向陈越姥姥哭诉----关键活动
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1 /* 2 * keyPath.c 3 * 4 * Created on: 2017年5月17日 5 * Author: ygh 6 */ 7 8 #include <stdio.h> 9 #include <stdlib.h> 10 11 #define MAX_VERTEX_NUM 100 /*define the max number of the vertex*/ 12 #define INFINITY 65535 /*define double byte no negitive integer max number is 65535*/ 13 #define ERROR -1 14 15 typedef int vertex; /*define the data type of the vertex*/ 16 typedef int weightType; /*define the data type of the weight*/ 17 typedef char dataType; /*define the data type of the vertex value*/ 18 19 vertex inputOrder[MAX_VERTEX_NUM][MAX_VERTEX_NUM]; 20 /*define the data structure of the Edge*/ 21 typedef struct eNode *ptrToENode; 22 typedef struct eNode { 23 vertex v1, v2; /*two vertex between the edge <v1,v2>*/ 24 weightType weight; /*the value of the edge\'s weight */ 25 }; 26 typedef ptrToENode edge; 27 28 /*==================A adjacent link to describe a graph=========================================*/ 29 /*define the data structure adjacent table node*/ 30 typedef struct adjNode *ptrToAdjNode; 31 typedef struct adjNode { 32 vertex adjVerx; /*the index of the vertex*/ 33 weightType weight; /*the value of the weight*/ 34 ptrToAdjNode next; /*the point to point the next node*/ 35 }; 36 37 /*define the data structure of the adjacent head*/ 38 typedef struct vNode *ptrToVNode; 39 typedef struct vNode { 40 ptrToAdjNode head; /*the point to point the adjacent table node*/ 41 dataType data; /*the space to store the name of the vertex,but some time the vertex has no names*/ 42 weightType earliest; /*The earliest data of the project*/ 43 weightType latest; /*The latest time*/ 44 } adjList[MAX_VERTEX_NUM]; 45 46 /*define the data structure of graph*/ 47 typedef struct gLNode *ptrTogLNode; 48 typedef struct gLNode { 49 int vertex_number; /*the number of the vertex*/ 50 int edge_nunber; /*the number of the edge*/ 51 adjList g; /*adjacent table*/ 52 }; 53 typedef ptrTogLNode adjacentTableGraph; /*a graph show by adjacent table*/ 54 55 /* 56 create a graph given the vertex number. 57 @param vertexNum The verter number of the graph 58 @return a graph with vertex but no any egdgs 59 */ 60 adjacentTableGraph createLGraph(int vertexNum) { 61 adjacentTableGraph graph; 62 63 vertex v; 64 graph = (adjacentTableGraph) malloc(sizeof(struct gLNode)); 65 graph->vertex_number = vertexNum; 66 graph->edge_nunber = 0; 67 /*initialize the adjacent table*/ 68 for (v = 0; v < graph->vertex_number; v++) { 69 graph->g[v].head = NULL; 70 graph->g[v].earliest = 0; 71 graph->g[v].latest = INFINITY; 72 } 73 return graph; 74 } 75 76 /* 77 insert a edge to graph.We will distinct oriented graph and undirected graph 78 The e->v1 and e->v2 are the vertexs\' indexs in the adjacent table 79 @param graph The graph you want to insert edge 80 @param e The edge you want to insert the graph 81 @param isOriented Whether the graph is oriented graph.If the graph is oriented 82 we will set adjacent table graph[v1]->head=v2 and set graph[v1].head=v2 83 otherwise we only set graph[v1].head=v2 84 */ 85 void insertEdgeToLink(adjacentTableGraph graph, edge e, int isOriented) { 86 /*build node<v1,v2>*/ 87 ptrToAdjNode newNode; 88 newNode = (ptrToAdjNode) malloc(sizeof(struct adjNode)); 89 newNode->adjVerx = e->v2; 90 newNode->weight = e->weight; 91 newNode->next = graph->g[e->v1].head; 92 graph->g[e->v1].head = newNode; 