最短路径Dijkstra算法

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最短路径Dijkstra算法

本文取自《数据结构与算法》(C语言版)(第三版)，出版社是清华大学出版社。

本博文作为学习资料整理。附书的截图：

最短路径的Dijkstra算法的基本思想是：设S为最短路径已确定的顶点集,V-S是最短距离尚未确定的顶点集。初始时,将源点V0添加到顶点集S中,即S={V0}。在当前顶点集V-S中选择一个最短路径最小的顶点来扩充顶点集S,以保证算法按路径长度递增的次序产生各顶点的最短路径。

Dijkstra算法的步骤示意图如下：

其程序如下:

   #include<stdio.h>   #include<stdlib.h>   #include<string.h>   #define MaxVertexNum 100   const int INF=25500000;   typedef struct node   {     int adjvex;     int hostvex;     struct node *nextrarc;     int info;   }EdgeNode;   typedef struct vnode   {     char vexdate;     int pos;     EdgeNode *firstarc;   }VertexNode;   typedef VertexNode AdjList[MaxVertexNum];   typedef struct   {     AdjList adjlist;     int n,e;   }ALGraph;   int initGraph(ALGraph* aGraph);   int mFind(char aChar, ALGraph* aGraph);   int createHead(char aChar, ALGraph* aGraph);   void addBody(char aChar, int aPos, ALGraph* aGraph, int weight);   void showGraph(ALGraph* aGraph);   EdgeNode* isEdge(VertexNode* start, VertexNode* end);   void Dijkstra(ALGraph* aGraph, int v);   void Dispath(int dist[], int path[], int s[], ALGraph* aGraph, int v);   void privatePrintPath(ALGraph* aGraph, int path[], int curr, int v);   int main(void)   {     char a;     int isFinish=0;     int headPos=-1;     char a1='@', a2='@', a3='@', a4='@', a5='@', a6='@', a7='@';     ALGraph g_graph;     initGraph(&g_graph);     printf("Input arcs like this '(start,end:weight)',end with $\n");     while(isFinish==0)     {        while(1)        {          a=getchar();          if(a=='$'||a=='#')          {            if(a=='#')              isFinish=1;            break;          }          if(a==' '||a=='\n')            continue;          a1=a2;          a2=a3;          a3=a4;          a4=a5;          a5=a6;          a6=a7;          a7=a;          if(a1=='('&&a3==','&&a5==':'&&a7==')')          {            if((headPos=mFind(a2,&g_graph))==-1)              headPos=createHead(a2,&g_graph);            addBody(a4,headPos,&g_graph,a6-48);          }        }     }     Dijkstra(&g_graph,2);     return 0;   }   EdgeNode* isEdge(VertexNode* start, VertexNode* end)   {     EdgeNode* temEdge=start->firstarc;     while(temEdge!=NULL)     {       if(temEdge->adjvex==end->pos)         return temEdge;       temEdge=temEdge->nextrarc;     }     return NULL;   }   void Dijkstra(ALGraph* aGraph, int v)   {     int dist[MaxVertexNum], path[MaxVertexNum];     int s[MaxVertexNum];     int mindis,i,j,u;     EdgeNode* temEdge;     for(i=0; i<aGraph->n; i++)     {       dist[i]=INF;       s[i]=0;       path[i]=-1;     }     temEdge=aGraph->adjlist[v].firstarc;     while(temEdge!=NULL)     {       dist[temEdge->adjvex]=temEdge->info;       path[temEdge->adjvex]=v;       temEdge=temEdge->nextrarc;     }     s[v]=1;path[v]=v;dist[v]=0;     for(i=0; i<aGraph->n; i++)     {       mindis=INF;       for(j=0; j<aGraph->n; j++)       {         if(s[j]==0&&dist[j]<mindis)         {           u=j;           mindis=dist[j];         }       }       s[u]=1;       for(j=0; j<aGraph->n; j++)       {         if(s[j]==0)         {           EdgeNode* temEdge=isEdge(&(aGraph->adjlist[u]), &(aGraph->adjlist[j]));           if(temEdge!=NULL)           {             if((dist[u]+temEdge->info)<dist[j])             {               dist[j]=dist[u]+temEdge->info;               path[j]=u;             }           }         }       }     }     Dispath(dist,path,s,aGraph,v);   }   void Dispath(int dist[], int path[], int s[], ALGraph* aGraph, int v)   {     int i;     for(i=0; i<aGraph->n; i++)     {       printf("%c->%c(distance is %d) \n%c", aGraph->adjlist[v].vexdate,              aGraph->adjlist[i].vexdate,dist[i],aGraph->adjlist[v].vexdate);       privatePrintPath(aGraph,path,i,v);       printf("\n");     }   }   void privatePrintPath(ALGraph* aGraph, int path[], int curr, int v)   {     char temChar=aGraph->adjlist[curr].vexdate;     int temPos=curr;     if(curr!=v)     {       privatePrintPath(aGraph,path,path[temPos],v);       printf(" ->%c",temChar);     }   }   void showGraph(ALGraph* aGraph)   {     int i=0;     for(i=0; i<aGraph->n; i++)     {       EdgeNode* pos;       printf(" %c->",aGraph->adjlist[i]);       pos=aGraph->adjlist[i].firstarc;       while(pos!=NULL)       {         printf(" %d ",pos->adjvex);         pos=pos->nextrarc;       }       printf("\n ");     }   }   void addBody(char aChar, int aPos, ALGraph* aGraph, int weight)   {     int inversePos;     EdgeNode* node=(EdgeNode*) malloc(sizeof(EdgeNode));     node->info=weight;     if((node->adjvex=mFind(aChar,aGraph))==-1)       node->adjvex=createHead(aChar,aGraph);     node->hostvex=aPos;     node->nextrarc=NULL;     if(aGraph->adjlist[aPos].firstarc==NULL)       aGraph->adjlist[aPos].firstarc=node;     else     {       EdgeNode* tail=aGraph->adjlist[aPos].firstarc;       while(tail->nextrarc!=NULL)         tail=tail->nextrarc;       tail->nextrarc=node;     }     aGraph->e++;     inversePos=node->adjvex;     node=(EdgeNode*) malloc(sizeof(EdgeNode));     node->info=weight;     node->hostvex=inversePos;     node->adjvex=aPos;     node->nextrarc=NULL;     if(aGraph->adjlist[inversePos].firstarc==NULL)       aGraph->adjlist[inversePos].firstarc=node;     else     {       EdgeNode* tail=aGraph->adjlist[inversePos].firstarc;       while(tail->nextrarc!=NULL)         tail=tail->nextrarc;       tail->nextrarc=node;     }     aGraph->e++;   }  int createHead(char aChar, ALGraph* aGraph)  {    int currPos=aGraph->n;    aGraph->adjlist[currPos].vexdate=aChar;    aGraph->adjlist[currPos].pos=currPos;    aGraph->n++;    return currPos;  }  int mFind(char aChar, ALGraph* aGraph)  {    int i=0;    for(i=0; i<aGraph->n; i++)    {      if(aChar==aGraph->adjlist[i].vexdate)        return i;    }    return -1;  }  int initGraph(ALGraph* aGraph)  {    int i=0;    aGraph->e=0;    aGraph->n=0;    for(i=0; i<MaxVertexNum; i++)    {      aGraph->adjlist[i].firstarc=NULL;    }    return 0;  }

在VC2010中 C++控制台程序运行的结果：如下图所示：

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