图论new三个模板

边双连通分量：模板

#include<bits/stdc++.h>
using namespace std;
const int N = 5e5+5;
int n, m, cnt, ans, dfn[N], low[N]; //dfn记录dfs序，low表示这个点除树边外能连到最浅 
vector<int> mp[N], mp2[N];
vector<int> s;
void shuru() {
	int u, v;
	cin >> n >> m;
	for(int i = 1; i <= m; i++){
		cin >> u >> v;
		mp[u].push_back(v);
		mp[v].push_back(u);
	}
}
void dfs(int u, int f){
	dfn[u] = low[u] = ++cnt; //记录dfs序并初始化low 
	int falg = 0; //用来判重边 
	s.push_back(u);
	for(auto v : mp[u]){
		if(v == f && !cnt){
			flag = 1; 
			continue;	
		}
		if(!dfn[v]) dfs(v, u);
		low[u] = min(low[u], low[v]);//更新low 
	}
	if(low[u] == dfn[u]){//把在一个连通分量的点染成一个颜色
		++ans; //增加一个连通分量 
		while(1) {
			int x = s.back();s.pop_back();
			mp2[ans].push_back(x);
			if(x == u) break; 
		}		
	}
}
void shuchu(){
	cout << ans << endl;
	for(int i = 1; i <= ans; i++){
		cout << mp2[i].size() << " ";
		for(auto x : mp2[i]) cout << x << " ";
		cout << endl;
	}
}
int main(){
	shuru();
	for(int i = 1; i <= n; i++){
        if(dfn[i]) continue;
		dfs(i,i);
	}
	shuchu();
	return 0;
}

割点：模板

#include<bits/stdc++.h>
using namespace std;
const int N = 2e4+5;
int n, m, cnt, tot, dfn[N], low[N], g[N];
vector<int> mp[N], v;
vector<int> s;
void shuru(){
	int u, v;
	cin >> n >> m;
	for(int i = 1; i <= m; i++){
		cin >> u >> v;
		if(u == v) continue; //特判自环 
		mp[u].push_back(v);
		mp[v].push_back(u);
	}
}
void dfs(int u, int f){
	dfn[u] = low[u] = ++cnt;
	for(auto v : mp[u]){
		if(v == f) continue;
		if(!dfn[v]){
			dfs(v, u);
			low[u] = min(low[u], low[v]);
			if(low[v] >= dfn[u]) g[u]++; //如果儿子的low比父亲还深，说明父亲是一个割点	
		}
		else low[u] = min(low[u], dfn[v]); //如果不是树边，就不会吃v==f的判断，用dfn判才不会影响判割点 
	}
}
int main(){
	shuru();
	for(int i = 1; i <= n; i++){
		if(dfn[i]) continue;
		dfs(i,i);
		g[i]--;//特判根节点 
	}
	for(int i = 1; i <= n; i++){
		if(g[i] > 0) v.push_back(i);
	}
	cout << v.size() << endl;
	for(auto x : v) cout << x << " ";
	return 0;
} 

点双连通分量：模板

#include<bits/stdc++.h>
using namespace std;
const int N = 5e5+5;
int n, m, cnt, ans, dfn[N], low[N];
vector<int> mp[N], mp2[N];
vector<int> s;
void shuru(){
	int u, v;
	cin >> n >> m;
	for(int i = 1; i <= m; i++){
		cin >> u >> v;
		if(u == v) continue;
		mp[u].push_back(v);
		mp[v].push_back(u);
	}
}
void dfs(int u, int f){ //本质就是找割点 
	if(u == f && mp[u].empty()) { //一个点也是点双连通分量，要特判 
		++ans;
		mp2[ans].push_back(u);
	}
	dfn[u] = low[u] = ++cnt;
	s.push_back(u);
	for(auto v : mp[u]){
		if(v == f) continue;
		if(!dfn[v]){
			dfs(v, u);
			low[u] = min(low[u], low[v]);
			if(low[v] >= dfn[u]){ //类似于边双连通，用栈维护 
				++ans;
				while(1){
					int x = s.back(); s.pop_back();
					mp2[ans].push_back(x);
					if(x == v) break; 
				}
				mp2[ans].push_back(u); //要把割点本身放进去 
			}
		}
		else low[u] = min(low[u], dfn[v]); //类似割点特判 
	}
}
void shuchu(){
	cout << ans << endl;
	for(int i = 1; i <= ans; i++){
		cout << mp2[i].size() << " ";
		for(auto x : mp2[i]) cout << x << " ";
		cout << endl;
	}
}
int main(){
	shuru();
	for(int i = 1; i <= n; i++){
		if(dfn[i]) continue;
		dfs(i,i);
	}
	shuchu();
	return 0;
}