Book Shortest Path algorithm

Use HDU2544 to sort out the shortest-path algorithm recently learned

1.Dijkstra algorithm

Principle: Set S Indicates the point where the shortest path has been found, d[] represents the distance from the current point to the source point

Initially, the collection has only the source points, when each point u enters the set S, with D[U]+W[U][V] to update the distance

Repeat this step to select the smallest entry set of d[] in all points outside s

Until all points are in the S collection

Limitation: The edge of the graph must be positive

Complexity: O (v*v), heap optimization ((e+v) LOGV)

(1) using adjacency matrix to implement

1#include <iostream>2#include <cstdio>3#include <cstring>4#include <cmath>5#include <stack>6#include <vector>7#include <map>8#include <Set>9#include <queue>Ten#include <algorithm> One using namespacestd; A  -typedefLong LongLL; - Const intINF = (1<< -)-1; the Const intMod=1000000007; - Const intmaxn=10005; - intW[MAXN][MAXN],D[MAXN],USED[MAXN]; - intn,m; +  - voidDijkstraints) { +memset (Used,0,sizeof(used)); A      for(intI=1; i<=n;i++) d[i]=INF; atd[s]=0; -      -      for(intk=1; k<=n;k++){ -         intp,m=INF; -          for(intI=1; i<=n;i++)if(!used[i]&&d[i]<m) m=d[p=i]; -used[p]=1; in          for(intI=1; i<=n;i++) D[i]=min (d[i],d[p]+w[p][i]); -     } to } +  - intMain () { the     inta,b,c; *      while(SCANF ("%d%d", &n,&m)!=eof&&n&&m) { $          for(intI=1; i<=n;i++){Panax Notoginseng              for(intj=1; j<=n;j++){ -                 if(I==J) w[i][j]=0; the                 Elsew[i][j]=INF; +             }             A         } the          +          for(intI=1; i<=m;i++){ -scanf" %d%d%d",&a,&b,&c); $w[a][b]=w[b][a]=C; $         } -Dijkstra1); -printf"%d\n", D[n]); the     } -     return 0;Wuyi}

View Code

(2) Using adjacency table to realize

Note Remember that each time you call Dijkstra (), first[] is set to 1

1#include <iostream>2#include <cstdio>3#include <cstring>4#include <cmath>5#include <stack>6#include <vector>7#include <map>8#include <Set>9#include <queue>Ten#include <algorithm> One using namespacestd; A  -typedefLong LongLL; - Const intINF = (1<< -)-1; the Const intMod=1000000007; - Const intmaxn=10005; - intD[MAXN],USED[MAXN],FIRSTT[MAXN],NEXTT[MAXN]; - intn,m,ecnt; +  - structedge{ +     intV,cost; A } E[MAXN]; at  - voidDijkstraints) { -memset (Used,0,sizeof(used)); -      for(intI=1; i<=n;i++) d[i]=INF; -d[s]=0; -      in      for(intk=1; k<=n;k++){ -         intp,m=INF; to          for(intI=1; i<=n;i++)if(!used[i]&&d[i]<m) m=d[p=i]; +used[p]=1; -          for(inti=firstt[p];i!=-1; i=Nextt[i]) { the             intv=e[i].v; *             if(d[v]>d[p]+e[i].cost) $d[v]=d[p]+E[i].cost;Panax Notoginseng         } -     } the } +  A voidAddedges (intUintVintW) { thenextt[++ecnt]=Firstt[u]; +e[ecnt].v=v; -e[ecnt].cost=W; $firstt[u]=ecnt;  $ } -  - intMain () { the     inta,b,c; -      while(SCANF ("%d%d", &n,&m)!=eof&&n&&m) {WuyiEcnt=0; thememset (firstt,-1,sizeof(FIRSTT)); -          Wu          for(intI=1; i<=m;i++){ -scanf" %d%d%d",&a,&b,&c); About addedges (a,b,c); $ addedges (b,a,c); -         } -Dijkstra1); -printf"%d\n", D[n]); A     } +     return 0; the}

View Code

Book Shortest Path algorithm