// // 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.Linq; using Google.OrTools.ConstraintSolver; public class APuzzle { /** * * From "God plays dice" * "A puzzle" * http://gottwurfelt.wordpress.com/2012/02/22/a-puzzle/ * And the sequel "Answer to a puzzle" * http://gottwurfelt.wordpress.com/2012/02/24/an-answer-to-a-puzzle/ * * This problem instance was taken from the latter blog post. * (Problem 1) * * """ * 8809 = 6 * 7111 = 0 * 2172 = 0 * 6666 = 4 * 1111 = 0 * 3213 = 0 * 7662 = 2 * 9312 = 1 * 0000 = 4 * 2222 = 0 * 3333 = 0 * 5555 = 0 * 8193 = 3 * 8096 = 5 * 7777 = 0 * 9999 = 4 * 7756 = 1 * 6855 = 3 * 9881 = 5 * 5531 = 0 * * 2581 = ? * """ * * Note: * This model yields 10 solutions, since x4 is not * restricted in the constraints. * All solutions has x assigned to the correct result. * * * (Problem 2) * The problem stated in "A puzzle" * http://gottwurfelt.wordpress.com/2012/02/22/a-puzzle/ * is * """ * 8809 = 6 * 7662 = 2 * 9312 = 1 * 8193 = 3 * 8096 = 5 * 7756 = 1 * 6855 = 3 * 9881 = 5 * * 2581 = ? * """ * This problem instance yields two different solutions of x, * one is the same (correct) as for the above problem instance, * and one is not. * This is because here x0,x1,x4 and x9 are underdefined. * * */ private static void Solve(int p = 1) { Solver solver = new Solver("APuzzle"); Console.WriteLine("\nSolving p{0}", p); // // Data // int n = 10; // // Decision variables // IntVar x0 = solver.MakeIntVar(0, n-1, "x0"); IntVar x1 = solver.MakeIntVar(0, n-1, "x1"); IntVar x2 = solver.MakeIntVar(0, n-1, "x2"); IntVar x3 = solver.MakeIntVar(0, n-1, "x3"); IntVar x4 = solver.MakeIntVar(0, n-1, "x4"); IntVar x5 = solver.MakeIntVar(0, n-1, "x5"); IntVar x6 = solver.MakeIntVar(0, n-1, "x6"); IntVar x7 = solver.MakeIntVar(0, n-1, "x7"); IntVar x8 = solver.MakeIntVar(0, n-1, "x8"); IntVar x9 = solver.MakeIntVar(0, n-1, "x9"); IntVar[] all = {x0,x1,x2,x3,x4,x5,x6,x7,x8,x9}; // The unknown, i.e. 2581 = x IntVar x = solver.MakeIntVar(0, n-1, "x"); // // Constraints // // Both problem are here shown in two // approaches: // - using equations // - using a a matrix and Sum of each row if (p == 1) { // Problem 1 solver.Add(x8+x8+x0+x9 == 6); solver.Add(x7+x1+x1+x1 == 0); solver.Add(x2+x1+x7+x2 == 0); solver.Add(x6+x6+x6+x6 == 4); solver.Add(x1+x1+x1+x1 == 0); solver.Add(x3+x2+x1+x3 == 0); solver.Add(x7+x6+x6+x2 == 2); solver.Add(x9+x3+x1+x2 == 1); solver.Add(x0+x0+x0+x0 == 4); solver.Add(x2+x2+x2+x2 == 0); solver.Add(x3+x3+x3+x3 == 0); solver.Add(x5+x5+x5+x5 == 0); solver.Add(x8+x1+x9+x3 == 3); solver.Add(x8+x0+x9+x6 == 5); solver.Add(x7+x7+x7+x7 == 0); solver.Add(x9+x9+x9+x9 == 4); solver.Add(x7+x7+x5+x6 == 1); solver.Add(x6+x8+x5+x5 == 3); solver.Add(x9+x8+x8+x1 == 5); solver.Add(x5+x5+x3+x1 == 0); // The unknown solver.Add(x2+x5+x8+x1 == x); } else if (p == 2) { // Another representation of Problem 1 int[,] problem1 = { {8,8,0,9, 6}, {7,1,1,1, 0}, {2,1,7,2, 0}, {6,6,6,6, 4}, {1,1,1,1, 0}, {3,2,1,3, 0}, {7,6,6,2, 2}, {9,3,1,2, 1}, {0,0,0,0, 4}, {2,2,2,2, 0}, {3,3,3,3, 0}, {5,5,5,5, 0}, {8,1,9,3, 3}, {8,0,9,6, 5}, {7,7,7,7, 0}, {9,9,9,9, 4}, {7,7,5,6, 1}, {6,8,5,5, 3}, {9,8,8,1, 5}, {5,5,3,1, 0} }; for(int i = 0; i < problem1.GetLength(0); i++) { solver.Add( (from j in Enumerable.Range(0, 4) select all[problem1[i,j]] ).ToArray().Sum() == problem1[i,4] ); } solver.Add(all[2]+all[5]+all[8]+all[1] == x); } else if (p == 3) { // Problem 2 solver.Add(x8+x8+x0+x9 == 6); solver.Add(x7+x6+x6+x2 == 2); solver.Add(x9+x3+x1+x2 == 1); solver.Add(x8+x1+x9+x3 == 3); solver.Add(x8+x0+x9+x6 == 5); solver.Add(x7+x7+x5+x6 == 1); solver.Add(x6+x8+x5+x5 == 3); solver.Add(x9+x8+x8+x1 == 5); // The unknown solver.Add(x2+x5+x8+x1 == x); } else { // Another representation of Problem 2 int[,] problem2 = { {8,8,0,9, 6}, {7,6,6,2, 2}, {9,3,1,2, 1}, {8,1,9,3, 3}, {8,0,9,6, 5}, {7,7,5,6, 1}, {6,8,5,5, 3}, {9,8,8,1, 5} }; for(int i = 0; i < problem2.GetLength(0); i++) { solver.Add( (from j in Enumerable.Range(0, 4) select all[problem2[i,j]] ).ToArray().Sum() == problem2[i,4] ); } solver.Add(all[2]+all[5]+all[8]+all[1] == x); } // // Search // DecisionBuilder db = solver.MakePhase(all, Solver.INT_VAR_DEFAULT, Solver.INT_VALUE_DEFAULT); solver.NewSearch(db); while (solver.NextSolution()) { Console.Write("x: {0} x0..x9: ", x.Value()); for(int i = 0; i < n; i++) { Console.Write(all[i].Value() + " "); } 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) { for(int p = 1; p <= 4; p++) { Solve(p); } } }