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sudoku_c.c

/* 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 <stdlib.h>
#include <stdio.h>
#include <string.h>
#include "gurobi_c.h"

#define SUBDIM  3
#define DIM    (SUBDIM*SUBDIM)

int
main(int   argc,
char *argv[])
{
FILE     *fp    = NULL;
GRBenv   *env   = NULL;
GRBmodel *model = NULL;
int       board[DIM][DIM];
char      inputline[100];
int       ind[DIM];
double    val[DIM];
double    lb[DIM*DIM*DIM];
char      vtype[DIM*DIM*DIM];
char     *names[DIM*DIM*DIM];
char      namestorage[10*DIM*DIM*DIM];
char     *cursor;
int       optimstatus;
double    objval;
int       zero = 0;
int       i, j, v, ig, jg, count;
int       error = 0;

if (argc < 2) {
fprintf(stderr, "Usage: sudoku_c datafile\n");
exit(1);
}

fp = fopen(argv[1], "r");
if (fp == NULL) {
fprintf(stderr, "Error: unable to open input file %s\n", argv[1]);
exit(1);
}

for (i = 0; i < DIM; i++) {
fgets(inputline, 100, fp);
if (strlen(inputline) < 9) {
fprintf(stderr, "Error: not enough board positions specified\n");
exit(1);
}
for (j = 0; j < DIM; j++) {
board[i][j] = (int) inputline[j] - (int) '1';
if (board[i][j] < 0 || board[i][j] >= DIM)
board[i][j] = -1;
}
}

/* Create an empty model */

cursor = namestorage;
for (i = 0; i < DIM; i++) {
for (j = 0; j < DIM; j++) {
for (v = 0; v < DIM; v++) {
if (board[i][j] == v)
lb[i*DIM*DIM+j*DIM+v] = 1;
else
lb[i*DIM*DIM+j*DIM+v] = 0;
vtype[i*DIM*DIM+j*DIM+v] = GRB_BINARY;

names[i*DIM*DIM+j*DIM+v] = cursor;
sprintf(names[i*DIM*DIM+j*DIM+v], "x[%d,%d,%d]", i, j, v+1);
cursor += strlen(names[i*DIM*DIM+j*DIM+v]) + 1;
}
}
}

/* Create environment */

error = GRBloadenv(&env, "sudoku.log");
if (error) goto QUIT;

/* Create new model */

error = GRBnewmodel(env, &model, "sudoku", DIM*DIM*DIM, NULL, lb, NULL,
vtype, names);
if (error) goto QUIT;

/* Each cell gets a value */

for (i = 0; i < DIM; i++) {
for (j = 0; j < DIM; j++) {
for (v = 0; v < DIM; v++) {
ind[v] = i*DIM*DIM + j*DIM + v;
val[v] = 1.0;
}

error = GRBaddconstr(model, DIM, ind, val, GRB_EQUAL, 1.0, NULL);
if (error) goto QUIT;
}
}

/* Each value must appear once in each row */

for (v = 0; v < DIM; v++) {
for (j = 0; j < DIM; j++) {
for (i = 0; i < DIM; i++) {
ind[i] = i*DIM*DIM + j*DIM + v;
val[i] = 1.0;
}

error = GRBaddconstr(model, DIM, ind, val, GRB_EQUAL, 1.0, NULL);
if (error) goto QUIT;
}
}

/* Each value must appear once in each column */

for (v = 0; v < DIM; v++) {
for (i = 0; i < DIM; i++) {
for (j = 0; j < DIM; j++) {
ind[j] = i*DIM*DIM + j*DIM + v;
val[j] = 1.0;
}

error = GRBaddconstr(model, DIM, ind, val, GRB_EQUAL, 1.0, NULL);
if (error) goto QUIT;
}
}

/* Each value must appear once in each subgrid */

for (v = 0; v < DIM; v++) {
for (ig = 0; ig < SUBDIM; ig++) {
for (jg = 0; jg < SUBDIM; jg++) {
count = 0;
for (i = ig*SUBDIM; i < (ig+1)*SUBDIM; i++) {
for (j = jg*SUBDIM; j < (jg+1)*SUBDIM; j++) {
ind[count] = i*DIM*DIM + j*DIM + v;
val[count] = 1.0;
count++;
}
}

error = GRBaddconstr(model, DIM, ind, val, GRB_EQUAL, 1.0, NULL);
if (error) goto QUIT;
}
}
}

/* Optimize model */

error = GRBoptimize(model);
if (error) goto QUIT;

/* Write model to 'sudoku.lp' */

error = GRBwrite(model, "sudoku.lp");
if (error) goto QUIT;

/* Capture solution information */

error = GRBgetintattr(model, GRB_INT_ATTR_STATUS, &optimstatus);
if (error) goto QUIT;

error = GRBgetdblattr(model, GRB_DBL_ATTR_OBJVAL, &objval);
if (error) goto QUIT;

printf("\nOptimization complete\n");
if (optimstatus == GRB_OPTIMAL)
printf("Optimal objective: %.4e\n", objval);
else if (optimstatus == GRB_INF_OR_UNBD)
printf("Model is infeasible or unbounded\n");
else
printf("Optimization was stopped early\n");
printf("\n");

QUIT:

/* Error reporting */

if (error) {
printf("ERROR: %s\n", GRBgeterrormsg(env));
exit(1);
}

/* Free model */

GRBfreemodel(model);

/* Free environment */

GRBfreeenv(env);

return 0;
}


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