93 /*if the graph is directed graph*/ 94 if (!isOriented) { 95 newNode = (ptrToAdjNode) malloc(sizeof(struct adjNode)); 96 newNode->adjVerx = e->v1; 97 newNode->weight = e->weight; 98 newNode->next = graph->g[e->v2].head; 99 graph->g[e->v2].head = newNode; 100 } 101 } 102 103 /* 104 build a graph stored by adjacent table 105 */ 106 adjacentTableGraph buildLGraph(int isOrdered) { 107 adjacentTableGraph graph; 108 edge e; 109 vertex i; 110 int vertex_num; 111 112 scanf("%d", &vertex_num); 113 graph = createLGraph(vertex_num); 114 scanf("%d", &(graph->edge_nunber)); 115 if (graph->edge_nunber) { 116 e = (edge) malloc(sizeof(struct eNode)); 117 for (i = 0; i < graph->edge_nunber; i++) { 118 scanf("%d %d %d", &e->v1, &e->v2, &e->weight); 119 e->v1--; 120 e->v2--; 121 insertEdgeToLink(graph, e, isOrdered); 122 } 123 } 124 125 return graph; 126 } 127 128 /*==============================define a queue=====================================================*/ 129 /*define a list to store the element in the queue*/ 130 typedef vertex elementType; 131 typedef struct node3 *pList; 132 typedef struct node3 { 133 elementType element; 134 struct node3 *next; 135 }; 136 137 /*define a queue to point the list*/ 138 typedef struct node4 *pQueue; 139 typedef struct node4 { 140 pList front; /*the front point to point the head of the list*/ 141 pList rear; /*the rear point to point the rear of of the list*/ 142 }; 143 144 /*create a empty list to store the queue element*/ 145 pList createEmptyList() { 146 pList list; 147 list = (pList) malloc(sizeof(struct node3)); 148 list->next = NULL; 149 return list; 150 } 151 /*create a empty queye*/ 152 pQueue createEmptyQueue() { 153 pQueue queue = (pQueue) malloc(sizeof(struct node4)); 154 queue->front = NULL; 155 queue->rear = NULL; 156 return queue; 157 } 158 159 /* 160 Wether the queue is empty 161 @param queue The queue need to adjust 162 @return If the queue is null,return 1 otherwise return 0 163 */ 164 int isQueueEmpty(pQueue queue) { 165 return (queue->front == NULL); 166 } 167 168 /* 169 Add a element to a queue,If the queue is null,we will create a new queue 170 @parama queue The queue we will add elememt to 171 @prama element The element we will add to queue 172 */ 173 void addQueue(pQueue queue, elementType element) { 174 if (isQueueEmpty(queue)) { 175 pList list = createEmptyList(); 176 list->element = element; 177 queue->front = queue->rear = list; 178 } else { 179 pList newNode = (pList) malloc(sizeof(struct node3)); 180 newNode->element = element; 181 newNode->next = queue->rear->next; 182 queue->rear->next = newNode; 183 queue->rear = newNode; 184 } 185 } 186 187 /* 188 delete a element from a queue 189 @param queue The queue will be deleted a element 190 @return The element has been deleted 191 */ 192 elementType deleteEleFromQueue(pQueue queue) { 193 if (isQueueEmpty(queue)) { 194 printf("the queue is empty,don\'t allow to delete elemet from it!"); 195 return -1; 196 } else { 197 pList oldNode = queue->front; 198 elementType element = oldNode->element; 199 if (queue->front == queue->rear) { 200 queue->rear = queue->front = NULL; 201 } else { 202 queue->front = queue->front->next; 203 } 204 free(oldNode); 205 return element; 206 } 207 } 208 209 /* 210 * We solve this problem by top sort,but we need to update the adjacent 211 * vertex earliest value at decreasing the adjacent vertex in-degree,the 212 * earliest the max value of parent\'s earliest value add the weight(last time). 