Dijkstra算法原理详细讲解

1、Dijkstra算法原理详细讲解如下图，设A为源点，求A到其他各顶点（B、C、D、E、F）的最短路径。 线上所标注为相邻线段之间的距离，即权值。（注：此图为随意所画，其相邻顶点间的距离与图中的目视长度不能一一对等）算法执行步骤如下表:S集合中AbiWs炳景潺役ATMO以A为中I簸，从A开嫩球合中怕。a RmAH6A *3中的IS点.二8划UTC=3的J湖短谊入mtnsK。c、&D也粗枳），），ATC0B&H以D力申同点， 从ATCT谜醯位 开蹴逸入E,此BJS富A C. B,D, !*tWftO2A-M0i-4C=3T*5,R ATCTE =7以E肿间点，从ATCTE寸这条觥

2、炳刑g 明） 岫到P&值映力ATCTDTP $发现HDTP珀瑚为炳6 AFUtB!S=U C. Bf以F供合己如查醍毕ttWit短路注ATM0 ATC=3,ATT 方ATC*6A C匕9枷故命独顾IB瞄城1AcutWs=a,c短签径ATMO,ATC二3以C为中词，从AT“3这条狼SJF速入B,此时S工&C、B牧时H短格经A-HW, ATC，3,ATCThS以B为铜点，从ATCTX5这必理V= A TC T45 （比上血* 一殉A晏短）CtW到8枷WA-HT邱ATCTHATC*7ATCTHIAU中的顶冬 8发现A HTg权值初t）g _iTlA TC TB TD *（比上面第二扳

3、的A TC TD，6要长）峋到D网更改力ATCTRATCTBTJC眦中的腹点=00溯UTCTDK成值为费短i.rV=A KTDTE 4 （比上面第二缁A K H H菱长）岫到E珈贼为 ATCTEm?的发现 ATCT5 权值为网ATCTET? M2(tt上面算四的ATCTDTP力Dijkstra算法的完整实现版本之算法的源代码样例图:输入格式:Turbu C*+ IDEvleAHEiiriiMJL Elie ouRber- fjf gjoints:F|，4I右噬tntt tIw M ntiAbfir af t|i 1*4e insult the uA1114 M mmh” of tlw 2 th

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6、twijet 3 th pa int towards th pc int ；4 i he- nikpibvr nf die 2 th vertex inknd to vArtv-x；J* Le-as E 4h|LLL Che lairit s. heitt tx linke! to vertciM 4-3Pleaurt he Vallie4 t)i pa int. t swrctn- 3 t)i |w int: 9The ibimber1of tIMT3 IhUBFLBXlinked La ver-leM 4-SPl4t IniMJit theM-twixt 4 t)i glmt tdwjua

7、 5 tJi point ：2I ho nun hr r of tlw 4 th vvrtflx I inked to vcrtoM 41 s 8P I a 1 n 1411 f Iw points n.葛上t峪po int& 电nd. ui h BThe timber of tlw? 1 th vertex 1 inlu*l to yerte-K 5siPleatv inpu.1 I he value betwixt S tli pa Ifkt tdtidrdft & th w Mt：；：；? The nufiliBr of tlNt 2 th urtax jinkt*d t

8、o veteM Sf3Plflnext=NULL;poin-work=NULL;restart:printf(Notice:if you wanna to input a vertex,you must use the format ofnumber!n);printf(Please input the number of points:n);scanf(%d,&num);if(nummaxver|num1|num%1!=0)(printf(nNumber of points exception!);goto restart;for(i=0;inext=poin;poin-vertex

9、0=v;poin-vertex1=0+i+1;poin-vertex2=0;linpre=lin=poin-work;linpre-next=NULL;for(j=0;jnext=NULL; break; else(lin=(struct Link *)malloc(sizeof(struct Link); linpre-next=lin;lin-vertex0=v;lin-vertex1=0+temp;lin-vertex2=0;printf(Please input the value betwixt %d th point towards %d thpoint:,i+1,temp);sc

10、anf(%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 * Crea

11、teTable(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;inext=p;if(i+1=vertex)( p-vertex0=v;p-vertex1=0+i+1;p-vertex2=0;p-cost=0; p-Known=0; else (p-vertex0=v;p-vertex1=0+i+1;p-vertex2=0; p-cost=maxium; p-Known=0; p-n

12、ext=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

13、=result-next;while(result!=NULL)( if(result-vertex1=now-vertex1) break;else result=result-next; linna=now-work-next;while(linna!=NULL) /* update all the vertexs linked to the signedvertex*/(temp=linna-vertex1; searc=tabhead-next;while(searc!=NULL)( if(searc-vertex1=temp)/*find thevertex linked to th

14、e signed vertex in the table and update*/(if(result-cost+linna-value)cost)( searc-cost=result-cost+linna-value;/*set the new value*/searc-path0=v;searc-path1=now-vertex1;searc-path2=0;break; else searc=searc-next; linna=linna-next;return 1; struct Point * FindSmallest(struct Table*head,struct Point

15、*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-costcost;result=poinhead;temp=head;status=1;head=head-next;poinhead=poinhead-next; if(status) (temp-Known=1;return result;elsereturn NULL;int PrintTable(int start,struct Table *head)(struct Table *begin=head;head=head-next;while(head!=NULL)(if(head-vertex1-0)!=start)PrintPath(start,head,begin); head=head-next; return OK; int PrintPath(int start,struct Table*head,struct Table