lapjv.cpp

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

#include "lapjv.h"

/** Column-reduction and reduction transfer for a dense cost matrix.
 */
int_t _ccrrt_dense(const uint_t n, cost_t *cost[],
	int_t *free_rows, int_t *x, int_t *y, cost_t *v)
{
	int_t n_free_rows;
	boolean *unique;

	for (uint_t i = 0; i < n; i++) {
		x[i] = -1;
		v[i] = LARGE;
		y[i] = 0;
	}
	for (uint_t i = 0; i < n; i++) {
		for (uint_t j = 0; j < n; j++) {
			const cost_t c = cost[i][j];
			if (c < v[j]) {
				v[j] = c;
				y[j] = i;
			}
			PRINTF("i=%d, j=%d, c[i,j]=%f, v[j]=%f y[j]=%d\n", i, j, c, v[j], y[j]);
		}
	}
	PRINT_COST_ARRAY(v, n);
	PRINT_INDEX_ARRAY(y, n);
	NEW(unique, boolean, n);
	memset(unique, TRUE, n);
	{
		int_t j = n;
		do {
			j--;
			const int_t i = y[j];
			if (x[i] < 0) {
				x[i] = j;
			}
			else {
				unique[i] = FALSE;
				y[j] = -1;
			}
		} while (j > 0);
	}
	n_free_rows = 0;
	for (uint_t i = 0; i < n; i++) {
		if (x[i] < 0) {
			free_rows[n_free_rows++] = i;
		}
		else if (unique[i]) {
			const int_t j = x[i];
			cost_t min = LARGE;
			for (uint_t j2 = 0; j2 < n; j2++) {
				if (j2 == (uint_t)j) {
					continue;
				}
				const cost_t c = cost[i][j2] - v[j2];
				if (c < min) {
					min = c;
				}
			}
			PRINTF("v[%d] = %f - %f\n", j, v[j], min);
			v[j] -= min;
		}
	}
	FREE(unique);
	return n_free_rows;
}


/** Augmenting row reduction for a dense cost matrix.
 */
int_t _carr_dense(
	const uint_t n, cost_t *cost[],
	const uint_t n_free_rows,
	int_t *free_rows, int_t *x, int_t *y, cost_t *v)
{
	uint_t current = 0;
	int_t new_free_rows = 0;
	uint_t rr_cnt = 0;
	PRINT_INDEX_ARRAY(x, n);
	PRINT_INDEX_ARRAY(y, n);
	PRINT_COST_ARRAY(v, n);
	PRINT_INDEX_ARRAY(free_rows, n_free_rows);
	while (current < n_free_rows) {
		int_t i0;
		int_t j1, j2;
		cost_t v1, v2, v1_new;
		boolean v1_lowers;

		rr_cnt++;
		PRINTF("current = %d rr_cnt = %d\n", current, rr_cnt);
		const int_t free_i = free_rows[current++];
		j1 = 0;
		v1 = cost[free_i][0] - v[0];
		j2 = -1;
		v2 = LARGE;
		for (uint_t j = 1; j < n; j++) {
			PRINTF("%d = %f %d = %f\n", j1, v1, j2, v2);
			const cost_t c = cost[free_i][j] - v[j];
			if (c < v2) {
				if (c >= v1) {
					v2 = c;
					j2 = j;
				}
				else {
					v2 = v1;
					v1 = c;
					j2 = j1;
					j1 = j;
				}
			}
		}
		i0 = y[j1];
		v1_new = v[j1] - (v2 - v1);
		v1_lowers = v1_new < v[j1];
		PRINTF("%d %d 1=%d,%f 2=%d,%f v1'=%f(%d,%g) \n", free_i, i0, j1, v1, j2, v2, v1_new, v1_lowers, v[j1] - v1_new);
		if (rr_cnt < current * n) {
			if (v1_lowers) {
				v[j1] = v1_new;
			}
			else if (i0 >= 0 && j2 >= 0) {
				j1 = j2;
				i0 = y[j2];
			}
			if (i0 >= 0) {
				if (v1_lowers) {
					free_rows[--current] = i0;
				}
				else {
					free_rows[new_free_rows++] = i0;
				}
			}
		}
		else {
			PRINTF("rr_cnt=%d >= %d (current=%d * n=%d)\n", rr_cnt, current * n, current, n);
			if (i0 >= 0) {
				free_rows[new_free_rows++] = i0;
			}
		}
		x[free_i] = j1;
		y[j1] = free_i;
	}
	return new_free_rows;
}


/** Find columns with minimum d[j] and put them on the SCAN list.
 */
uint_t _find_dense(const uint_t n, uint_t lo, cost_t *d, int_t *cols, int_t *y)
{
	uint_t hi = lo + 1;
	cost_t mind = d[cols[lo]];
	for (uint_t k = hi; k < n; k++) {
		int_t j = cols[k];
		if (d[j] <= mind) {
			if (d[j] < mind) {
				hi = lo;
				mind = d[j];
			}
			cols[k] = cols[hi];
			cols[hi++] = j;
		}
	}
	return hi;
}


