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Sudoku.java

/* Copyright 2019, Gurobi Optimization, LLC */ /* Sudoku example. The Sudoku board is a 9x9 grid, which is further divided into a 3x3 grid of 3x3 grids. Each cell in the grid must take a value from 0 to 9. No two grid cells in the same row, column, or 3x3 subgrid may take the same value. In the MIP formulation, binary variables x[i,j,v] indicate whether cell  takes value 'v'. The constraints are as follows: 1. Each cell must take exactly one value (sum_v x[i,j,v] = 1) 2. Each value is used exactly once per row (sum_i x[i,j,v] = 1) 3. Each value is used exactly once per column (sum_j x[i,j,v] = 1) 4. Each value is used exactly once per 3x3 subgrid (sum_grid x[i,j,v] = 1) Input datasets for this example can be found in examples/data/sudoku*. */ import gurobi.*; import java.io.*; public class Sudoku { public static void main(String[] args) { int n = 9; int s = 3; if (args.length < 1) { System.out.println("Usage: java Sudoku filename"); System.exit(1); } 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_" + String.valueOf(i) + "_" + String.valueOf(j) + "_" + String.valueOf(v); 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 = new GRBLinExpr(); expr.addTerms(null, vars[i][j]); String st = "V_" + String.valueOf(i) + "_" + String.valueOf(j); model.addConstr(expr, GRB.EQUAL, 1.0, st); } } // Each value appears once per row for (int i = 0; i < n; i++) { for (int v = 0; v < n; v++) { expr = new GRBLinExpr(); for (int j = 0; j < n; j++) expr.addTerm(1.0, vars[i][j][v]); String st = "R_" + String.valueOf(i) + "_" + String.valueOf(v); model.addConstr(expr, GRB.EQUAL, 1.0, st); } } // Each value appears once per column for (int j = 0; j < n; j++) { for (int v = 0; v < n; v++) { expr = new GRBLinExpr(); for (int i = 0; i < n; i++) expr.addTerm(1.0, vars[i][j][v]); String st = "C_" + String.valueOf(j) + "_" + String.valueOf(v); model.addConstr(expr, GRB.EQUAL, 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 = new GRBLinExpr(); 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_" + String.valueOf(v) + "_" + String.valueOf(i0) + "_" + String.valueOf(j0); model.addConstr(expr, GRB.EQUAL, 1.0, st); } } } // Fix variables associated with pre-specified cells File file = new File(args[0]); FileInputStream fis = new FileInputStream(file); byte[] input = new byte[n]; for (int i = 0; i < n; i++) { fis.read(input); for (int j = 0; j < n; j++) { int val = (int) input[j] - 48 - 1; // 0-based if (val >= 0) vars[i][j][val].set(GRB.DoubleAttr.LB, 1.0); } // read the endline byte fis.read(); } // Optimize model model.optimize(); // Write model to file model.write("sudoku.lp"); double[][][] x = model.get(GRB.DoubleAttr.X, vars); System.out.println(); 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) { System.out.print(v+1); } } } System.out.println(); } // Dispose of model and environment model.dispose(); env.dispose(); } catch (GRBException e) { System.out.println("Error code: " + e.getErrorCode() + ". " + e.getMessage()); } catch (IOException e) { System.out.println("IO Error"); } } }