/*
 * steiner_triples.c
 *
 *  Created on: 26/03/2017
 *      Author: pedro
 *
 *      http://www.csplib.org/Problems/prob044/
 *      https://github.com/MiniZinc/minizinc-benchmarks/tree/master/steiner-triples
 *
 *		Steiner Triples:
 *      The following program computes so-called Steiner triplets. These are triplets
 *      of numbers from 1 to n such that any two triplets have at most one element in common.
 */

#include "steiner.h"

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

#include "../config.h"
#include "../constraints/at_most_one.h"
#include "../constraints/le.h"
#include "../constraints/linear_var.h"
#include "../constraints/lt.h"
#include "../split.h"
#include "../variables.h"

/*
 * Solve an instance of Steiner Triples problems with N numbers
 */
void run_steiner(int* csp_dims) {
	int n = csp_dims[0];
	unsigned long result;
	int n_triples = (n * (n - 1)) / 6;
	unsigned int* sum_vs_id = malloc((unsigned long)n_triples * sizeof(unsigned int));
	int cs[] = {(n + 1) * (n + 1), n + 1, 1};
	unsigned int* triples = malloc((unsigned long)n_triples * 3 * sizeof(unsigned int));
	int* cards = malloc((unsigned long)n_triples * sizeof(int));
	int i;

	for (i = 0; i < n_triples * 3; i++) {
		triples[i] = v_new_range(0, (unsigned int)n - 1, true);
	}

	for (i = 0; i < n_triples; i++) {
		cards[i] = 3;
	}

	c_at_most_one(triples, cards, (unsigned int)n_triples);

	for (i = 0; i < n_triples; i++) {
		c_lt(triples[i * 3], triples[i * 3 + 1]);
		c_lt(triples[i * 3], triples[i * 3 + 2]);
		c_lt(triples[i * 3 + 1], triples[i * 3 + 2]);

		sum_vs_id[i] = v_new_range(0, ((unsigned int)n + 1) * ((unsigned int)n + 1) * (unsigned int)n + ((unsigned int)n + 1) * ((unsigned int)n - 1) + (unsigned int)n - 2, false);

		c_linear_var(cs, &triples[i * 3], 3, sum_vs_id[i]);
	}

	// Symmetry breaking
	for (i = 1; i < n_triples; i++) {
		c_le(sum_vs_id[i - 1], sum_vs_id[i]);
	}

	if (FINDING_ONE_SOLUTION) {
		printf("\nFinding one solution for Steiner Triples with N=%u.\n", n);
	} else {
		printf("\nCounting all the solutions for Steiner Triples with N=%u.\n", n);
	}

	// Solve the CSP
	result = solve_CSP();

	if (FINDING_ONE_SOLUTION && result == 1) {
		printf("Solution:\n");

		printf("{%u,%u,%u}", v_get_min(triples[0]) + 1, v_get_min(triples[1]) + 1, v_get_min(triples[2]) + 1);
		for (i = 1; i < n_triples; i++) {
			printf(",{%u,%u,%u}", v_get_min(triples[i * 3]) + 1, v_get_min(triples[i * 3 + 1]) + 1, v_get_min(triples[i * 3 + 2]) + 1);
		}
		printf("\n");

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

	free(triples);
	free(cards);
	free(sum_vs_id);
}