"Codeforces" 915 D. Almost acyclic Graph topological sort finding ring

"topic" D. Almost acyclic Graph

"Test Instructions" given n points of the direction of the graph (no heavy edges), asked whether the deletion of an edge so that the full picture is not ring. N<=500,m<=10^5.

"Algorithm" topology sequencing

"Solving" to find a simple ring, the edge you want to delete must pass through the ring. Try each edge on the ring (up to n edges) again to determine whether the full graph has a ring.

Topology sequencing to the simple ring: The remaining graph is the ring + ring inside the DAG,DFS process will walk into the dead end of the point mark-1, access to the superscript 1, find the point visited is a simple ring. Change the starting point until the ring is found.

Complexity of O (nm).

#include <cstdio>#include<queue>#include<algorithm>using namespacestd;Const intmaxn= -, maxm=100010;structedge{intV from;} E[MAXM];intMAP[MAXN][MAXN],TOT,CNT,N,M,FIRST[MAXN],P,VIS[MAXN],inch[Maxn],deg[maxn],suc[maxn];queue<int>Q;voidInsertintUintV) {Tot++;e[tot].v=v;e[tot]. from=first[u];first[u]=tot;inch[v]++;}voidDfsintXintFA) {    if(p| | vis[x]==-1)return; if(vis[x]==1) {p=x;suc[fa]=x;return;} VIS[X]=1;  for(intI=first[x];i;i=e[i]. from)if(deg[e[i].v]>0) {DFS (e[i].v,x); if(p) {if(Fa&&!suc[p]) suc[fa]=x; Break;} }    if(!p) vis[x]=-1;}BOOLSolveinto) {CNT=0;  for(intI=1; i<=n;i++) {deg[i]=inch[i];if(I==E[O].V) deg[i]--;if(deg[i]==0) Q.push (i), cnt++;}  while(!Q.empty ()) {        intx=Q.front ();        Q.pop ();  for(intI=first[x];i;i=e[i]. from)if(i!=o&&--deg[e[i].v]==0) Q.push (E[I].V), cnt++; }    if(cnt==n)return 1; return 0;} intMain () {scanf ("%d%d",&n,&m);  for(intI=1; i<=m;i++){        intu,v; scanf ("%d%d",&u,&v); Insert (U,V); Map[u][v]=tot; } CNT=0;  for(intI=1; i<=n;i++) {deg[i]=inch[i];if(inch[i]==0) Q.push (i), cnt++;}  while(!Q.empty ()) {        intx=Q.front ();        Q.pop ();  for(intI=first[x];i;i=e[i]. from)if(--deg[e[i].v]==0) Q.push (E[I].V), cnt++; }    if(cnt==n) {printf ("YES");return 0;}  for(intI=1; i<=n;i++)if(deg[i]>0&AMP;&AMP;!P) DFS (i,0); intpp=p;  Do{        if(Solve (map[p][suc[p])) {printf ("YES");return 0;} P=Suc[p]; } while(p!=PP); printf ("NO"); return 0;}

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Another solution: Enumeration point i,in[i]--, topological sorting to find the ring. This is equivalent to deleting an edge that points to n after the full-view look-up loop.

"Codeforces" 915 D. Almost acyclic Graph topological sort finding ring