< learning notes > A * algorithm for K-short

A tunnel to the surface

A simple problem surface

• The first line gives N (points), M (number of sides) (1 <= N <=, 0 <= M <= 100000).
• The following M-line gives three number Ai,bi,ti per row, indicating a one-way edge with a weight of t from A to B.
• Finally, the s,t,k is given, which indicates that the S-T short circuit is obtained.
• Special:
  
  • S–>s (d=0) cannot be counted as a road at the same time as the beginning and the end.
  • The topic will give you multiple sets of data.
  • Even though there are several paths to t that are the same distances, they are still recorded as different paths.

Positive SolutionA * algorithm

G[i] for the distance from the beginning S to I, H[i] (expected) for the end point T to i the shortest, with SPFA pretreatment. Using the Dijkstra approach, start with S, and each time the smallest point of the current H[i]+g[i] is ejected from the heap. When the end-point T is ejected from the K-time, the g[i at this time] is the S-to-t-K short.

code QWQ

1#include <iostream>2#include <cstdio>3#include <cstring>4#include <algorithm>5#include <cmath>6#include <queue>7 using namespacestd;8 9 intn,m,a,b,c,s,t,k,cnt;Ten intfirst[1010],next[100010],h[1010]; One BOOLused[1010]; A  - structmaple{ -     intf,t,d; the}rode[100010]; -  - structleaf{ -     intf,g,h; +     BOOL operator< (ConstLeaf &a)Const{ -          returna.g+a.h<g+h;  +     } A };  at  - voidBuild (intFintTintd) - { -rode[++cnt]=(Maple) {f,t,d}; -next[cnt]=First[f]; -first[f]=CNT; in } -  to voidSPFA () + { -queue<int> q;//  thememset (H, the,sizeof(h)); *memset (Used,0,sizeof(used)); $h[t]=0;Panax Notoginsengused[t]=1; - Q.push (T); the      while(!q.empty ()) +     { A         intA=Q.front (); the Q.pop (); +used[a]=0; -          for(intI=first[a];i;i=Next[i]) $            if(h[rode[i].t]>h[a]+rode[i].d) $            { -h[rode[i].t]=h[a]+rode[i].d; -                   if(!used[rode[i].t]) the                   { -used[rode[i].t]=1;Wuyi Q.push (rode[i].t); the                   } -            }  Wu     } - } About  $ intSearch () - { -      if(h[s]>1e9+7)return-1;//from the beginning to the end -      if(s==t) + +K; APriority_queue<leaf> Q;//define the function without emptying the QWQ. +Q.push (leaf) {S,0, H[s]}); the       while(!q.empty ()) -      { $Leaf a=q.top (); the Q.pop (); the          if(a.f==T) the          { the--K; -               if(k==0)returnA.G; in          } the           for(intI=first[a.f];i;i=Next[i]) theQ.push (leaf) {rode[i].t,a.g+rode[i].d,h[rode[i].t]}); About      }  the      return-1;//I can't find the K-short . the } the intMain () + { -      while(SCANF ("%d%d", &n,&m)! =EOF) the     {BayiCnt=0; thememset (First,0,sizeof(first)); theMemset (Next,0,sizeof(next)); -           for(intI=1; i<=m;++i) -          {  thescanf"%d%d%d",&a,&b,&c); the Build (b,a,c); the          } thescanf"%d%d%d",&s,&t,&K);  - SPFA (); thememset (First,0,sizeof(first)); theMemset (Next,0,sizeof(next)); theCnt=0;94           for(intI=1; i<=m;++i) theBuild (RODE[I].T,RODE[I].F,RODE[I].D);//re-build the Edge the          intans=search (); theprintf"%d\n", ans);98     } About     return 0; -}

< Learning notes > A * algorithm for K-short circuits