213 * The vertex which has no in-degree will set earliest to 0 at first time 214 * 215 * Top sort algorithms thoughts: 216 * 1.we first initialize all vertex in-degree is zero,then we according to 217 * the graph to set the each vertex in-degree. 218 * 2.find zero in-degree vertex and put it in queue. 219 * 3.get a vertex from a queue and record its index 220 * 4.get the all adjacent vertex of the vertex and let them in-degree decrement,at this moment,if 221 * some vertex has decrease into zero,we put them into queue. 222 * 5.Execute this operation until the queue is empty 223 * 224 * @param grap A graph which use adjacent list is used to store the vertex 225 * @param topOrder A <code>vertex</code> array to store the index of the 226 * vertex about the top queue 227 * @return If the graph is no circle,indicate the top sort is correct 1 will be return 228 * otherwise will return 0 229 */ 230 int getEarliestDate(adjacentTableGraph graph, vertex topOrder[]) { 231 vertex v; 232 ptrToAdjNode w; 233 int indegree[MAX_VERTEX_NUM], vertexConter = 0; 234 /* 235 * Create a queue to store the vertex whose in-degree is zero 236 */ 237 pQueue queue = createEmptyQueue(); 238 /* 239 * Initialize topOrder 240 */ 241 for (v = 0; v < graph->vertex_number; v++) { 242 indegree[v] = 0; 243 } 244 for (v = 0; v < graph->vertex_number; v++) { 245 for (w = graph->g[v].head; w; w = w->next) { 246 indegree[w->adjVerx]++; 247 } 248 } 249 250 /* 251 * Add in-degree vertex to queue 252 */ 253 for (v = 0; v < graph->vertex_number; v++) { 254 if (indegree[v] == 0) { 255 addQueue(queue, v); 256 graph->g[v].earliest = 0; 257 } 258 } 259 while (!isQueueEmpty(queue)) { 260 v = deleteEleFromQueue(queue); 261 /* 262 * Record the vertex of top sort 263 */ 264 topOrder[vertexConter++] = v; 265 for (w = graph->g[v].head; w; w = w->next) { 266 if ((graph->g[v].earliest + w->weight) 267 > (graph->g[w->adjVerx].earliest)) { 268 graph->g[w->adjVerx].earliest = graph->g[v].earliest 269 + w->weight; 270 } 271 if (--indegree[w->adjVerx] == 0) { 272 addQueue(queue, w->adjVerx); 273 } 274 } 275 } 276 277 /* 278 *Adjust whether all vertexes have been recorded 279 */ 280 if (vertexConter == graph->vertex_number) { 281 return 1; 282 } else { 283 return 0; 284 } 285 } 286 287 /* 288 * You know ,we need to let these vertex whose out-degree is zero 289 * latest equal earliest.These whose out-degree is zero is the vertex which 290 * the project\'s finish vertex 291 * @param grap A graph which use adjacent list is used to store the vertex 292 */ 293 void initLatest(adjacentTableGraph graph) { 294 vertex v; 295 ptrToAdjNode w; 296 vertex outdegree[graph->vertex_number]; 297 for (v = 0; v < graph->vertex_number; v++) { 298 outdegree[v] = 0; 299 } 300 for (v = 0; v < graph->vertex_number; v++) { 301 for (w = graph->g[v].head; w; w = w->next) { 302 outdegree[v]++; 303 } 304 } 305 /* 306 *find out-degree vertex and set them latest equal earliest 307 */ 308 for (v = 0; v < graph->vertex_number; v++) { 309 if (outdegree[v] == 0) { 310 graph->g[v].latest = graph->g[v].earliest; 311 } 312 } 313 } 314 315 /* 316 * Calculate the the latest by the earliest and the top sort result 317 * From the class,we can know the latest value is minimal value amount the child vertex\'s latest 318 * minus the weight(we use the weight as the lasting time).Before caller this method,we have 319 * initialize the terminal vertex latest value.You can see the method above. 