Poj2449:k Short Circuit

Remmarguts ' Date

Time Limit: 4000MS		Memory Limit: 65536K
Total Submissions: 26355		Accepted: 7170

Description

"Good man never makes girls wait or breaks an appointment!" said the Mandarin duck father. Softly touching he little Ducks ' head, he told them a story.

"Prince Remmarguts lives in his kingdom udf–united Delta of Freedom. One day their neighboring country sent them Princess Uyuw on a diplomatic mission. "

"Erenow, the princess sent remmarguts a letter, informing him that she would come to the hall and hold commercial talks WI Th UDF if and only if the Prince go and meet her via the k-th shortest path. (In fact, UYUW-does not want-come at all) "

Being interested in the trade development and such a lovely girl, Prince remmarguts really became enamored. He needs you-the Prime Minister ' s help!

Details:udf ' s capital consists of N stations. The hall is numbered S, while the station numbered T denotes Prince ' current place. M Muddy directed sideways connect some of the stations. Remmarguts ' path to welcome the princess might include the same station twice or more than twice, even it's the station W ITH number S or T. Different paths with same length would be considered disparate.

Input

The first line contains the numbers n and M (1 <= n <=, 0 <= M <= 100000). Stations is numbered from 1 to N. Each of the following M lines contains three integer numbers a, B and T (1 <= A, b <= N, 1 <= T <= 100). It shows that there is a directed sideway from A-th station to B-th station with time T.

The last line consists of three integer numbers S, T and K (1 <= S, T <= N, 1 <= K <= 1000).

Output

A single line consisting of a single integer number:the length (time required) to welcome Princess Uyuw using the k-th sh Ortest path. If k-th Shortest path does not exist, you should output "-1" (without quotes) instead.

Sample Input

2 21 2 52 1 41 2 2

Sample Output

14

Idea: Using a * algorithm to find the shortest way. The first search to the end of the shortest, the second search to the end of the short-circuit ... K to the end of the search to a short circuit. The valuation function of the A * algorithm f (x) =g (x) +h (x). g (x): The distance from the starting point to the current node. H (x): The distance from the current node to the end point. The reverse edge can be constructed using SPFA.

#include <cstdio>#include<cstring>#include<queue>using namespacestd;Const intmaxn=1005;Const intinf=0x3f3f3f3f;structedge{intTo,w,next;} es[100005],rves[100005];intn,m;intsrc,tml,kth;intHead[maxn],tot;intRhead[maxn],rtot;voidAddedge (intUintVintW) {es[tot].to=v; ES[TOT].W=W; Es[tot].next=Head[u]; Head[u]=tot++; Rves[rtot].to=T; RVES[RTOT].W=W; Rves[rtot].next=Rhead[v]; RHEAD[V]=rtot++;}intD[MAXN],VIS[MAXN];voidSPFA (intS//Determining the Valuation function h (x) using the inverse edge: the distance from I to tml{     for(intI=1; i<=n;i++) {D[i]=INF; Vis[i]=0; } Queue<int>que;    Que.push (s); D[s]=0; Vis[s]=1;  while(!Que.empty ()) {        intu=Que.front (); Que.pop (); Vis[u]=0;  for(inti=rhead[u];i!=-1; i=Rves[i].next) {Edge e=Rves[i]; if(d[e.to]>d[u]+e.w) {d[e.to]=d[u]+E.W; if(!Vis[e.to]) {Vis[e.to]=1;                Que.push (e.to); }            }        }    } }structnode{intnod,g,h; Node () {} node (intCnod,intCgintch): Nod (Cnod), G (CG), h (ch) {}BOOL operator< (ConstNode &node)Const    {        returnG+h > node.g+node.h; }};intAstarints) {Priority_queue<Node>que; Que.push (Node (s),0, D[s]));//g (x): The distance from SRC to I. h (x): The distance from I to tml.     while(!Que.empty ()) {Node now=que.top (); Que.pop (); intu=Now.nod; if(u==tml) {kth--; if(kth==0)returnNow.g+now.h;//section K Shortest Way        }         for(inti=head[u];i!=-1; i=Es[i].next) {Edge e=Es[i]; intg=now.g+E.W; intH=D[e.to];            Que.push (Node (e.to,g,h)); }    }    return-1;}intMain () { while(SCANF ("%d%d", &n,&m)! =EOF) {memset (head,-1,sizeof(head)); memset (Rhead,-1,sizeof(Rhead)); Tot=0; Rtot=0;  for(intI=0; i<m;i++)        {            intu,v,w; scanf ("%d%d%d",&u,&v,&W);        Addedge (U,V,W); } scanf ("%d%d%d",&src,&tml,&kth); if(src==tml) kth++;//if SRC equals tml then the shortest circuit is 0, not countingSPFA (tml); printf ("%d\n", Astar (SRC)); }        return 0;}

Poj2449:k Short Circuit