211 lines
7.4 KiB
C#
211 lines
7.4 KiB
C#
//
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// Copyright 2012 Hakan Kjellerstrand
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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using System;
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using System.Collections;
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using System.Collections.Generic;
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using System.Linq;
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using Google.OrTools.ConstraintSolver;
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public class EinavPuzzle2
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{
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/**
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*
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* A programming puzzle from Einav.
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*
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* From
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* "A programming puzzle from Einav"
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* http://gcanyon.wordpress.com/2009/10/28/a-programming-puzzle-from-einav/
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* """
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* My friend Einav gave me this programming puzzle to work on. Given
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* this array of positive and negative numbers:
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* 33 30 -10 -6 18 7 -11 -23 6
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* ...
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* -25 4 16 30 33 -23 -4 4 -23
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*
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* You can flip the sign of entire rows and columns, as many of them
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* as you like. The goal is to make all the rows and columns sum to positive
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* numbers (or zero), and then to find the solution (there are more than one)
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* that has the smallest overall sum. So for example, for this array:
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* 33 30 -10
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* -16 19 9
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* -17 -12 -14
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* You could flip the sign for the bottom row to get this array:
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* 33 30 -10
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* -16 19 9
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* 17 12 14
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* Now all the rows and columns have positive sums, and the overall total is
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* 108.
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* But you could instead flip the second and third columns, and the second
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* row, to get this array:
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* 33 -30 10
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* 16 19 9
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* -17 12 14
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* All the rows and columns still total positive, and the overall sum is just
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* 66. So this solution is better (I don't know if it's the best)
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* A pure brute force solution would have to try over 30 billion solutions.
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* I wrote code to solve this in J. I'll post that separately.
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* """
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*
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* Note:
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* This is a port of Larent Perrons's Python version of my own
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* einav_puzzle.py. He removed some of the decision variables and made it more
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* efficient. Thanks!
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*
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* Also see http://www.hakank.org/or-tools/einav_puzzle2.py
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*
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*/
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private static void Solve()
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{
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Solver solver = new Solver("EinavPuzzle2");
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//
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// Data
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//
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// Small problem
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// int rows = 3;
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// int cols = 3;
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// int[,] data = {
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// { 33, 30, -10},
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// {-16, 19, 9},
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// {-17, -12, -14}
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// };
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// Full problem
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int rows = 27;
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int cols = 9;
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int[,] data = { { 33, 30, 10, -6, 18, -7, -11, 23, -6 }, { 16, -19, 9, -26, -8, -19, -8, -21, -14 },
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{ 17, 12, -14, 31, -30, 13, -13, 19, 16 }, { -6, -11, 1, 17, -12, -4, -7, 14, -21 },
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{ 18, -31, 34, -22, 17, -19, 20, 24, 6 }, { 33, -18, 17, -15, 31, -5, 3, 27, -3 },
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{ -18, -20, -18, 31, 6, 4, -2, -12, 24 }, { 27, 14, 4, -29, -3, 5, -29, 8, -12 },
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{ -15, -7, -23, 23, -9, -8, 6, 8, -12 }, { 33, -23, -19, -4, -8, -7, 11, -12, 31 },
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{ -20, 19, -15, -30, 11, 32, 7, 14, -5 }, { -23, 18, -32, -2, -31, -7, 8, 24, 16 },
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{ 32, -4, -10, -14, -6, -1, 0, 23, 23 }, { 25, 0, -23, 22, 12, 28, -27, 15, 4 },
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{ -30, -13, -16, -3, -3, -32, -3, 27, -31 }, { 22, 1, 26, 4, -2, -13, 26, 17, 14 },
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{ -9, -18, 3, -20, -27, -32, -11, 27, 13 }, { -17, 33, -7, 19, -32, 13, -31, -2, -24 },
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{ -31, 27, -31, -29, 15, 2, 29, -15, 33 }, { -18, -23, 15, 28, 0, 30, -4, 12, -32 },
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{ -3, 34, 27, -25, -18, 26, 1, 34, 26 }, { -21, -31, -10, -13, -30, -17, -12, -26, 31 },
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{ 23, -31, -19, 21, -17, -10, 2, -23, 23 }, { -3, 6, 0, -3, -32, 0, -10, -25, 14 },
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{ -19, 9, 14, -27, 20, 15, -5, -27, 18 }, { 11, -6, 24, 7, -17, 26, 20, -31, -25 },
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{ -25, 4, -16, 30, 33, 23, -4, -4, 23 } };
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IEnumerable<int> ROWS = Enumerable.Range(0, rows);
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IEnumerable<int> COLS = Enumerable.Range(0, cols);
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//
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// Decision variables
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//
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IntVar[,] x = solver.MakeIntVarMatrix(rows, cols, -100, 100, "x");
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IntVar[] x_flat = x.Flatten();
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int[] signs_domain = { -1, 1 };
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// This don't work at the moment...
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IntVar[] row_signs = solver.MakeIntVarArray(rows, signs_domain, "row_signs");
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IntVar[] col_signs = solver.MakeIntVarArray(cols, signs_domain, "col_signs");
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// To optimize
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IntVar total_sum = x_flat.Sum().VarWithName("total_sum");
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//
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// Constraints
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//
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foreach (int i in ROWS)
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{
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foreach (int j in COLS)
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{
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solver.Add(x[i, j] == data[i, j] * row_signs[i] * col_signs[j]);
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}
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}
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// row sums
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IntVar[] row_sums = (from i in ROWS select(from j in COLS select x[i, j]).ToArray().Sum().Var()).ToArray();
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foreach (int i in ROWS)
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{
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row_sums[i].SetMin(0);
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}
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// col sums
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IntVar[] col_sums = (from j in COLS select(from i in ROWS select x[i, j]).ToArray().Sum().Var()).ToArray();
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foreach (int j in COLS)
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{
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col_sums[j].SetMin(0);
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}
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//
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// Objective
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//
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OptimizeVar obj = total_sum.Minimize(1);
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//
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// Search
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//
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DecisionBuilder db = solver.MakePhase(col_signs.Concat(row_signs).ToArray(), Solver.CHOOSE_MIN_SIZE_LOWEST_MIN,
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Solver.ASSIGN_MAX_VALUE);
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solver.NewSearch(db, obj);
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while (solver.NextSolution())
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{
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Console.WriteLine("Sum: {0}", total_sum.Value());
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Console.Write("row_sums: ");
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foreach (int i in ROWS)
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{
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Console.Write(row_sums[i].Value() + " ");
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}
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Console.Write("\nrow_signs: ");
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foreach (int i in ROWS)
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{
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Console.Write(row_signs[i].Value() + " ");
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}
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Console.Write("\ncol_sums: ");
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foreach (int j in COLS)
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{
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Console.Write(col_sums[j].Value() + " ");
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}
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Console.Write("\ncol_signs: ");
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foreach (int j in COLS)
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{
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Console.Write(col_signs[j].Value() + " ");
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}
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Console.WriteLine("\n");
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foreach (int i in ROWS)
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{
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foreach (int j in COLS)
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{
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Console.Write("{0,3} ", x[i, j].Value());
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}
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Console.WriteLine();
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}
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Console.WriteLine();
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}
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Console.WriteLine("\nSolutions: {0}", solver.Solutions());
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Console.WriteLine("WallTime: {0}ms", solver.WallTime());
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Console.WriteLine("Failures: {0}", solver.Failures());
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Console.WriteLine("Branches: {0} ", solver.Branches());
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solver.EndSearch();
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}
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public static void Main(String[] args)
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{
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Solve();
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}
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}
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