最短路径--狄克斯特拉(Dijkstra)

狄克斯特拉(Dijkstra)用来求一个顶点到其他所有顶点间的最短路径，其基本思想是：设G=(V,E)是一个带权有向图，把图中顶点V分成两个集合，第一组 为已经求出最短路径的集合，用S表示，第二组为没确定出最短路径的集合，用U表示，然后，按最短路径长度的递增顺序依次将第二组中的顶点加入S中，在加入的过程中，保持源点V到S中各个顶点的最短路径长度不大于从源点到U中顶点的最短路径长度，U中顶点的距离从V到此顶点只包括S中的顶点为中间顶点的当前最短路径长度，狄克斯特拉(Dijkstra)的时间复杂度为O(n2)。

完整代码如下：

#include "stdio.h"

#include "malloc.h"

#define maxium 32767

#define maxver 9 /*defines the max number of vertexs which the programm can handle*/

#define OK 1

struct Point

{

       char vertex[3];

       struct Link *work;

       struct Point *next;

};

struct Link

{

       char vertex[3];

       int value;

       struct Link *next;

};

struct Table /*the workbannch of the algorithm*/

{

       int cost;

       int Known;

       char vertex[3];

       char path[3];

       struct Table *next;

};

int Dijkstra(struct Point *,struct Table *);

int PrintTable(int,struct Table *);

int PrintPath(int,struct Table *,struct Table *);

struct Table * CreateTable(int,int);

struct Point * FindSmallest(struct Table *,struct Point *);/*Find the vertex which has the smallest value reside in the table*/

int main()

{

       int i,j,num,temp,val;

       char c;

       struct Point *poinpre,*poinhead,*poin;

       struct Link *linpre,*linhead,*lin;

       struct Table *tabhead;

       poinpre=poinhead=poin=(struct Point *)malloc(sizeof(struct Point));

       poin->next=NULL;

       poin->work=NULL;

       restart:

       printf("Notice:if you wanna to input a vertex,you must use the format of number!/n");

       printf("Please input the number of points:/n");

       scanf("%d",&num);

       if(num>maxver||num<1||num%1!=0)

       {

              printf("/nNumber of points exception!");

              goto restart;

       }

       for(i=0;i<num;i++)

       {

              printf("Please input the points next to point %d,end with 0:/n",i+1);

              poin=(struct Point *)malloc(sizeof(struct Point));

              poinpre->next=poin;

              poin->vertex[0]='v';

              poin->vertex[1]='0'+i+1;

              poin->vertex[2]='/0';

              linpre=lin=poin->work;

              linpre->next=NULL;

              for(j=0;j<num-1;j++)

              {

              printf("The number of the %d th vertex linked to vertex %d:",j+1,i+1);

              scanf("%d",&temp);

              if(temp==0)

                     {

                     lin->next=NULL;

                     break;

                     }

              else

                     {

                     lin=(struct Link *)malloc(sizeof(struct Link));

                     linpre->next=lin;

                     lin->vertex[0]='v';

                     lin->vertex[1]='0'+temp;

                     lin->vertex[2]='/0';

                     printf("Please input the value betwixt %d th point towards %d th point:",i+1,temp);

                     scanf("%d",&val);

                     lin->value=val;

                     linpre=linpre->next;

                     lin->next=NULL;

                     }

              }

              poinpre=poinpre->next;

              poin->next=NULL;

       }

       printf("Please enter the vertex where Dijkstra algorithm starts:/n");

       scanf("%d",&temp);

       tabhead=CreateTable(temp,num);

       Dijkstra(poinhead,tabhead);

       PrintTable(temp,tabhead);

       return OK;

}

struct Table * CreateTable(int vertex,int total)

{

       struct Table *head,*pre,*p;

       int i;

       head=pre=p=(struct Table *)malloc(sizeof(struct Table));

       p->next=NULL;

       for(i=0;i<total;i++)

       {

              p=(struct Table *)malloc(sizeof(struct Table));

              pre->next=p;

              if(i+1==vertex)

              {

                     p->vertex[0]='v';

                     p->vertex[1]='0'+i+1;

                     p->vertex[2]='/0';

                     p->cost=0;

                     p->Known=0;

              }

              else

              {

                     p->vertex[0]='v';

                     p->vertex[1]='0'+i+1;

                     p->vertex[2]='/0';

                     p->cost=maxium;

                     p->Known=0;

              }

              p->next=NULL;

              pre=pre->next;

       }

       return head;

}

int Dijkstra(struct Point *p1,struct Table *p2) /* Core of the programm*/

{

       int costs;

       char temp;

       struct Point *poinhead=p1,*now;

       struct Link *linna;

       struct Table *tabhead=p2,*searc,*result;

       while(1)

       {

              now=FindSmallest(tabhead,poinhead);

              if(now==NULL)

                     break;

              result=p2;

              result=result->next;

              while(result!=NULL)

              {

                     if(result->vertex[1]==now->vertex[1])

                            break;

                     else

                            result=result->next;

              }

              linna=now->work->next;

              while(linna!=NULL) /* update all the vertexs linked to the signed vertex*/

              {

                     temp=linna->vertex[1];

                     searc=tabhead->next;

                     while(searc!=NULL)

                     {

                            if(searc->vertex[1]==temp)/*find the vertex linked to the signed vertex in the table and update*/

                            {

                                   if((result->cost+linna->value)<searc->cost)

                                   {

                                   searc->cost=result->cost+linna->value;/*set the new value*/

                                   searc->path[0]='v';

                                   searc->path[1]=now->vertex[1];

                                   searc->path[2]='/0';

                                   }

                                   break;

                            }

                            else

                                   searc=searc->next;

                     }

                     linna=linna->next;

              }

       }

       return 1;

}

struct Point * FindSmallest(struct Table *head,struct Point *poinhead)

{

       struct Point *result;

       struct Table *temp;

       int min=maxium,status=0;

       head=head->next;

       poinhead=poinhead->next;

       while(head!=NULL)

       {

              if(!head->Known&&head->cost<min)

              {

                     min=head->cost;

                     result=poinhead;

                     temp=head;

                     status=1;

              }

              head=head->next;

              poinhead=poinhead->next;

       }

       if(status)

       {

              temp->Known=1;

              return result;

       }

       else

              return NULL;

}

int PrintTable(int start,struct Table *head)

{

       struct Table *begin=head;

       head=head->next;

       while(head!=NULL)

       {

              if((head->vertex[1]-'0')!=start)

                     PrintPath(start,head,begin);

              head=head->next;

       }

       return OK;

}

int PrintPath(int start,struct Table *head,struct Table *begin)

{

       struct Table *temp=begin->next,*p,*t;

       p=head;

       t=begin;

       if((p->vertex[1]-'0')!=start&&p!=NULL)

       {

              while(temp->vertex[1]!=p->path[1]&&temp!=NULL)

                     temp=temp->next;

              PrintPath(start,temp,t);

              printf("%s",p->vertex);

       }

       else

              if(p!=NULL)

              printf("/n%s",p->vertex);

       return OK;

}