// Scan all columns in TODO starting from arbitrary column in SCAN
// and try to decrease d of the TODO columns using the SCAN column.
int_t _scan_dense(const uint_t n, cost_t *cost[],
	uint_t *plo, uint_t*phi,
	cost_t *d, int_t *cols, int_t *pred,
	int_t *y, cost_t *v)
{
	uint_t lo = *plo;
	uint_t hi = *phi;
	cost_t h, cred_ij;

	while (lo != hi) {
		int_t j = cols[lo++];
		const int_t i = y[j];
		const cost_t mind = d[j];
		h = cost[i][j] - v[j] - mind;
		PRINTF("i=%d j=%d h=%f\n", i, j, h);
		// For all columns in TODO
		for (uint_t k = hi; k < n; k++) {
			j = cols[k];
			cred_ij = cost[i][j] - v[j] - h;
			if (cred_ij < d[j]) {
				d[j] = cred_ij;
				pred[j] = i;
				if (cred_ij == mind) {
					if (y[j] < 0) {
						return j;
					}
					cols[k] = cols[hi];
					cols[hi++] = j;
				}
			}
		}
	}
	*plo = lo;
	*phi = hi;
	return -1;
}


/** Single iteration of modified Dijkstra shortest path algorithm as explained in the JV paper.
 *
 * This is a dense matrix version.
 *
 * \return The closest free column index.
 */
int_t find_path_dense(
	const uint_t n, cost_t *cost[],
	const int_t start_i,
	int_t *y, cost_t *v,
	int_t *pred)
{
	uint_t lo = 0, hi = 0;
	int_t final_j = -1;
	uint_t n_ready = 0;
	int_t *cols;
	cost_t *d;

	NEW(cols, int_t, n);
	NEW(d, cost_t, n);

	for (uint_t i = 0; i < n; i++) {
		cols[i] = i;
		pred[i] = start_i;
		d[i] = cost[start_i][i] - v[i];
	}
	PRINT_COST_ARRAY(d, n);
	while (final_j == -1) {
		// No columns left on the SCAN list.
		if (lo == hi) {
			PRINTF("%d..%d -> find\n", lo, hi);
			n_ready = lo;
			hi = _find_dense(n, lo, d, cols, y);
			PRINTF("check %d..%d\n", lo, hi);
			PRINT_INDEX_ARRAY(cols, n);
			for (uint_t k = lo; k < hi; k++) {
				const int_t j = cols[k];
				if (y[j] < 0) {
					final_j = j;
				}
			}
		}
		if (final_j == -1) {
			PRINTF("%d..%d -> scan\n", lo, hi);
			final_j = _scan_dense(
				n, cost, &lo, &hi, d, cols, pred, y, v);
			PRINT_COST_ARRAY(d, n);
			PRINT_INDEX_ARRAY(cols, n);
			PRINT_INDEX_ARRAY(pred, n);
		}
	}

	PRINTF("found final_j=%d\n", final_j);
	PRINT_INDEX_ARRAY(cols, n);
	{
		const cost_t mind = d[cols[lo]];
		for (uint_t k = 0; k < n_ready; k++) {
			const int_t j = cols[k];
			v[j] += d[j] - mind;
		}
	}

	FREE(cols);
	FREE(d);

	return final_j;
}


/** Augment for a dense cost matrix.
 */
int_t _ca_dense(
	const uint_t n, cost_t *cost[],
	const uint_t n_free_rows,
	int_t *free_rows, int_t *x, int_t *y, cost_t *v)
{
	int_t *pred;

	NEW(pred, int_t, n);

	for (int_t *pfree_i = free_rows; pfree_i < free_rows + n_free_rows; pfree_i++) {
		int_t i = -1, j;
		uint_t k = 0;

		PRINTF("looking at free_i=%d\n", *pfree_i);
		j = find_path_dense(n, cost, *pfree_i, y, v, pred);
		ASSERT(j >= 0);
		ASSERT(j < n);
		while (i != *pfree_i) {
			PRINTF("augment %d\n", j);
			PRINT_INDEX_ARRAY(pred, n);
			i = pred[j];
			PRINTF("y[%d]=%d -> %d\n", j, y[j], i);
			y[j] = i;
			PRINT_INDEX_ARRAY(x, n);
			SWAP_INDICES(j, x[i]);
			k++;
			if (k >= n) {
				ASSERT(FALSE);
			}
		}
	}
	FREE(pred);
	return 0;
}


/** Solve dense sparse LAP.
 */
int lapjv_internal(
	const uint_t n, cost_t *cost[],
	int_t *x, int_t *y)
{
	int ret;
	int_t *free_rows;
	cost_t *v;

	NEW(free_rows, int_t, n);
	NEW(v, cost_t, n);
	ret = _ccrrt_dense(n, cost, free_rows, x, y, v);
	int i = 0;
	while (ret > 0 && i < 2) {
		ret = _carr_dense(n, cost, ret, free_rows, x, y, v);
		i++;
	}
	if (ret > 0) {
		ret = _ca_dense(n, cost, ret, free_rows, x, y, v);
	}
	FREE(v);
	FREE(free_rows);
	return ret;
}