Prim与Kruskal算法
- Prime算法
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#include <stdio.h> #include <stdlib.h> #define MAX 100 /********ÁÚ½Ó¾ØÕó½á¹¹***************/ typedef struct graph { char vers[MAX]; int numVertex,numEdge; int arc[MAX][MAX]; }Graph; void CreateGraph(Graph *G) { int i,j; G->numEdge=10; G->numVertex=8; G->vers[0]='B'; G->vers[1]='I'; G->vers[2]='U'; G->vers[3]='Y'; G->vers[4]='T'; G->vers[5]='G'; G->vers[6]='C'; G->vers[7]='D'; for (i=0; i<8; ++i) { for (j=0; j<8; ++j) { G->arc[i][j]=MAX; } } G->arc[1][2]=1; G->arc[1][4]=2; G->arc[1][5]=3; G->arc[2][5]=4; G->arc[2][7]=5; G->arc[0][2]=6; G->arc[0][5]=7; G->arc[3][4]=8; G->arc[3][5]=9; G->arc[4][6]=10; for (i=0; i<8; ++i) { for (j=0; j<8; ++j) { G->arc[j][i]=G->arc[i][j]; } } } void PrintGraph(Graph *G) { int i, j; for (i=0; i<8; ++i) { for (j=0; j<8; ++j) { printf("%d ",G->arc[i][j]); } printf("\n"); } } void Prim(Graph *G) { int min,k,i,j; int lowcost[8]; int vers[8]; for (i=0; i<G->numVertex; i++) { lowcost[i]=G->arc[0][i]; vers[i]=0; } printf("%c\n", G->vers[0]); for (i=1; i<G->numVertex; ++i) { min=MAX; j=1; k=0; while(j<G->numVertex) { if (lowcost[j] && lowcost[j]<min) { min=lowcost[j]; k=j; } j++; } printf("(%c, %c)\n", G->vers[vers[k]], G->vers[k]); //printf("%c\n", G->vers[k]); lowcost[k]=0; for(j=1; j<G->numVertex; j++) { if (lowcost[j] && G->arc[k][j] < lowcost[j]) { lowcost[j]=G->arc[k][j]; vers[j]=k; } } } } int main() { Graph G; CreateGraph(&G); Prim(&G); return 0; }
Kruskal算法
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#include <stdio.h> #include <stdlib.h> #include <string.h> #define MAX 100 /********邻接矩阵结构***************/ typedef struct graph { char vers[MAX]; int numVertex,numEdge; int arc[MAX][MAX]; }Graph; /*******定义边******/ typedef struct { int begin; int end; int weight; }Edge; void CreateGraph(Graph *G) { int i,j; G->numEdge=10; G->numVertex=8; G->vers[0]='B'; G->vers[1]='I'; G->vers[2]='U'; G->vers[3]='Y'; G->vers[4]='T'; G->vers[5]='G'; G->vers[6]='C'; G->vers[7]='D'; for (i=0; i<8; ++i) { for (j=0; j<8; ++j) { if (i==j) { G->arc[i][j]=0; } else { G->arc[i][j]=MAX; } } } G->arc[1][2]=1; G->arc[1][4]=2; G->arc[1][5]=3; G->arc[2][5]=4; G->arc[2][7]=5; G->arc[0][2]=6; G->arc[0][5]=7; G->arc[3][4]=8; G->arc[3][5]=9; G->arc[4][6]=10; for (i=0; i<8; ++i) { for (j=0; j<8; ++j) { G->arc[j][i]=G->arc[i][j]; } } } void PrintGraph(Graph *G) { int i, j; for (i=0; i<8; ++i) { for (j=0; j<8; ++j) { printf("%d ",G->arc[i][j]); } printf("\n"); } } int Find(int *parent, int f) { while ( parent[f] > 0) { f = parent[f]; } return f; } void Kruskal(Graph *G) { int i,j,k=0; Edge edge[MAX]; int parent[MAX]; for(i=0; i<G->numVertex; i++) { for (j=i+1; j<G->numVertex; j++) { edge[k].begin=i; edge[k].end=j; edge[k].weight=G->arc[i][j]; k++; } } for (i=0; i<k; i++) { for (j=i+1; j<k; j++) { if (edge[i].weight > edge[j].weight) { int temp; temp = edge[i].begin; edge[i].begin = edge[j].begin; edge[j].begin = temp; temp = edge[i].end; edge[i].end = edge[j].end; edge[j].end = temp; temp = edge[i].weight; edge[i].weight = edge[j].weight; edge[j].weight = temp; } } } for (i=0; i<G->numVertex; i++) { parent[i]=0; } printf("打印最小生成树：\n"); int n,m; for (i = 0; i < G->numEdge; i++) { /******判断遍历的边是存在环*****/ n = Find(parent,edge[i].begin); m = Find(parent,edge[i].end); if (n != m) { parent[n] = m; printf("(%d, %d) %d\n", edge[i].begin, edge[i].end, edge[i].weight); } } } int main() { Graph G; CreateGraph(&G); Kruskal(&G); return 0; }
Floyd算法
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#include <stdio.h> #include <stdlib.h> #define MAX 100 typedef struct { int vexs[MAX]; int arc[MAX][MAX]; int numVertex; int numEdge; }Graph; typedef int Path[MAX][MAX];//arc[i][j]从vi到vj的最短路径 typedef int Distance[MAX][MAX]; void CreateGraph(Graph *G) { int i, j; G->numEdge=16; G->numVertex=9; for (i = 0; i < G->numVertex; i++) { G->vexs[i]=i; } for (i = 0; i < G->numVertex; i++) { for ( j = 0; j < G->numVertex; j++) { if (i==j) G->arc[i][j]=0; else G->arc[i][j] = G->arc[j][i] =MAX; } } G->arc[0][1]=1; G->arc[0][2]=5; G->arc[1][2]=3; G->arc[1][3]=7; G->arc[1][4]=5; G->arc[2][4]=1; G->arc[2][5]=7; G->arc[3][4]=2; G->arc[3][6]=3; G->arc[4][5]=3; G->arc[4][6]=6; G->arc[4][7]=9; G->arc[5][7]=5; G->arc[6][7]=2; G->arc[6][8]=7; G->arc[7][8]=4; for(i = 0; i < G->numVertex; i++) { for(j = i; j < G->numVertex; j++) { G->arc[j][i] =G->arc[i][j]; } } } void Floyd(Graph *G, Path *P, Distance *D) { int v,w,k; for(v=0; v<G->numVertex; ++v) { for(w=0; w<G->numVertex; ++w) { (*D)[v][w]=G->arc[v][w]; (*P)[v][w]=w; } } for(k=0; k<G->numVertex; ++k) { for(v=0; v<G->numVertex; ++v) { for(w=0; w<G->numVertex; ++w) { if ((*D)[v][w]>(*D)[v][k]+(*D)[k][w]) { (*D)[v][w]=(*D)[v][k]+(*D)[k][w]; (*P)[v][w]=(*P)[v][k]; } } } } } int main(void) { int v,w,k; Graph G; Path P; Distance D; CreateGraph(&G); Floyd(&G,&P,&D); printf("各顶点间最短路径如下:\n"); for(v=0; v<G.numVertex; ++v) { for(w=v+1; w<G.numVertex; w++) { printf("v%d-v%d weight: %d ",v,w,D[v][w]); k=P[v][w]; printf(" path: %d",v); while(k!=w) { printf("--->%d",k); k=P[k][w]; } printf("--->%d\n",w); } printf("\n"); } printf("最短距离D\n"); for(v=0; v<G.numVertex; ++v) { for(w=0; w<G.numVertex; ++w) { printf("%d\t",D[v][w]); } printf("\n"); } printf("最短路径P\n"); for(v=0; v<G.numVertex; ++v) { for(w=0; w<G.numVertex; ++w) { printf("%d ",P[v][w]); } printf("\n"); } return 0; }
拓扑排序
