最短路径（迪杰斯特拉算法）

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#include<stdio.h>//包含图文件及图的类型定义#include<string.h>#include<malloc.h>#include<stdlib.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 100//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的最短距离数组typedef enum {DG,DN,UG,UN} GraphKind;//图的类型:有向图，有向网，无向图，无向网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;//与弧或边相关的信息}ArcNode,AdjMatrix[MAXSIZE][MAXSIZE];typedef struct//图的类型定义{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;//顶点数和边的数目  GraphKind kind;//图的类型}MGraph;typedef struct//添加一个存储网的行、列和权值的类型定义{int row;int col;int weight;}GNode;void CreateGraph(MGraph *N,GNode *value,int vnum,int arcnum,VertexType *ch);void DisplayGraph(MGraph N);void Dijkstra(MGraph N,int v0,PathMatrix path,ShortPathLength dist);void main(){int i,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    DisplayGraph(N);//输出有向网    Dijkstra(N,0,path,dist);printf("%s到各顶点的最短路径长度:\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]);}void CreateGraph(MGraph *N,GNode *value,int vnum,int arcnum,VertexType *ch)//采用邻接矩阵表示法创建有向网{int i, j, k, w, InfoFlag, len;char s[MAXSIZE];    VertexType v1,v2;N->vexnum=vnum;N->arcnum=arcnum;    for(i=0;i<vnum;i++)//将各个顶点赋值给vex域strcpy(N->vex[i],ch[i]);    for(i=0;i<N->vexnum;i++)//初始化邻接矩阵        for(j=0;j<N->vexnum;j++){N->arc[i][j].adj=INFINITY;N->arc[i][j].info=NULL;//弧的初始化信息为空}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}void DisplayGraph(MGraph N)//输出邻接矩阵存储表示的图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");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");}}void Dijkstra(MGraph N,int v0,PathMatrix path,ShortPathLength dist){int v , w ,i ,k, min;int final[MAXSIZE];for(v=0;v<N.vexnum ;v++){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){path[v][v0] = 1;path[v][v] = 1;}}dist[v0] = 0;final[v0] = 1;for(i = 1; i<N.vexnum  ;i++ ){min = INFINITY;for(w=0;w<N.vexnum ;w++)if(!final[w] && dist[w]<min){v=w;min = dist[w];}final[v]=1;for(w=0;w<N.vexnum ;w++)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;}}}
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