From 055b34b100eef3ba3290681108f360bff8d49d7d Mon Sep 17 00:00:00 2001 From: hakank Date: Sun, 5 Feb 2012 19:19:24 +0000 Subject: [PATCH] Added einav_puzzle2.cs --- csharp/einav_puzzle2.cs | 231 ++++++++++++++++++++++++++++++++++++++++ 1 file changed, 231 insertions(+) create mode 100644 csharp/einav_puzzle2.cs diff --git a/csharp/einav_puzzle2.cs b/csharp/einav_puzzle2.cs new file mode 100644 index 0000000000..be41018b2b --- /dev/null +++ b/csharp/einav_puzzle2.cs @@ -0,0 +1,231 @@ +// +// 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[] row_signs = solver.MakeIntVarArray(rows, -1, 1, "row_signs"); + IntVar[] col_signs = solver.MakeIntVarArray(cols, -1, 1, "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].Var() + ).ToArray().Sum().Var()).ToArray(); + + foreach(int i in ROWS) { + row_sums[i].SetMin(0); + solver.Add(row_signs[i] != 0); + } + + // col sums + IntVar[] col_sums = (from j in COLS + select (from i in ROWS + select x[i,j].Var() + ).ToArray().Sum().Var()).ToArray(); + + foreach(int j in COLS) { + col_sums[j].SetMin(0); + solver.Add(col_signs[j] != 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(); + } +}