AOE關鍵路徑

這個算法來求關鍵路徑，其實就是利用拓撲排序，首先求出，每一個節點最晚開始時間，再倒退求每一個最先開始的時間。

從而算出活動最先開始的時間和最晚開始的時間，若是這兩個時間相等，則爲關鍵路徑。

時間複雜度爲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) //把入度爲0的，即沒有入度的點入棧
            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){ //一次遍歷鏈表，減小各個子節點的入度
            k = e->data; if(!(--g->headlist[k].in)) stack[++top] = k; if((etv[gettop]+e->weight)>etv[k]) //選取最大值
                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("\n-------------------------------------------\n"); for(i=0;i<g->numVertexes;i++){ printf("%d ",etv[i]); } printf("\n-------------------------------------------\n"); 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("\n-------------------------------------------\n"); printf("\n"); for(j=0;j<g->numVertexes;j++){ for(e=g->headlist[j].fnode; e; e=e->next){ k = e->data; ete = etv[j];//活動最先
            lte = ltv[k] - e->weight;//活動最遲
            if(ete == lte) printf("<v%d v%d>length:%d\n",g->headlist[j].data,g->headlist[k].data,e->weight); } } return 1; }

所有代碼：

 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("\n-------------------------------------------\n");  53     for(i=0;i<g->numVertexes;i++){  54         printf("%d ",etv[i]);  55  }  56     printf("\n-------------------------------------------\n");  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("\n-------------------------------------------\n");  76     printf("\n");  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];//活動最先
 81             lte = ltv[k] - e->weight;//活動最遲
 82             if(ete == lte)  83                 printf("<v%d v%d>length:%d\n",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) //把入度爲0的，即沒有入度的點入棧
 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){ //一次遍歷鏈表，減小各個子節點的入度
115             k = e->data; 116             if(!(--g->headlist[k].in)) 117                 stack[++top] = k; 118             if((etv[gettop]+e->weight)>etv[k]) //選取最大值
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\n",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("\n"); 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 }

View Code

運行示例：