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### Sudoku.java

/* Copyright 2021, 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 <i,j> 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);
}
}
}

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();
String st = "V_" + String.valueOf(i) + "_" + String.valueOf(j);
}
}

// 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++)
String st = "R_" + String.valueOf(i) + "_" + String.valueOf(v);
}
}

// 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++)
String st = "C_" + String.valueOf(j) + "_" + String.valueOf(v);
}
}

// 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++) {
}
}
String st = "Sub_" + String.valueOf(v) + "_" + String.valueOf(i0)
+ "_" + String.valueOf(j0);
}
}
}

// 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++) {
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);
}
}

// 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");
}
}
}


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