[13] | 1 | /* |
---|
| 2 | * $Id: graph_dfs.c,v 1.9 2005/04/15 23:24:21 fabio Exp $ |
---|
| 3 | */ |
---|
| 4 | |
---|
| 5 | #include "graph_int.h" |
---|
| 6 | |
---|
| 7 | static vertex_t * |
---|
| 8 | find_an_end_vertex(vertex_t *v, st_table *visit_list) |
---|
| 9 | { |
---|
| 10 | edge_t *e; |
---|
| 11 | vertex_t *dest; |
---|
| 12 | lsGen gen; |
---|
| 13 | |
---|
| 14 | if (lsLength(g_get_out_edges(v)) == 0) { |
---|
| 15 | return(v); |
---|
| 16 | } |
---|
| 17 | foreach_out_edge (v,gen,e) { |
---|
| 18 | (void) lsFinish(gen); |
---|
| 19 | dest = g_e_dest(e); |
---|
| 20 | if (st_insert(visit_list,(char *) dest,(char *) 0) == 1) { |
---|
| 21 | return(NIL(vertex_t)); |
---|
| 22 | } |
---|
| 23 | return(find_an_end_vertex(dest,visit_list)); |
---|
| 24 | /* NOTREACHED */ |
---|
| 25 | } |
---|
| 26 | /* no free out_edges */ |
---|
| 27 | return(NIL(vertex_t)); |
---|
| 28 | } |
---|
| 29 | |
---|
| 30 | static int |
---|
| 31 | dfs_recurr(vertex_t *v, st_table *dfs_list, array_t *dfs_array) |
---|
| 32 | { |
---|
| 33 | edge_t *e; |
---|
| 34 | lsGen gen; |
---|
| 35 | int val; |
---|
| 36 | |
---|
| 37 | if (st_lookup_int(dfs_list,(char *) v, &val)) { |
---|
| 38 | return(val == 0); |
---|
| 39 | } |
---|
| 40 | (void) st_insert(dfs_list,(char *) v,(char *) 1); |
---|
| 41 | |
---|
| 42 | foreach_in_edge (v,gen,e) { |
---|
| 43 | if (!dfs_recurr(g_e_source(e),dfs_list,dfs_array)) { |
---|
| 44 | return(0); |
---|
| 45 | } |
---|
| 46 | } |
---|
| 47 | (void) st_insert(dfs_list,(char *) v,(char *) 0); |
---|
| 48 | array_insert_last(vertex_t *,dfs_array,v); |
---|
| 49 | return(1); |
---|
| 50 | } |
---|
| 51 | |
---|
| 52 | static array_t * |
---|
| 53 | g_dfs_int(graph_t *g) |
---|
| 54 | { |
---|
| 55 | vertex_t *v; |
---|
| 56 | lsGen gen; |
---|
| 57 | array_t *dfs_array; |
---|
| 58 | st_table *visit_list,*dfs_list; |
---|
| 59 | int cycle = FALSE; |
---|
| 60 | |
---|
| 61 | dfs_array = array_alloc(vertex_t *,0); |
---|
| 62 | visit_list = st_init_table(st_ptrcmp,st_ptrhash); |
---|
| 63 | dfs_list = st_init_table(st_ptrcmp,st_ptrhash); |
---|
| 64 | |
---|
| 65 | foreach_vertex (g,gen,v) { |
---|
| 66 | if (!st_is_member(dfs_list,(char *) v)) { |
---|
| 67 | (void) st_insert(visit_list,(char *) v,(char *) 0); |
---|
| 68 | v = find_an_end_vertex(v,visit_list); |
---|
| 69 | if (v == NIL(vertex_t) || !dfs_recurr(v,dfs_list,dfs_array)) { |
---|
| 70 | cycle = TRUE; |
---|
| 71 | (void) lsFinish(gen); |
---|
| 72 | break; |
---|
| 73 | } |
---|
| 74 | } |
---|
| 75 | } |
---|
| 76 | |
---|
| 77 | st_free_table(visit_list); |
---|
| 78 | st_free_table(dfs_list); |
---|
| 79 | if (cycle == TRUE) { |
---|
| 80 | array_free(dfs_array); |
---|
| 81 | return(NIL(array_t)); |
---|
| 82 | } |
---|
| 83 | return(dfs_array); |
---|
| 84 | } |
---|
| 85 | |
---|
| 86 | array_t * |
---|
| 87 | g_dfs(graph_t *g) |
---|
| 88 | { |
---|
| 89 | array_t *x; |
---|
| 90 | |
---|
| 91 | x = g_dfs_int(g); |
---|
| 92 | if (x == NIL(array_t)) { |
