// // Copyright 2012 Hakan Kjellerstrand // // 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. using System; using System.Collections; using System.Collections.Generic; using System.Linq; using Google.OrTools.ConstraintSolver; public class EinavPuzzle2 { /** * * A programming puzzle from Einav. * * 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. * """ * * Note: * This is a port of Larent Perrons's Python version of my own einav_puzzle.py. * He removed some of the decision variables and made it more efficient. * Thanks! * * Also see http://www.hakank.org/or-tools/einav_puzzle2.py * */ private static void Solve() { Solver solver = new Solver("EinavPuzzle2"); // // Data // // 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} }; IEnumerable ROWS = Enumerable.Range(0, rows); IEnumerable COLS = Enumerable.Range(0, cols); // // Decision variables // IntVar[,] x = solver.MakeIntVarMatrix(rows, cols, -100, 100, "x"); IntVar[] x_flat = x.Flatten(); int[] signs_domain = {-1,1}; // This don't work at the moment... IntVar[] row_signs = solver.MakeIntVarArray(rows, signs_domain, "row_signs"); IntVar[] col_signs = solver.MakeIntVarArray(cols, signs_domain, "col_signs"); // To optimize IntVar total_sum = x_flat.Sum().VarWithName("total_sum"); // // Constraints // foreach(int i in ROWS) { foreach(int j in COLS) { solver.Add(x[i,j] == data[i,j] * row_signs[i] * col_signs[j]); } } // row sums IntVar[] row_sums = (from i in ROWS select (from j in COLS select x[i,j] ).ToArray().Sum().Var()).ToArray(); foreach(int i in ROWS) { row_sums[i].SetMin(0); } // col sums IntVar[] col_sums = (from j in COLS select (from i in ROWS select x[i,j] ).ToArray().Sum().Var()).ToArray(); foreach(int j in COLS) { col_sums[j].SetMin(0); } // // Objective // OptimizeVar obj = total_sum.Minimize(1); // // Search // DecisionBuilder db = solver.MakePhase(col_signs.Concat(row_signs).ToArray(), Solver.CHOOSE_MIN_SIZE_LOWEST_MIN, Solver.ASSIGN_MAX_VALUE); solver.NewSearch(db, obj); while (solver.NextSolution()) { Console.WriteLine("Sum: {0}",total_sum.Value()); Console.Write("row_sums: "); foreach(int i in ROWS) { Console.Write(row_sums[i].Value() + " "); } Console.Write("\nrow_signs: "); foreach(int i in ROWS) { Console.Write(row_signs[i].Value() + " "); } Console.Write("\ncol_sums: "); foreach(int j in COLS) { Console.Write(col_sums[j].Value() + " "); } Console.Write("\ncol_signs: "); foreach(int j in COLS) { Console.Write(col_signs[j].Value() + " "); } Console.WriteLine("\n"); foreach(int i in ROWS) { foreach(int j in COLS) { Console.Write("{0,3} ", x[i,j].Value()); } Console.WriteLine(); } Console.WriteLine(); } Console.WriteLine("\nSolutions: {0}", solver.Solutions()); Console.WriteLine("WallTime: {0}ms", solver.WallTime()); Console.WriteLine("Failures: {0}", solver.Failures()); Console.WriteLine("Branches: {0} ", solver.Branches()); solver.EndSearch(); } public static void Main(String[] args) { Solve(); } }