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#include <stdio.h> #include <stdlib.h> #include <string.h> #define MAX 100 typedef struct graph { int vers[MAX]; int numVertex; int numEdge; int arc[MAX][MAX]; }Grpah; typedef struct edgenode { int nodevalue; int weight; struct edgenode* next; }Edgenode; typedef struct adjlist { int in; //表示节点的度 int data; Edgenode* firstnode; }Adjlist[MAX]; typedef struct { Adjlist adjlist; int numVertex; int numEdge; }GraphList; void CreateGraph(Grpah *G) { int i,j; G->numEdge=20; G->numVertex=14; for (i = 0; i < G->numVertex; i++) { G->vers[i]=i; } for (i = 0; i < G->numVertex; i++) { for ( j = 0; j < G->numVertex; j++) { G->arc[i][j]=0; } } G->arc[0][4]=1; G->arc[0][5]=1; G->arc[0][11]=1; G->arc[1][2]=1; G->arc[1][4]=1; G->arc[1][8]=1; G->arc[2][5]=1; G->arc[2][6]=1; G->arc[2][9]=1; G->arc[3][2]=1; G->arc[3][13]=1; G->arc[4][7]=1; G->arc[5][8]=1; G->arc[5][12]=1; G->arc[6][5]=1; G->arc[8][7]=1; G->arc[9][10]=1; G->arc[9][11]=1; G->arc[10][13]=1; G->arc[12][9]=1; } void CreateGraphList(Grpah *G, GraphList *GL) { int i,j; Edgenode *e; GL->numEdge=G->numEdge; GL->numVertex=G->numVertex; for (i=0; i<GL->numVertex; ++i) { GL->adjlist[i].firstnode=NULL; GL->adjlist[i].in=0; GL->adjlist[i].data=G->vers[i]; } for (i=0; i<GL->numVertex; ++i) { for (j=0; j<GL->numVertex; ++j) { if (G->arc[i][j]==1) { e=(Edgenode* )malloc(sizeof(Edgenode)); e->nodevalue=j; e->weight=G->arc[i][j]; e->next=GL->adjlist[i].firstnode; GL->adjlist[i].firstnode=e; GL->adjlist[j].in++; } } } } void PrintGraph(Grpah *G) { int i,j; for (i=0; i<G->numVertex; i++) { for (j=0; j<G->numVertex; ++j) { printf("%d ",G->arc[i][j]); } printf("\n"); } } void PrintGraphList(GraphList *GL) { int i; Edgenode *p; for (i=0; i<GL->numVertex; ++i) { p=GL->adjlist[i].firstnode; printf("%d", GL->adjlist[i].data); while(p) { printf("<--->%d", p->nodevalue); p=p->next; } printf("\n"); } }; void TopSort(GraphList *GL) { Edgenode *e; int i,k,gettop; int top=0; int *stack; stack=(int *)malloc(GL->numVertex * sizeof(int)); for(i = 0; i<GL->numVertex; i++) { if(0 == GL->adjlist[i].in) { stack[++top]=i; } } while(top!=0) { gettop=stack[top--]; printf("%d<--->",GL->adjlist[gettop].data); for(e = GL->adjlist[gettop].firstnode; e; e = e->next) { k=e->nodevalue; if(!(--GL->adjlist[k].in)) { stack[++top]=k; } } } } int main() { Grpah G; GraphList GL; CreateGraph(&G); PrintGraph(&G); CreateGraphList(&G,&GL); PrintGraphList(&GL); TopSort(&GL); return 0; }
最佳路径
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#include <stdlib.h> #include <stdio.h> #include <string.h> #define MAX 100 int *etv; //事件最早发生时间 int *ltv; //事件最迟发生时间 int *stack2; int top2=0; typedef struct graph { int vers[MAX]; int numVertex; int numEdge; int arc[MAX][MAX]; }Grpah; typedef struct edgenode { int nodevalue; int weight; struct edgenode* next; }Edgenode; typedef struct adjlist { int in; //表示节点的度 int data; Edgenode* firstnode; }Adjlist[MAX]; typedef struct { Adjlist adjlist; int numVertex; int numEdge; }GraphList; void CreateGraph(Grpah *G) { int i,j; G->numEdge=13; G->numVertex=10; for (i = 0; i < G->numVertex; i++) { G->vers[i]=i; } for (i = 0; i < G->numVertex; i++) { for ( j = 0; j < G->numVertex; j++) { G->arc[i][j]=0; } } G->arc[0][1]=3; G->arc[0][2]=4; G->arc[1][3]=5; G->arc[1][4]=6; G->arc[2][3]=8; G->arc[2][5]=7; G->arc[3][4]=3; G->arc[4][6]=9; G->arc[4][7]=4; G->arc[5][7]=6; G->arc[6][9]=2; G->arc[7][8]=5; G->arc[8][9]=3; } void CreateGraphList(Grpah *G, GraphList *GL) { int i,j; Edgenode *e; GL->numEdge=G->numEdge; GL->numVertex=G->numVertex; for (i=0; i<GL->numVertex; ++i) { GL->adjlist[i].firstnode=NULL; GL->adjlist[i].in=0; GL->adjlist[i].data=G->vers[i]; } for (i=0; i<GL->numVertex; ++i) { for (j=0; j<GL->numVertex; ++j) { if (G->arc[i][j]) { e=(Edgenode* )malloc(sizeof(Edgenode)); e->nodevalue=j; e->weight=G->arc[i][j]; e->next=GL->adjlist[i].firstnode; GL->adjlist[i].firstnode=e; GL->adjlist[j].in++; } } } } void PrintGraph(Grpah *G) { int i,j; for (i=0; i<G->numVertex; i++) { for (j=0; j<G->numVertex; ++j) { printf("%d ",G->arc[i][j]); } printf("\n"); } } void PrintGraphList(GraphList *GL) { int i; Edgenode *p; for (i=0; i<GL->numVertex; ++i) { p=GL->adjlist[i].firstnode; printf("%d", GL->adjlist[i].data); while(p) { printf("<--->%d", p->nodevalue); p=p->next; } printf("\n"); } }; void TopSort(GraphList *GL) { Edgenode *e; int i,k,gettop; int top=0; int *stack; stack=(int *)malloc(GL->numVertex * sizeof(int)); stack2=(int *)malloc(GL->numVertex * sizeof(int)); etv=(int* )malloc(GL->numVertex*sizeof(int)); for (i=0; i<GL->numVertex; i++) { etv[i]=0; } for(i = 0; i<GL->numVertex; i++) { if(0 == GL->adjlist[i].in) { stack[++top]=i; } } printf("拓扑排序：\n"); while(top!=0) { gettop=stack[top--]; stack2[++top2]=gettop; printf("%d<--->",GL->adjlist[gettop].data); for(e = GL->adjlist[gettop].firstnode; e; e = e->next) { k=e->nodevalue; if(!(--GL->adjlist[k].in)) { stack[++top]=k; } if (etv[gettop]+e->weight > etv[k]) { etv[k]=etv[gettop]+e->weight; } } } printf("\n"); } void CriticalPath(GraphList *GL) { Edgenode *p; int i,j,k; TopSort(GL); ltv=(int *)malloc(sizeof(int)*GL->numVertex); for (i=0; i<GL->numVertex; i++) { ltv[i]=etv[GL->numVertex-1]; } printf("事件最早发生时间：\n"); for (i=0; i<GL->numVertex; ++i) { printf("%d<--->",etv[i]); } printf("\n"); while(top2) { int gettop=stack2[top2--]; p=GL->adjlist[gettop].firstnode; while(p) { k=p->nodevalue; if (ltv[k]-p->weight<ltv[gettop]) { ltv[gettop]=ltv[k]-p->weight; } p=p->next; } } printf("事件最迟发生时间：\n"); for (i=0; i<GL->numVertex; ++i) { printf("%d<--->",ltv[i]); } printf("\n"); int e,l; for(i=0; i<GL->numVertex; i++) { for(p = GL->adjlist[i].firstnode; p; p = p->next) { k=p->nodevalue; e= etv[i]; l= ltv[k]-p->weight; if(e == l) printf("v%d <---> v%d length: %d \n",GL->adjlist[i].data,GL->adjlist[k].data, p->weight); } } } int main() { Grpah G; GraphList GL; CreateGraph(&G); PrintGraph(&G); CreateGraphList(&G,&GL); PrintGraphList(&GL); CriticalPath(&GL); return 0; }