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### sudoku_c++.cpp

/* Copyright 2016, Gurobi Optimization, Inc. */
/*
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*.
*/

#include "gurobi_c++.h"
#include <sstream>
using namespace std;

#define sd 3
#define n (sd*sd)

string itos(int i) {stringstream s; s << i; return s.str(); }

int
main(int   argc,
char *argv[])
{
try {
GRBEnv env = GRBEnv();
GRBModel model = GRBModel(env);

GRBVar vars[n][n][n];
int i, j, v;

// Create 3-D array of model variables

for (i = 0; i < n; i++) {
for (j = 0; j < n; j++) {
for (v = 0; v < n; v++) {
string s = "G_" + itos(i) + "_" + itos(j) + "_" + itos(v);
vars[i][j][v] = model.addVar(0.0, 1.0, 0.0, GRB_BINARY, s);
}
}
}

// Integrate variables into model

model.update();

// Each cell must take one value

for (i = 0; i < n; i++) {
for (j = 0; j < n; j++) {
GRBLinExpr expr = 0;
for (v = 0; v < n; v++)
expr += vars[i][j][v];
string s = "V_" + itos(i) + "_" + itos(j);
}
}

// Each value appears once per row

for (i = 0; i < n; i++) {
for (v = 0; v < n; v++) {
GRBLinExpr expr = 0;
for (j = 0; j < n; j++)
expr += vars[i][j][v];
string s = "R_" + itos(i) + "_" + itos(v);
}
}

// Each value appears once per column

for (j = 0; j < n; j++) {
for (v = 0; v < n; v++) {
GRBLinExpr expr = 0;
for (i = 0; i < n; i++)
expr += vars[i][j][v];
string s = "C_" + itos(j) + "_" + itos(v);
}
}

// Each value appears once per sub-grid

for (v = 0; v < n; v++) {
for (int i0 = 0; i0 < sd; i0++) {
for (int j0 = 0; j0 < sd; j0++) {
GRBLinExpr expr = 0;
for (int i1 = 0; i1 < sd; i1++) {
for (int j1 = 0; j1 < sd; j1++) {
expr += vars[i0*sd+i1][j0*sd+j1][v];
}
}

string s = "Sub_" + itos(v) + "_" + itos(i0) + "_" + itos(j0);
}
}
}

// Fix variables associated with pre-specified cells

char input[10];
for (i = 0; i < n; i++) {
cin >> input;
for (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");

cout << endl;
for (i = 0; i < n; i++) {
for (j = 0; j < n; j++) {
for (v = 0; v < n; v++) {
if (vars[i][j][v].get(GRB_DoubleAttr_X) > 0.5)
cout << v+1;
}
}
cout << endl;
}
cout << endl;
} catch(GRBException e) {
cout << "Error code = " << e.getErrorCode() << endl;
cout << e.getMessage() << endl;
} catch (...) {
cout << "Error during optimization" << endl;
}

return 0;
}


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