[Luogu] P3388 【模板】割点（割顶）

题目描述

给出一个n个点，m条边的无向图，求图的割点。

题目解析

割点判定条件：

x == from时：子树个数>1

x != from时：low[l[i].to] >= dfn[x]

Code

#include<iostream>
#include<cstdio>
using namespace std;

const int MAXN = 20000 + 5;
const int MAXM = 100000 + 5;

struct Edge {
    int nxt;
    int to;
} l[MAXM<<1];

int n,m,ans;
int head[MAXN],cnt;
int low[MAXN],dfn[MAXN],stamp;
int stack[MAXN],top;
bool cut[MAXN];

inline int rd() {
    int x=0,f=1;char ch=getchar();
    while(!isdigit(ch)) {f=ch=='-'?-1:1;ch=getchar();}
    while(isdigit(ch)) {x=x*10+ch-'0';ch=getchar();}
    return x*f;
}

inline void add(int x,int y) {
    cnt++;
    l[cnt].nxt = head[x];
    l[cnt].to = y;
    head[x] = cnt;
    return;
}

void tarjan(int x,int from) {
    low[x] = dfn[x] = ++stamp;
    int son = 0;
    for(int i = head[x];i;i = l[i].nxt) {
        if(!dfn[l[i].to]) {
            tarjan(l[i].to,x);
            low[x] = min(low[x],low[l[i].to]);
            if(low[l[i].to] >= dfn[x] && x != from) cut[x] = true;
            if(x == from) son++;
        }
        low[x] = min(low[x],dfn[l[i].to]);
    }
    if(son > 1 && x == from) cut[x] = true;
    return;
}

int main() {
    scanf("%d%d",&n,&m);
    int x,y;
    for(register int i = 1;i <= m;i++) {
        x = rd(), y = rd();
        add(x,y), add(y,x);
    }
    for(register int i = 1;i <= n;i++) {
        if(!dfn[i]) tarjan(i,i);
    }
    for(register int i = 1;i <= n;i++) ans += cut[i];
    printf("%d\n",ans);
    for(int i = 1;i <= n;i++) {
        if(cut[i]) printf("%d ",i);
    }
    return 0;
}