_DataStructure_C_Impl:Dijkstra算法求最短路径

// _DataStructure_C_Impl:Dijkstra#include<stdio.h>#include<stdlib.h>#include<string.h>typedef char VertexType[4];typedef char InfoPtr;typedef int VRType;#define INFINITY 100000//定义一个无限大的值#define MaxSize 50//最大顶点个数typedef int PathMatrix[MaxSize][MaxSize];//定义一个保存最短路径的二维数组typedef int ShortPathLength[MaxSize];//定义一个保存从顶点v0到顶点v的最短距离的数组typedef enum{DG,DN,UG,UN}GraphKind;typedef struct{VRType adj;//对于无权图，用1表示相邻，0表示不相邻；对于带权图，存储权值InfoPtr *info;//与弧或边的相关信息}ArcNode,AdjMatrix[MaxSize][MaxSize];//图的类型定义typedef struct{VertexType vex[MaxSize];//用于存储顶点AdjMatrix arc;//邻接矩阵，存储边或弧的信息int vexnum,arcnum;//顶点数和边（弧）的数目GraphKind kind;//图的类型}MGraph;//添加一个存储网的行、列和权值的类型定义typedef struct{int row;int col;int weight;}GNode;//采用邻接矩阵表示法创建有向网Nvoid CreateGraph(MGraph *N,GNode *value,int vnum,int arcnum,VertexType *ch){int i,j,k,w;char s[MaxSize];VertexType v1,v2;N->vexnum=vnum;N->arcnum=arcnum;for(i=0;i<vnum;i++)strcpy(N->vex[i],ch[i]);//初始化邻接矩阵for(i=0;i<N->vexnum;i++)for(j=0;j<N->vexnum;j++){N->arc[i][j].adj=INFINITY;N->arc[i][j].info=NULL;//弧的信息初始化为空}for(k=0;k<arcnum;k++){i=value[k].row;j=value[k].col;N->arc[i][j].adj=value[k].weight;}N->kind=DN;//图的类型为有向网}//输出邻接矩阵存储表示的图Nvoid DisplayGraph(MGraph N){int i,j;printf("有向网具有%d个顶点%d条弧，顶点依次是: ",N.vexnum,N.arcnum);for(i=0;i<N.vexnum;++i)//输出网的顶点printf("%s ",N.vex[i]);printf("\n有向网N的:\n");//输出网N的弧printf("序号i=");for(i=0;i<N.vexnum;i++)printf("%8d",i);printf("\n");for(i=0;i<N.vexnum;i++){printf("%8d",i);for(j=0;j<N.vexnum;j++)printf("%8d",N.arc[i][j].adj);printf("\n"); }}/*用Dijkstra算法求有向网N的v0顶点到其余各顶点v的最短路径P[v]及带权长度D[v]*//*final[v]为1表示v∈S，即已经求出从v0到v的最短路径*/void Dijkstra(MGraph N,int v0,PathMatrix path,ShortPathLength dist){int v,w,i,k,min;int final[MaxSize];//记录v0到该顶点的最短路径是否已求出for(v=0;v<N.vexnum;v++){//数组dist存储v0到v的最短距离，初始化为v0到v的弧的距离final[v]=0;dist[v]=N.arc[v0][v].adj;for(w=0;w<N.vexnum;w++)path[v][w]=0;if(dist[v]<INFINITY){//如果从v0到v有直接路径，则初始化路径数组path[v][v0]=1;path[v][v]=1;}}dist[v0]=0;//v0到v0的路径为0final[v0]=1;//v0顶点并入集合S/*从v0到其余G.vexnum-1个顶点的最短路径，并将该顶点并入集合S*/for(i=1;i<N.vexnum;i++){min=INFINITY;for(w=0;w<N.vexnum;w++)if(!final[w]&&dist[w]<min){//在不属于集合S的顶点中找到离v0最近的顶点v=w;//将其离v0最近的顶点w赋给v，其距离赋给minmin=dist[w];}final[v]=1;  //将v并入集合Sfor(w=0;w<N.vexnum;w++)//利用新并入集合S的顶点，更新v0到不属于集合S的顶点的最短路径长度和最短路径数组if(!final[w]&&min<INFINITY&&N.arc[v][w].adj<INFINITY&&(min+N.arc[v][w].adj<dist[w])){dist[w]=min+N.arc[v][w].adj;for(k=0;k<N.vexnum;k++)path[w][k]=path[v][k];path[w][w]=1;}}}void main(){int i,j,vnum=6,arcnum=9;MGraph N;GNode value[]={{0,1,30},{0,2,60},{0,4,150},{0,5,40},{1,2,40},{1,3,100},{2,3,50},{3,4,30},{4,5,10}};VertexType ch[]={"v0","v1","v2","v3","v4","v5"};PathMatrix path;/*用二维数组存放最短路径所经过的顶点*/ShortPathLength dist;/*用一维数组存放最短路径长度*/CreateGraph(&N,value,vnum,arcnum,ch); /*创建有向网N*/DisplayGraph(N);/*输出有向网N*/Dijkstra(N,0,path,dist);printf("%s到各顶点的最短路径长度为：\n",N.vex[0]);for(i=0;i<N.vexnum;++i)if(i!=0)printf("%s-%s:%d\n",N.vex[0],N.vex[i],dist[i]);system("pause");}