Heap optimization of Dijkstra (Dijkstra) Shortest Path algorithm

The Dijkstra (Dijkstra) Shortest path algorithm is a short-circuit algorithm that has been rigorously proven for time complexity.

Optimization is the use of heap optimization each time the minimum value, but in the shortest path relaxation process, dist is constantly modified, so, in order to be able to reduce the complexity to O (NLOGN), dist modification, in the heap also to be modified.

Note that the Dijkstra (Dijkstra) Shortest path algorithm can only be used for positive weight edges.

1#include <cstdio>2#include <cstring>3#include <iostream>4#include <algorithm>5 using namespacestd;6 7 Const intmaxn=10001;8 Const intmaxm=400002;9 intn,m;Ten intDIST[MAXN]; One  A intLen; - intHEAD[MAXN],NEXT[MAXM],ADJ[MAXM],WEIGHT[MAXM]; - intC; the  - intPOS[MAXN]; -  - structnode + { -     intDist,id; + }HEAP[MAXN]; A  at voidPushdown (intx) - { -     inti; -      while((i=x<<1) <=len)//Len -     { -         if(i<len&&heap[i].dist>heap[i+1].dist) i++;//I<len in         if(heap[i].dist<heap[x].dist) -         { to swap (heap[i],heap[x]); +pos[heap[i].id]=i; -pos[heap[x].id]=x; thex=i; *         } $         Else  Break;Panax Notoginseng     } - } the  + voidbuild () A { the      for(intI=1; i<=n;i++) +     { -heap[i].dist=Dist[i]; $Heap[i].id=i; $pos[i]=i; -     } -      for(inti=n/2; i>=1; i--) the pushdown (i); - }Wuyi  the voidAdjustintID) - { Wu     intI=Pos[id]; -heap[i].dist=Dist[id]; About      while(i>1&&heap[i].dist2].dist) $     { -Swap (heap[i],heap[i/2]); -I/=2; -pos[heap[i*2].id]=i*2; A     } +pos[id]=i; the } -  $ inttaketop () the { the     inttop=heap[1].id; theheap[1]=heap[len--]; thePushdown (1); -     returntop; in } the  the voidAddedge (intUintVintW) About { theC++; theadj[c]=v; thenext[c]=Head[u]; +Weight[c]=w;// -head[u]=C; the }Bayi  the voidDijkstraints) the { -memset (Dist,0x7f7f7f7f,sizeof(Dist)); -dist[s]=0; theBuild ();// the      for(intA=1; a<=n;a++) the     { the         intp=taketop (); -          for(intI=head[p];i;i=Next[i]) the         { the             intv=Adj[i]; the             if(dist[v]>dist[p]+Weight[i])94             { thedist[v]=dist[p]+Weight[i]; the Adjust (v); the             }98         } About     } -     101 }102 103 intMain ()104 { theFreopen ("dijkstra.in","R", stdin);106Freopen ("Dijkstra.out","W", stdout);107scanf"%d%d",&n,&m);108     ints,e;109scanf"%d%d",&s,&e); thelen=N;111      for(intI=1; i<=m;i++) the     {113         inta,b,w; thescanf" %d%d%d",&a,&b,&W); the Addedge (a,b,w); the Addedge (b,a,w);117     }118 Dijkstra (s);119 //for (int i=1;i<=n;i++) - //printf ("%d:%d\n", I,dist[i]);121printf"%d", Dist[e]);122     return 0;123}

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Dijkstra (Dijkstra) Shortest path algorithm for heap optimization