---|
| 93 | fail("g_dfs: Graph has cycle"); |
---|
| 94 | } |
---|
| 95 | return(x); |
---|
| 96 | } |
---|
| 97 | |
---|
| 98 | int |
---|
| 99 | g_is_acyclic(graph_t *g) |
---|
| 100 | { |
---|
| 101 | array_t *x; |
---|
| 102 | |
---|
| 103 | x = g_dfs_int(g); |
---|
| 104 | if (x) { |
---|
| 105 | array_free(x); |
---|
| 106 | return(TRUE); |
---|
| 107 | } |
---|
| 108 | return(FALSE); |
---|
| 109 | } |
---|
| 110 | |
---|
| 111 | |
---|
| 112 | static int |
---|
| 113 | reachable_recurr(vertex_t *v, st_table *dfs_list) |
---|
| 114 | { |
---|
| 115 | edge_t *e; |
---|
| 116 | lsGen gen; |
---|
| 117 | int val; |
---|
| 118 | |
---|
| 119 | if (st_lookup_int(dfs_list,(char *) v, &val)) { |
---|
| 120 | return(val == 0); |
---|
| 121 | } |
---|
| 122 | (void) st_insert(dfs_list,(char *) v,(char *) 1); |
---|
| 123 | |
---|
| 124 | foreach_out_edge (v,gen,e) { |
---|
| 125 | reachable_recurr(g_e_dest(e),dfs_list); |
---|
| 126 | } |
---|
| 127 | (void) st_insert(dfs_list,(char *) v,(char *) 0); |
---|
| 128 | |
---|
| 129 | return(1); |
---|
| 130 | } |
---|
| 131 | |
---|
| 132 | /* compute reachable states from the initial states */ |
---|
| 133 | st_table * |
---|
| 134 | g_reachable(graph_t *g, st_table *init) |
---|
| 135 | { |
---|
| 136 | vertex_t *v; |
---|
| 137 | st_table *dfs_list; |
---|
| 138 | st_generator *stgen; |
---|
| 139 | |
---|
| 140 | dfs_list = st_init_table(st_ptrcmp, st_ptrhash); |
---|
| 141 | |
---|
| 142 | st_foreach_item(init, stgen, &v, NIL(char *)) { |
---|
| 143 | reachable_recurr(v,dfs_list); |
---|
| 144 | } |
---|
| 145 | |
---|
| 146 | return (dfs_list); |
---|
| 147 | } |
---|
| 148 | |
---|
| 149 | |
---|
| 150 | static int |
---|
| 151 | EF_recurr(vertex_t *v, st_table *EF_list) |
---|
| 152 | { |
---|
| 153 | edge_t *e; |
---|
| 154 | lsGen gen; |
---|
| 155 | int val; |
---|
| 156 | |
---|
| 157 | if (st_lookup_int(EF_list,(char *) v, &val)) { |
---|
| 158 | return(val == 0); |
---|
| 159 | } |
---|
| 160 | (void) st_insert(EF_list,(char *) v,(char *) 1); |
---|
| 161 | |
---|
| 162 | foreach_in_edge (v,gen,e) { |
---|
| 163 | EF_recurr(g_e_source(e),EF_list); |
---|
| 164 | } |
---|
| 165 | (void) st_insert(EF_list,(char *) v,(char *) 0); |
---|
| 166 | |
---|
| 167 | return(1); |
---|
| 168 | } |
---|
| 169 | |
---|
| 170 | /* compute EF(goal) of an automaton, might include unreachable states */ |
---|
| 171 | st_table * |
---|
| 172 | g_EF(graph_t *g, st_table *goal) |
---|
| 173 | { |
---|
| 174 | vertex_t *v; |
---|
| 175 | st_table *EF_list; |
---|
| 176 | st_generator *stgen; |
---|
| 177 | |
---|
| 178 | EF_list = st_init_table(st_ptrcmp, st_ptrhash); |
---|
| 179 | |
---|
| 180 | st_foreach_item(goal, stgen, &v, NIL(char *)) { |
---|
| 181 | EF_recurr(v,EF_list); |
---|
| 182 | } |
---|
| 183 | |
---|
| 184 | return (EF_list); |
---|
| 185 | } |
---|
| 186 | |
---|
| 187 | static void |
---|
| 188 | searchSCC( |
---|
| 189 | vertex_t *v, |
---|
| 190 | st_table *scc, |
---|
