2 * Specialized implementation for perfect bipartite matching.
3 * @author Sebastian Hack
15 #include "bipartite.h"
23 bipartite_t *bipartite_new(int n_left, int n_right)
28 size = n_left > 0 ? n_left - 1 : 0;
29 gr = xmalloc(sizeof(*gr) + size * sizeof(void *));
30 memset(gr, 0, sizeof(*gr));
33 gr->n_right = n_right;
35 for(i = 0; i < n_left; ++i)
36 gr->adj[i] = bitset_malloc(n_right);
41 void bipartite_free(bipartite_t *gr)
44 for(i = 0; i < gr->n_left; ++i)
45 bitset_free(gr->adj[i]);
49 void bipartite_add(bipartite_t *gr, int i, int j)
51 assert(i < gr->n_left && j < gr->n_right);
52 bitset_set(gr->adj[i], j);
55 void bipartite_remv(bipartite_t *gr, int i, int j)
57 assert(i < gr->n_left && j < gr->n_right);
58 bitset_clear(gr->adj[i], j);
61 int bipartite_adj(const bipartite_t *gr, int i, int j)
63 assert(i < gr->n_left && j < gr->n_right);
64 return bitset_is_set(gr->adj[i], j);
67 static int apply_alternating_path(const bipartite_t *gr, int *matching,
68 bitset_t *matched_left, bitset_t *matched_right)
71 int done_something = 0;
72 bitset_t *tmp = bitset_alloca(gr->n_right);
74 for(left = 0; left < gr->n_left; ++left) {
75 bitset_t *left_adj = gr->adj[left];
78 bitset_copy(tmp, left_adj);
80 if(matching[left] >= 0) {
81 int old_right = matching[left];
83 /* Check of all neighbors of the left node are already matched.
84 * We cannot improve this edge then. */
85 if(bitset_contains(left_adj, matched_right))
88 bitset_andnot(tmp, matched_right);
89 right = bitset_next_set(tmp, 0);
94 We have to find another left node which has the old right one as a neighbor.
95 This node must not be part of a matching
97 for(i = 0; i < gr->n_left; ++i)
98 if(i != left && bitset_is_set(gr->adj[i], old_right) && !bitset_is_set(matched_left, i))
101 /* If no such node can be found, exit. */
105 /* Else, we can improve this edge. */
106 matching[left] = right;
107 matching[i] = old_right;
108 bitset_set(matched_left, i);
109 bitset_set(matched_right, right);
114 /* We have to create a new single edge */
116 assert(!bitset_is_set(matched_left, left));
118 bitset_andnot(tmp, matched_right);
119 if(bitset_popcnt(tmp) == 0)
122 right = bitset_min(tmp);
123 assert(!bitset_is_set(matched_right, right));
124 matching[left] = right;
125 bitset_set(matched_left, left);
126 bitset_set(matched_right, right);
131 return done_something;
134 void bipartite_matching(const bipartite_t *gr, int *matching)
136 bitset_t *matched_left = bitset_alloca(gr->n_left);
137 bitset_t *matched_right = bitset_alloca(gr->n_right);
139 memset(matching, -1, gr->n_left * sizeof(int));
140 while(apply_alternating_path(gr, matching, matched_left, matched_right));
143 void bipartite_dump_f(FILE *f, const bipartite_t *gr)
147 for(i = 0; i < gr->n_left; ++i) {
148 fprintf(f, "%d: ", i);
149 bitset_fprint(f, gr->adj[i]);
154 void bipartite_dump(const char *name, const bipartite_t *gr) {
155 FILE *f = fopen(name, "w");
158 bipartite_dump_f(f, gr);