算法导论 单源最短路径 Bellman-Ford

#include <stdio.h>#include <stdlib.h>//图节点typedef struct VertexNode{char name;int key;VertexNode *p;}Vertex,*pVertex;//图typedef struct {int vn;int **E;pVertex *V;}Graph,*pGraph;//根据算法导论 图24-4 初始化图pGraph initGraph(){pGraph g=(pGraph)malloc(sizeof(Graph));g->vn=5;pVertex vs=(pVertex)malloc(sizeof(Vertex));vs->name='s';vs->key=0;vs->p=NULL;pVertex vt=(pVertex)malloc(sizeof(Vertex));vt->name='t';vt->key=INT_MAX;vt->p=NULL;pVertex vy=(pVertex)malloc(sizeof(Vertex));vy->name='y';vy->key=INT_MAX;vy->p=NULL;pVertex vx=(pVertex)malloc(sizeof(Vertex));vx->name='x';vx->key=INT_MAX;vx->p=NULL;pVertex vz=(pVertex)malloc(sizeof(Vertex));vz->name='z';vz->key=INT_MAX;vz->p=NULL;g->V=(pVertex*)malloc(g->vn*sizeof(pVertex));g->V[0]=vs;g->V[1]=vt;g->V[2]=vy;g->V[3]=vx;g->V[4]=vz;g->E = (int**)malloc(g->vn*sizeof(int*));for(int i=0;i<g->vn;i++){g->E[i]=(int*)malloc(g->vn*sizeof(int));}for(int i=0;i<g->vn;i++){for(int j=0;j<g->vn;j++){g->E[i][j]=INT_MAX;}}g->E[0][1]=6;g->E[0][2]=7;g->E[1][2]=8;g->E[1][3]=5;g->E[1][4]=-4;g->E[2][3]=-3;g->E[2][4]=9;g->E[3][1]=-2;g->E[4][3]=7;return g;}void relax(pGraph g,int u,int v){//无边，不进行松弛if(g->E[u][v]==INT_MAX)return;int sum,uk=g->V[u]->key,vk=g->V[v]->key,ew=g->E[u][v];//根据规则，加上无穷等于无穷if(uk==INT_MAX || ew==INT_MAX)sum=INT_MAX;elsesum=uk+ew;if(vk>sum){g->V[v]->key=sum;g->V[v]->p=g->V[u];}}bool BellmanFord(pGraph g){for(int i=1;i<=g->vn-1;i++){for(int j=0;j<g->vn;j++){for(int k=0;k<g->vn;k++){if(g->E[j][k]<INT_MAX)relax(g,j,k);}}}for(int u=0;u<g->vn;u++){for(int v=0;v<g->vn;v++){if(g->E[u][v]>0){int sum,uk=g->V[u]->key,vk=g->V[v]->key,ew=g->E[u][v];//根据规则，加上无穷等于无穷if(uk==INT_MAX || ew==INT_MAX)sum=INT_MAX;elsesum=uk+ew;if(vk>sum)return false;}}}return true;}void printKey(pGraph g){for(int i=0;i<g->vn;i++){pVertex v=g->V[i];printf("%c %d\n",v->name,v->key);}}void main(){pGraph g=initGraph();bool b=BellmanFord(g);if(b)printKey(g);elseprintf("No Path!");getchar();}