| 191 | st_table *old /*visited*/, |
---|
| 192 | lsList stack, |
---|
| 193 | st_table *onstack, |
---|
| 194 | int *countr) |
---|
| 195 | { |
---|
| 196 | int lowlink_v, dfnumber_v, lowlink_w, dfnumber_w; |
---|
| 197 | vertex_t *x, *w; |
---|
| 198 | st_table *component; |
---|
| 199 | lsGen gen; |
---|
| 200 | edge_t *e; |
---|
| 201 | |
---|
| 202 | lowlink_v = dfnumber_v = *countr; |
---|
| 203 | (*countr)++; |
---|
| 204 | st_insert(old, (char *)v, (char *)(long)dfnumber_v); |
---|
| 205 | st_insert(onstack, (char *)v, (char *)(long)lowlink_v); |
---|
| 206 | lsNewBegin(stack, (lsGeneric)v, NIL(lsHandle)); |
---|
| 207 | |
---|
| 208 | foreach_out_edge (v,gen,e) { |
---|
| 209 | w = g_e_dest(e); |
---|
| 210 | if (!st_is_member(old, (char *)w)) { |
---|
| 211 | searchSCC(w,scc,old,stack,onstack,countr); |
---|
| 212 | if(st_lookup_int(onstack, (char *)w, &lowlink_w) && |
---|
| 213 | lowlink_w < lowlink_v) { |
---|
| 214 | lowlink_v = lowlink_w; |
---|
| 215 | st_insert(onstack, (char *)v, (char *)(long)lowlink_v); |
---|
| 216 | } |
---|
| 217 | }else { |
---|
| 218 | st_lookup_int(old, (char *)w, &dfnumber_w); |
---|
| 219 | if (dfnumber_w < dfnumber_v && st_is_member(onstack, (char *)w)) { |
---|
| 220 | if (dfnumber_w < lowlink_v) { |
---|
| 221 | lowlink_v = dfnumber_w; |
---|
| 222 | st_insert(onstack, (char *)v, (char *)(long)lowlink_v); |
---|
| 223 | } |
---|
| 224 | } |
---|
| 225 | } |
---|
| 226 | } |
---|
| 227 | |
---|
| 228 | /* put current SCC into st_table, and then insert into 'scc' */ |
---|
| 229 | if (dfnumber_v == lowlink_v) { |
---|
| 230 | component = st_init_table(st_ptrcmp, st_ptrhash); |
---|
| 231 | while (lsDelBegin(stack, &x) != LS_NOMORE) { |
---|
| 232 | st_insert(component, (char *)x, NIL(char)); |
---|
| 233 | st_delete(onstack, &x, NIL(char *)); |
---|
| 234 | if (v == x) break; |
---|
| 235 | } |
---|
| 236 | st_insert(scc, (char *)component, NIL(char)); /* is component fair? */ |
---|
| 237 | } |
---|
| 238 | } |
---|
| 239 | |
---|
| 240 | /* compute the strongly connected components of a graph (Tarjan's alg.) */ |
---|
| 241 | st_table * |
---|
| 242 | g_SCC(graph_t *g, st_table *init) |
---|
| 243 | { |
---|
| 244 | vertex_t *v; |
---|
| 245 | lsList stack; |
---|
| 246 | st_table *old, *onstack, *scc; |
---|
| 247 | st_generator *stgen; |
---|
| 248 | int countr = 0; |
---|
| 249 | |
---|
| 250 | scc = st_init_table(st_ptrcmp, st_ptrhash); |
---|
| 251 | |
---|
| 252 | stack = lsCreate(); |
---|
| 253 | old = st_init_table(st_ptrcmp, st_ptrhash); |
---|
| 254 | onstack = st_init_table(st_ptrcmp, st_ptrhash); |
---|
| 255 | st_foreach_item(init, stgen, &v, NIL(char *)) { |
---|
| 256 | if (!st_is_member(old, (char *)v)) |
---|
| 257 | searchSCC(v,scc,old,stack,onstack,&countr); |
---|
| 258 | } |
---|
| 259 | lsDestroy(stack, (void (*)(lsGeneric))0 ); |
---|
| 260 | st_free_table(old); |
---|
| 261 | st_free_table(onstack); |
---|
| 262 | |
---|
| 263 | return scc; |
---|
| 264 | } |
---|