320 *@param grap A graph which use adjacent list is used to store the vertex 321 *@param topOrder a <code>vertex</code> array to store the top sort result 322 * 323 */ 324 void calculateTheLatest(adjacentTableGraph graph, vertex topOrder[]) { 325 int length = graph->vertex_number, i; 326 ptrToAdjNode w; 327 vertex v; 328 for (i = length - 1; i >= 0; i--) { 329 for (v = 0; v < graph->vertex_number; v++) { 330 for (w = graph->g[v].head; w; w = w->next) { 331 if (w->adjVerx == topOrder[i]) { 332 if (graph->g[v].latest 333 > (graph->g[topOrder[i]].latest - w->weight)) { 334 graph->g[v].latest = graph->g[topOrder[i]].latest 335 - w->weight; 336 } 337 338 } 339 } 340 } 341 } 342 } 343 344 /* 345 * Print the key path,we know when child vertex\'s latest minus parent vertex\'s earliest 346 * and minus the weight(we use the weight as the lasting time),if the result is equal zero 347 * indicating this is key path.we print them. 348 *@param grap A graph which use adjacent list is used to store the vertex 349 */ 350 void recordKeyActivity(adjacentTableGraph graph) { 351 vertex v; 352 ptrToAdjNode w; 353 for (v = 0; v < graph->vertex_number; v++) { 354 for (w = graph->g[v].head; w; w = w->next) { 355 if (graph->g[w->adjVerx].latest - graph->g[v].earliest 356 == w->weight) { 357 printf("%d->%d\\n", v + 1, w->adjVerx + 1); 358 } 359 } 360 } 361 } 362 363 /* 364 * Get the earliest max value from all vertex.we search each vertex and find the max earliest 365 * and return 366 * @param grap A graph which use adjacent list is used to store the vertex 367 */ 368 int getEarliestTime(adjacentTableGraph graph) { 369 weightType maxTime = -1; 370 vertex v; 371 for (v = 0; v < graph->vertex_number; v++) { 372 if (graph->g[v].earliest > maxTime) { 373 maxTime = graph->g[v].earliest; 374 } 375 } 376 return maxTime; 377 } 378 379 /* 380 * Access graph vertex by the index of the vertex 381 */ 382 void visit(adjacentTableGraph graph, vertex v) { 383 printf("%d %d %d\\n", v, graph->g[v].earliest, graph->g[v].latest); 384 } 385 386 /* 387 Depth first search a graph 388 @param graph The graph need to search 389 @param startPoint The fisrt point we start search the graph 390 @paran int *visited The array we use to tag the vertex we has accessed. 391 */ 392 void DFS(adjacentTableGraph graph, vertex startPoint, int *visited) { 393 ptrToAdjNode p; 394 visit(graph, startPoint); 395 visited[startPoint] = 1; 396 for (p = graph->g[startPoint].head; p; p = p->next) { 397 if (visited[p->adjVerx] == 0) { 398 DFS(graph, p->adjVerx, visited); 399 } 400 } 401 } 402 403 /* 404 * Fill a array with value 405 * @param arr The array need to be filled 406 * @param length The length of the array 407 * @param filledValue The value the array will be filled 408 */ 409 void fullArray(int *arr, int length, int filledValue) { 410 int i; 411 for (i = 0; i < length; i++) { 412 arr[i] = filledValue; 413 } 414 } 415 416 int main() { 417 adjacentTableGraph graph = buildLGraph(1); 418 vertex topOrder[graph->vertex_number]; 419 vertex keyActivities[MAX_VERTEX_NUM][MAX_VERTEX_NUM]; 420 int bool = getEarliestDate(graph, topOrder); 421 if (bool) { 422 printf("%d\\n", getEarliestTime(graph)); 423 } else { 424 printf(以上是关于向陈越姥姥哭诉----关键活动的主要内容，如果未能解决你的问题，请参考以下文章