sudoku_cs.cs

/* Copyright 2021, 狗万app足彩Gurobi Optimization, LLC */ /*数独示例。数独板是一个9x9的网格，它被进一步分成一个3x3的网格。网格中的每个单元格必须取从0到9的值。在同一行、列或3x3子网格中的两个网格单元格不能取相同的值。在MIP公式中，二进制变量x[i,j,v]表示cell 是否取值'v'。约束条件如下:1.单击“确定”。每个cell必须取一个值(sum_v x[i,j,v] = 1) 2。每个值在每行中使用一次(sum_i x[i,j,v] = 1) 3。每个值在每个列(sum_j x[i,j,v] = 1)中使用一次。每个值在3x3的subgrid (sum_grid x[i,j,v] = 1)中精确使用一次(sum_grid x[i,j,v] = 1)。 */ using System; using System.IO; using Gurobi; class sudoku_cs { static void Main(string[] args) { int n = 9; int s = 3; if (args.Length < 1) { Console.Out.WriteLine("Usage: sudoku_cs filename"); return; } try { GRBEnv env = new GRBEnv(); GRBModel model = new GRBModel(env); // Create 3-D array of model variables GRBVar[,,] vars = new GRBVar[n,n,n]; for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { for (int v = 0; v < n; v++) { string st = "G_" + i.ToString() + "_" + j.ToString() + "_" + v.ToString(); vars[i,j,v] = model.AddVar(0.0, 1.0, 0.0, GRB.BINARY, st); } } } // Add constraints GRBLinExpr expr; // Each cell must take one value for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { expr = 0.0; for (int v = 0; v < n; v++) expr.AddTerm(1.0, vars[i,j,v]); string st = "V_" + i.ToString() + "_" + j.ToString(); model.AddConstr(expr == 1.0, st); } } // Each value appears once per row for (int i = 0; i < n; i++) { for (int v = 0; v < n; v++) { expr = 0.0; for (int j = 0; j < n; j++) expr.AddTerm(1.0, vars[i,j,v]); string st = "R_" + i.ToString() + "_" + v.ToString(); model.AddConstr(expr == 1.0, st); } } // Each value appears once per column for (int j = 0; j < n; j++) { for (int v = 0; v < n; v++) { expr = 0.0; for (int i = 0; i < n; i++) expr.AddTerm(1.0, vars[i,j,v]); string st = "C_" + j.ToString() + "_" + v.ToString(); model.AddConstr(expr == 1.0, st); } } // Each value appears once per sub-grid for (int v = 0; v < n; v++) { for (int i0 = 0; i0 < s; i0++) { for (int j0 = 0; j0 < s; j0++) { expr = 0.0; for (int i1 = 0; i1 < s; i1++) { for (int j1 = 0; j1 < s; j1++) { expr.AddTerm(1.0, vars[i0*s+i1,j0*s+j1,v]); } } string st = "Sub_" + v.ToString() + "_" + i0.ToString() + "_" + j0.ToString(); model.AddConstr(expr == 1.0, st); } } } // Fix variables associated with pre-specified cells StreamReader sr = File.OpenText(args[0]); for (int i = 0; i < n; i++) { string input = sr.ReadLine(); for (int j = 0; j < n; j++) { int val = (int) input[j] - 48 - 1; // 0-based if (val >= 0) vars[i,j,val].LB = 1.0; } } // Optimize model model.Optimize(); // Write model to file model.Write("sudoku.lp"); double[,,] x = model.Get(GRB.DoubleAttr.X, vars); Console.WriteLine(); for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { for (int v = 0; v < n; v++) { if (x[i,j,v] > 0.5) { Console.Write(v+1); } } } Console.WriteLine(); } // Dispose of model and env model.Dispose(); env.Dispose(); } catch (GRBException e) { Console.WriteLine("Error code: " + e.ErrorCode + ". " + e.Message); } } }