有向图上支配树

Posted 2021-02-10 wang9897

　按照论文的做法  引入半支配点 然后用处理DAG图的做法去处理支配树即可 存模板

#include <algorithm>
#include <iostream>
#include <cstring>
#include <cstdio>
#include <vector>
#include <stack>
#include <queue>
#include <cmath>
#include <set>
#include <map>
#define mp make_pair
#define pb push_back
#define pii pair<int,int>
#define link(x) for(edge *j=h[x];j;j=j->next)
#define inc(i,l,r) for(int i=l;i<=r;i++)
#define dec(i,r,l) for(int i=r;i>=l;i--)
const int MAXN=3e5+10;
const double eps=1e-8;
#define ll long long
using namespace std;
struct edge{int t;edge*next;}e[MAXN<<1],*h[MAXN],*o=e;
void add(int x,int y){o->t=y;o->next=h[x];h[x]=o++;}
ll read(){
    ll x=0,f=1;char ch=getchar();
    while(!isdigit(ch)){if(ch==‘-‘)f=-1;ch=getchar();}
    while(isdigit(ch))x=x*10+ch-‘0‘,ch=getchar();
    return x*f;
}
bool vis[MAXN];
int p[MAXN],tot,fp[MAXN],Dep[MAXN];
int fa[MAXN],du[MAXN];
vector<int>vec[MAXN],v1[MAXN],v2[MAXN];
void dfs(int x,int pre,int deep){
    p[x]=++tot;fp[p[x]]=x;fa[x]=pre;Dep[x]=deep+1;
    link(x){
	if(vis[j->t])continue;
	vis[j->t]=1;v1[x].pb(j->t);du[j->t]++,v2[j->t].pb(x);
	dfs(j->t,x,deep+1);
    }
}
int Min(int x,int y){
    if(Dep[x]<Dep[y])return x;
    return y;
}


int f[MAXN],key[MAXN],n;
int find1(int x){
    if(x==f[x])return x;
    int y=find1(f[x]);
    key[x]=Min(key[x],key[f[x]]);
    f[x]=y;
    return y;
}
queue<int>que;
int F[MAXN][21],dep[MAXN];



int Lca(int x,int y){
    if(dep[x]<dep[y])swap(x,y);
    int tmp=dep[x]-dep[y];
    for(int i=0;i<=20;i++)if(tmp&(1<<i))x=F[x][i];
    if(x==y)return x;
    for(int i=20;i>=0;i--){
	if(F[x][i]!=F[y][i])x=F[x][i],y=F[y][i];
    }
    return F[x][0];
}

void Topu(int s){
    F[s][0]=0;dep[s]=1;que.push(s);
    while(!que.empty()){
	int x=que.front();que.pop();
	for(int i=0;i<v1[x].size();i++){
	    int y=v1[x][i];du[y]--;
	    if(!du[y]){
		que.push(y);int lca=x;
		for(int j=0;j<v2[y].size();j++)lca=Lca(lca,v2[y][j]);
		F[y][0]=lca;dep[y]=dep[lca]+1;add(lca,y);
		inc(j,1,20)F[y][j]=F[F[y][j-1]][j-1];
	    }
	}
    }
}
int sz[MAXN];
vector<int>ans;
void dfs1(int x,int pre){
    link(x){
	dfs1(j->t,x);sz[x]+=sz[j->t];
    }
}
int main(){
    n=read();int m=read();int s=read();
    inc(i,1,n+m)Dep[i]=n+m+1;
    int cnt=n;
    int x,y;
    inc(i,1,m)x=read(),y=read(),cnt++,add(x,cnt),add(cnt,y),vec[y].pb(cnt),vec[cnt].pb(x);
    inc(i,1,cnt)f[i]=key[i]=i;
    vis[s]=1;dfs(s,0,0);
    dec(i,tot,1){
	y=fp[i];
	for(int j=0;j<vec[fp[i]].size();j++){
	    x=vec[fp[i]][j];
	    find1(x);
	    key[y]=Min(key[y],key[x]);
	}
	if(fa[y])f[y]=fa[y],v1[key[y]].pb(y),du[y]++,v2[y].pb(key[y]);
    }
    memset(h,0,sizeof(h));o=e;
    Topu(s);
    inc(i,1,n)sz[i]=1;
    dfs1(s,0);
    inc(i,1,m)if(!sz[i+n])ans.pb(i);
    printf("%d
",ans.size());
    for(int i=0;i<ans.size();i++)printf("%d ",ans[i]);
    printf("
");
}