. Given * this array of positive and negative numbers: * 33 30 -10 -6 18 7 -11 -23 6 * ... * -25 4 16 30 33 -23 -4 4 -23 * * You can flip the sign of entire rows and columns, as many of them * as you like. The goal is to make all the rows and columns sum to positive * numbers (or zero), and then to find the solution (there are more than one) * that has the smallest overall sum. So for example, for this array: * 33 30 -10 * -16 19 9 * -17 -12 -14 * You could flip the sign for the bottom row to get this array: * 33 30 -10 * -16 19 9 * 17 12 14 * Now all the rows and columns have positive sums, and the overall total is * 108. * But you could instead flip the second and third columns, and the second * row, to get this array: * 33 -30 10 * 16 19 9 * -17 12 14 * All the rows and columns still total positive, and the overall sum is just * 66. So this solution is better (I don't know if it's the best) * A pure brute force solution would have to try over 30 billion solutions. * I wrote code to solve this in J. I'll post that separately. * """ * * * Choco3 model by Hakan Kjellerstrand (hakank@gmail.com) * http://www.hakank.org/choco3/ * */ import org.kohsuke.args4j.Option; import org.slf4j.LoggerFactory; import samples.AbstractProblem; import solver.ResolutionPolicy; import solver.Solver; import solver.constraints.Constraint; import solver.constraints.IntConstraintFactory; import solver.constraints.IntConstraintFactory.*; import solver.search.strategy.IntStrategyFactory; import solver.search.loop.monitors.SearchMonitorFactory; import solver.variables.IntVar; import solver.variables.BoolVar; import solver.variables.VariableFactory; import solver.search.strategy.strategy.AbstractStrategy; import util.ESat; import util.tools.ArrayUtils; public class EinavPuzzle extends AbstractProblem { // Small problem // int rows = 3; // int cols = 3; // int[][] data = { // { 33, 30, -10}, // {-16, 19, 9}, // {-17, -12, -14} // }; // Full problem int rows = 27; int cols = 9; int[][] data = {{33,30,10,-6,18,-7,-11,23,-6}, {16,-19,9,-26,-8,-19,-8,-21,-14}, {17,12,-14,31,-30,13,-13,19,16}, {-6,-11,1,17,-12,-4,-7,14,-21}, {18,-31,34,-22,17,-19,20,24,6}, {33,-18,17,-15,31,-5,3,27,-3}, {-18,-20,-18,31,6,4,-2,-12,24}, {27,14,4,-29,-3,5,-29,8,-12}, {-15,-7,-23,23,-9,-8,6,8,-12}, {33,-23,-19,-4,-8,-7,11,-12,31}, {-20,19,-15,-30,11,32,7,14,-5}, {-23,18,-32,-2,-31,-7,8,24,16}, {32,-4,-10,-14,-6,-1,0,23,23}, {25,0,-23,22,12,28,-27,15,4}, {-30,-13,-16,-3,-3,-32,-3,27,-31}, {22,1,26,4,-2,-13,26,17,14}, {-9,-18,3,-20,-27,-32,-11,27,13}, {-17,33,-7,19,-32,13,-31,-2,-24}, {-31,27,-31,-29,15,2,29,-15,33}, {-18,-23,15,28,0,30,-4,12,-32}, {-3,34,27,-25,-18,26,1,34,26}, {-21,-31,-10,-13,-30,-17,-12,-26,31}, {23,-31,-19,21,-17,-10,2,-23,23}, {-3,6,0,-3,-32,0,-10,-25,14}, {-19,9,14,-27,20,15,-5,-27,18}, {11,-6,24,7,-17,26,20,-31,-25}, {-25,4,-16,30,33,23,-4,-4,23}}; IntVar[][] x; IntVar[] x_flat; IntVar[] row_signs; IntVar[] col_signs; IntVar[] row_sums; IntVar[] col_sums; IntVar total_sum; @Override public void buildModel() { x = VariableFactory.boundedMatrix("x", rows, cols, -100, 100, solver); x_flat = ArrayUtils.flatten(x); total_sum = VariableFactory.bounded("total_sum", 0, 1000, solver); int[] signs_domain = {-1,1}; // It would be nice with a variant where one can state the domains via // an array of possible values row_signs = VariableFactory.boundedArray("row_signs", rows, -1, 1, solver); col_signs = VariableFactory.boundedArray("col_signs", cols, -1, 1, solver); // Remove 0 from row_signs and col_signs IntVar zero = VariableFactory.fixed(0, solver); for(int i = 0; i < rows; i++) { solver.post(IntConstraintFactory.arithm(row_signs[i],"!=", zero)); } for(int j = 0; j < cols; j++) { solver.post(IntConstraintFactory.arithm(col_signs[j],"!=", zero)); } solver.post(IntConstraintFactory.sum(x_flat, total_sum)); for(int i = 0; i < rows; i++) { for(int j = 0; j < cols; j++) { // x[i][j] == data[i][j] * row_signs[i] * col_signs[j] IntVar t = VariableFactory.bounded("t_"+i+"_"+j, -100, 100, solver); solver.post(IntConstraintFactory.times(row_signs[i], col_signs[j], t)); solver.post(IntConstraintFactory.times(t, VariableFactory.fixed(data[i][j], solver), x[i][j])); } } row_sums = VariableFactory.boundedArray("row_sums", rows, 0, 1000, solver); for(int i = 0; i < rows; i++) { solver.post(IntConstraintFactory.sum(x[i], row_sums[i])); } col_sums = VariableFactory.boundedArray("col_sums", cols, 0, 1000, solver); for(int j = 0; j < cols; j++) { solver.post(IntConstraintFactory.sum(ArrayUtils.getColumn(x, j), col_sums[j])); } } @Override public void createSolver() { solver = new Solver("EinavPuzzle"); } @Override public void configureSearch() { solver.set(IntStrategyFactory.firstFail_InDomainMin(ArrayUtils.append(col_signs,row_signs))); } @Override public void solve() { // solver.findSolution(); solver.findOptimalSolution(ResolutionPolicy.MINIMIZE, total_sum); } @Override public void prettyOut() { if(solver.isFeasible() == ESat.TRUE) { int num_solutions = 0; do { System.out.println("total_sum: " + total_sum.getValue()); System.out.println("x: "); for(int i = 0; i < rows; i++) { for(int j = 0; j < cols; j++) { System.out.format("%3d ", x[i][j].getValue()); } System.out.println(); } System.out.println(); System.out.print("row_sums: "); for(int i = 0; i < rows; i++) { System.out.print(row_sums[i].getValue() + " "); } System.out.println(); System.out.print("col_sums: "); for(int j = 0; j < cols; j++) { System.out.print(col_sums[j].getValue() + " "); } System.out.println(); System.out.print("row_signs: "); for(int i = 0; i < rows; i++) { System.out.print(row_signs[i].getValue() + " "); } System.out.println(); System.out.print("col_signs: "); for(int j = 0; j < cols; j++) { System.out.print(col_signs[j].getValue() + " "); } System.out.println(); System.out.println(); num_solutions++; } while (solver.nextSolution() == Boolean.TRUE); System.out.println("It was " + num_solutions + " solutions."); } else { System.out.println("Problem is not feasible."); } } // // main // public static void main(String args[]) { new EinavPuzzle().execute(args); } }