/*
 * latin_squares.c
 *
 *  Created on: 12/04/2017

 *      Author: pedro

 *
 *      https://www.cril.univ-artois.fr/~lecoutre/benchmarks.html#
 *
 *      Pandiagonal Latin Square problem:
 *      All rows and columns of a matrix must contain different values (taken from 0 to n-1).
 *
 */

#include "latin_squares.h"

#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>

#include "../config.h"
#include "../constraints/fake_all_different.h"
#include "../split.h"
#include "../variables.h"

/*
 * Solve an instance of Latin Square problem with N values
 */

void run_latin_squares(int* csp_dims) {

	int n = csp_dims[0];
	unsigned long result;
	int i, j;

	// vector with the IDs of all the variables

	unsigned int** vs_id = malloc((unsigned int)n * 2 * sizeof(unsigned int*));

	for (i = 0; i < n * 2; i++) {

		vs_id[i] = malloc((unsigned int)n * 2 * sizeof(unsigned int));

	}

	unsigned int* c_vs_id = malloc((unsigned int)n * sizeof(unsigned int));

	// Create all the variables
	for (i = 0; i < n; i++) {
		for (j = 0; j < n; j++) {

			vs_id[i][j] = v_new_range(0, (unsigned int)n - 1, true);

		}
	}

	// horizontal lines all_diff constraints
	for (i = 0; i < n; i++) {
		for (j = 0; j < n; j++) {
			c_vs_id[j] = vs_id[i][j];
		}

		c_fake_all_different(c_vs_id, (unsigned int)n);

	}

	// vertical lines all_diff constraints
	for (i = 0; i < n; i++) {
		for (j = 0; j < n; j++) {
			c_vs_id[j] = vs_id[j][i];
		}

		c_fake_all_different(c_vs_id, (unsigned int)n);

	}

	if (FINDING_ONE_SOLUTION) {
		printf("\nFinding one solution for Latin Squares with %u numbers.\n", n);
	} else {
		printf("\nCounting all the solutions for Latin Squares with %u numbers.\n", n);
	}

	// Solve the CSP
	result = solve_CSP();

	if (FINDING_ONE_SOLUTION && result == 1) {
		printf("Solution:\n");
		for (i = 0; i < n; i++) {

			vs_print_single_val(vs_id[i], (unsigned int)n, 1);

			printf("\n");
		}
	} else {
		printf("%lu solution(s) found\n", result);
	}

	for (i = 0; i < n * 2; i++) {
		free(vs_id[i]);
	}
	free(vs_id);
	free(c_vs_id);
}