void bipartite_matching(bipartite_t const *const gr, int *const matching)
{
bitset_t *const matched_left = bitset_alloca(gr->n_left);
bitset_t *const matched_right = bitset_alloca(gr->n_right);
memset(matching, -1, gr->n_left * sizeof(int));
while (apply_alternating_path(gr, matching, matched_left, matched_right)) {
}
}
static int apply_alternating_path(bipartite_t const *const gr,
int *const matching,
bitset_t *const matched_left,
bitset_t *const matched_right)
{
bool done_something = false;
bitset_t *const tmp = bitset_alloca(gr->n_right);
for (unsigned left = 0; left < gr->n_left; ++left) {
bitset_t *left_adj = gr->adj[left];
bitset_copy(tmp, left_adj);
if (matching[left] >= 0) {
int old_right = matching[left];
/* Check of all neighbors of the left node are already matched.
* We cannot improve this edge then. */
if (bitset_contains(left_adj, matched_right))
continue;
bitset_andnot(tmp, matched_right);
unsigned right = bitset_next_set(tmp, 0);
assert(right != ~0u);
/* We have to find another left node which has the old right one as
* a neighbor. This node must not be part of a matching */
unsigned i;
for (i = 0; i < gr->n_left; ++i)
if (i != left && bitset_is_set(gr->adj[i], old_right) && !bitset_is_set(matched_left, i))
break;
/* If no such node can be found, exit. */
if (i >= gr->n_left)
continue;
/* Else, we can improve this edge. */
matching[left] = right;
matching[i] = old_right;
bitset_set(matched_left, i);
bitset_set(matched_right, right);
done_something = true;
} else {
/* We have to create a new single edge */
assert(!bitset_is_set(matched_left, left));
bitset_andnot(tmp, matched_right);
if (bitset_is_empty(tmp))
continue;
unsigned right = bitset_next_set(tmp, 0);
assert(!bitset_is_set(matched_right, right));
matching[left] = right;
bitset_set(matched_left, left);
bitset_set(matched_right, right);
done_something = true;
}
}
return done_something;
}
/* kill all double-entries (Mij and Mji are set) */
matrix_foreach(m, e) {
double t_val;
assert(e->row != e->col && "Root has itself as arg. Ok. But the arg (=root) will always have the same color as root");
t_val = matrix_get(m, e->col, e->row);
if (fabs(t_val) > 1e-10) {
matrix_set(m, e->col, e->row, 0);
matrix_set(m, e->row, e->col, e->val + t_val);
}
}
c = ALLOCAN(int, size);
redo = 1;
fullrow = bitset_alloca(size);
/* kill 'all' rows containing only 1 entry */
while (redo) {
redo = 0;
/* count elements in rows */
memset(c, 0, size * sizeof(*c));
matrix_foreach(m, e)
c[e->row]++;
for (i = 0; i<size; ++i)
if (c[i] == 1 && ! bitset_is_set(fullrow, i)) {
redo = 1;
/* if the other row isn't empty move the e in there, else fill e's row */
matrix_elem_t const *const e = matrix_row_first(m, i);
