这个算法来求关键路径，其实就是利用拓扑排序，首先求出，每个节点最晚开始时间，再倒退求每个最早开始的时间。
从而算出活动最早开始的时间和最晚开始的时间，如果这两个时间相等，则为关键路径。
时间复杂度为O(n+e)
主要算法：
int topSort(Graph *g){ EdgeNode *e; int i,k,gettop; int top = 0 ; int count = 0; int *stack; stack = (int *)malloc(g->numVertexes * sizeof(int)); for(i=0;i<g->numVertexes;i++){ if(g->headlist[i].in == 0) //把入度为0的，即没有入度的点入栈 stack[++top] = i; } top2 = 0; etv = (int *)malloc(g->numVertexes*sizeof(int)); for(i=0;i<g->numVertexes;i++){ etv[i] = 0; } stack2=(int *)malloc(g->numVertexes*sizeof(int)); while(top){ gettop = stack[top--]; printf("%d ",gettop); count++; stack2[++top2] = gettop; for(e = g->headlist[gettop].fnode; e ; e=e->next){ //一次遍历链表，减少各个子节点的入度 k = e->data; if(!(--g->headlist[k].in)) stack[++top] = k; if((etv[gettop]+e->weight)>etv[k]) //选取最大值 etv[k] = etv[gettop]+e->weight; } } if(count < g->numVertexes) return ERROR; else return OK; }
int critical(Graph *g){ EdgeNode *e; int i,gettop,k,j; int ete,lte; topSort(g); printf(" ------------------------------------------- "); for(i=0;i<g->numVertexes;i++){ printf("%d ",etv[i]); } printf(" ------------------------------------------- "); ltv = (int *)malloc(sizeof(int)*g->numVertexes); for(i=0;i<g->numVertexes;i++){ ltv[i] = etv[g->numVertexes-1]; } while(top2!=0){ gettop = stack2[top2--]; for(e = g->headlist[gettop].fnode;e;e = e->next){ k = e->data; if(ltv[k]-e->weight < ltv[gettop]){ ltv[gettop] = ltv[k] - e->weight; } } } for(i=0;i<g->numVertexes;i++){ printf("%d ",ltv[i]); } printf(" ------------------------------------------- "); printf(" "); for(j=0;j<g->numVertexes;j++){ for(e=g->headlist[j].fnode; e; e=e->next){ k = e->data; ete = etv[j];//活动最早 lte = ltv[k] - e->weight;//活动最迟 if(ete == lte) printf("<v%d v%d>length:%d ",g->headlist[j].data,g->headlist[k].data,e->weight); } } return 1; }
全部代码：
1 #include <stdio.h> 2 #include <stdlib.h> 3 #include <string.h> 4 #define MAX 9 5 #define ERROR 1 6 #define OK 0 7 typedef struct edgeNode{ 8 int data; 9 int weight; 10 struct edgeNode *next; 11 }EdgeNode; 12 typedef struct headNode{ 13 int in; 14 int data; 15 EdgeNode *fnode; 16 }HeadNode,HeadList[MAX]; 17 typedef struct{ 18 HeadList headlist; 19 int numEdges,numVertexes; 20 }Graph,*graph; 21 22 int *etv,*ltv; 23 int *stack2; 24 int top2; 25 26 void initialGraph(Graph *g); 27 void headinfo(Graph *g,int in,int node); 28 void linkinfo(Graph *g,int node,int link,int weight); 29 void printGraph(Graph *g); 30 int topSort(Graph *g); 31 int critical(Graph *g); 32 33 int main(){ 34 Graph *g = (Graph *)malloc(sizeof(Graph)); 35 g->numEdges = 0; 36 g->numVertexes = 0; 37 initialGraph(g); 38 printGraph(g); 39 40 critical(g); 41 //topSort(g); 42 43 getchar(); 44 return 0; 45 } 46 int critical(Graph *g){ 47 EdgeNode *e; 48 int i,gettop,k,j; 49 int ete,lte; 50 51 topSort(g); 52 printf(" ------------------------------------------- "); 53 for(i=0;i<g->numVertexes;i++){ 54 printf("%d ",etv[i]); 55 } 56 printf(" ------------------------------------------- "); 57 ltv = (int *)malloc(sizeof(int)*g->numVertexes); 58 for(i=0;i<g->numVertexes;i++){ 59 ltv[i] = etv[g->numVertexes-1]; 60 } 61 62 while(top2!