343 lines
6.7 KiB
C++
343 lines
6.7 KiB
C++
#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;
|
|
} |