最短路径Dijkstra算法
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加入到顶点集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算法的步骤示意图例如以下：
其程序例如以下:
#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++控制台程序执行的结果：例如以下图所看到的：