=0){ 63 gettop = stack2[top2--]; 64 for(e = g->headlist[gettop].fnode;e;e = e->next){ 65 k = e->data; 66 if(ltv[k]-e->weight < ltv[gettop]){ 67 ltv[gettop] = ltv[k] - e->weight; 68 } 69 } 70 } 71 72 for(i=0;i<g->numVertexes;i++){ 73 printf("%d ",ltv[i]); 74 } 75 printf(" ------------------------------------------- "); 76 printf(" "); 77 for(j=0;j<g->numVertexes;j++){ 78 for(e=g->headlist[j].fnode; e; e=e->next){ 79 k = e->data; 80 ete = etv[j];//活动最早 81 lte = ltv[k] - e->weight;//活动最迟 82 if(ete == lte) 83 printf("<v%d v%d>length:%d ",g->headlist[j].data,g->headlist[k].data,e->weight); 84 } 85 } 86 return 1; 87 } 88 89 int topSort(Graph *g){ 90 EdgeNode *e; 91 int i,k,gettop; 92 int top = 0 ; 93 int count = 0; 94 int *stack; 95 stack = (int *)malloc(g->numVertexes * sizeof(int)); 96 for(i=0;i<g->numVertexes;i++){ 97 if(g->headlist[i].in == 0) //把入度为0的，即没有入度的点入栈 98 stack[++top] = i; 99 } 100 101 top2 = 0; 102 etv = (int *)malloc(g->numVertexes*sizeof(int)); 103 for(i=0;i<g->numVertexes;i++){ 104 etv[i] = 0; 105 } 106 stack2=(int *)malloc(g->numVertexes*sizeof(int)); 107 108 while(top){ 109 gettop = stack[top--]; 110 printf("%d ",gettop); 111 count++; 112 stack2[++top2] = gettop; 113 114 for(e = g->headlist[gettop].fnode; e ; e=e->next){ //一次遍历链表，减少各个子节点的入度 115 k = e->data; 116 if(!(--g->headlist[k].in)) 117 stack[++top] = k; 118 if((etv[gettop]+e->weight)>etv[k]) //选取最大值 119 etv[k] = etv[gettop]+e->weight; 120 } 121 } 122 if(count < g->numVertexes) 123 return ERROR; 124 else 125 return OK; 126 } 127 128 void printGraph(graph g){ 129 int i; 130 printf("vertex:%d,edges:%d ",g->numVertexes,g->numEdges); 131 EdgeNode *e = (EdgeNode *)malloc(sizeof(EdgeNode)); 132 for(i=0;i<MAX;i++){ 133 printf("[in:%d]%d",g->headlist[i].in,g->headlist[i].data); 134 e = g->headlist[i].fnode; 135 while(e != NULL){ 136 printf("->%d(%d)",e->data,e->weight); 137 e = e->next; 138 } 139 printf(" "); 140 } 141 free(e); 142 } 143 void initialGraph(Graph *g){ 144 headinfo(g,0,0); 145 linkinfo(g,0,2,4); 146 linkinfo(g,0,1,3); 147 148 headinfo(g,1,1); 149 linkinfo(g,1,3,5); 150 linkinfo(g,1,4,6); 151 152 headinfo(g,1,2); 153 linkinfo(g,2,3,8); 154 linkinfo(g,2,5,7); 155 156 headinfo(g,2,3); 157 linkinfo(g,3,4,3); 158 159 headinfo(g,2,4); 160 linkinfo(g,4,6,9); 161 linkinfo(g,4,7,4); 162 163 headinfo(g,1,5); 164 linkinfo(g,5,7,6); 165 166 headinfo(g,1,6); 167 linkinfo(g,6,9,2); 168 169 headinfo(g,2,7); 170 linkinfo(g,7,8,5); 171 172 headinfo(g,1,8); 173 linkinfo(g,8,9,3); 174 175 headinfo(g,2,9); 176 } 177 void headinfo(Graph *g,int in,int node){ 178 g->headlist[node].in = in; 179 g->headlist[node].data = node; 180 g->headlist[node].fnode = NULL; 181 g->numVertexes++; 182 } 183 void linkinfo(Graph *g,int node,int link,int weight){ 184 EdgeNode *en = (EdgeNode *)malloc(sizeof(EdgeNode)); 185 if(g->headlist[node].fnode != NULL){ 186 en->next = g->headlist[node].fnode; 187 }else{ 188 en->next = NULL; 189 } 190 g->headlist[node].fnode = en; 191 en->data = link; 192 en->weight = weight; 193 g->numEdges++; 194 }
运行示例：
