mmrz's library

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verify/yosupo/two_edge_connected_components.test.cpp

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• Last update: 2025-07-01 03:22:56+09:00
• Problem: https://judge.yosupo.jp/problem/two_edge_connected_components

Depends on

• Union-Find (data_structure/union_find.hpp)
• lowlinkを用いた橋・関節点の検出 (graph/lowlink.hpp)
• 二重辺連結成分分解 (graph/two_edge_connected_components.hpp)
• template/template.hpp

Code

#define PROBLEM "https://judge.yosupo.jp/problem/two_edge_connected_components"

#include "./../../template/template.hpp"
#include "./../../graph/two_edge_connected_components.hpp"

void mmrz::solve(){
	int n, m;
	cin >> n >> m;
	vector<vector<int>> g(n);
	while(m--){
		int a, b;
		cin >> a >> b;
		g[a].pb(b);
		g[b].pb(a);
	}

	auto [groups, comp, tree] = two_edge_connected_components(g);

	cout << len(groups) << '\n';
	for(auto v : groups){
		cout << len(v);
		for(auto c : v){
			cout << " " << c;
		}
		cout << '\n';
	}
}

#line 1 "verify/yosupo/two_edge_connected_components.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/two_edge_connected_components"

#line 1 "template/template.hpp"
# include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
const double pi = acos(-1);
template<class T>constexpr T inf() { return ::std::numeric_limits<T>::max(); }
template<class T>constexpr T hinf() { return inf<T>() / 2; }
template <typename T_char>T_char TL(T_char cX) { return tolower(cX); }
template <typename T_char>T_char TU(T_char cX) { return toupper(cX); }
template<class T> bool chmin(T& a,T b) { if(a > b){a = b; return true;} return false; }
template<class T> bool chmax(T& a,T b) { if(a < b){a = b; return true;} return false; }
int popcnt(unsigned long long n) { int cnt = 0; for (int i = 0; i < 64; i++)if ((n >> i) & 1)cnt++; return cnt; }
int d_sum(ll n) { int ret = 0; while (n > 0) { ret += n % 10; n /= 10; }return ret; }
int d_cnt(ll n) { int ret = 0; while (n > 0) { ret++; n /= 10; }return ret; }
ll gcd(ll a, ll b) { if (b == 0)return a; return gcd(b, a%b); };
ll lcm(ll a, ll b) { ll g = gcd(a, b); return a / g*b; };
ll MOD(ll x, ll m){return (x%m+m)%m; }
ll FLOOR(ll x, ll m) {ll r = (x%m+m)%m; return (x-r)/m; }
template<class T> using dijk = priority_queue<T, vector<T>, greater<T>>;
# define all(qpqpq)           (qpqpq).begin(),(qpqpq).end()
# define UNIQUE(wpwpw)        (wpwpw).erase(unique(all((wpwpw))),(wpwpw).end())
# define LOWER(epepe)         transform(all((epepe)),(epepe).begin(),TL<char>)
# define UPPER(rprpr)         transform(all((rprpr)),(rprpr).begin(),TU<char>)
# define rep(i,upupu)         for(ll i = 0, i##_len = (upupu);(i) < (i##_len);(i)++)
# define reps(i,opopo)        for(ll i = 1, i##_len = (opopo);(i) <= (i##_len);(i)++)
# define len(x)                ((ll)(x).size())
# define bit(n)               (1LL << (n))
# define pb push_back
# define eb emplace_back
# define exists(c, e)         ((c).find(e) != (c).end())

struct INIT{
	INIT(){
		std::ios::sync_with_stdio(false);
		std::cin.tie(0);
		cout << fixed << setprecision(20);
	}
}INIT;

namespace mmrz {
	void solve();
}

int main(){
	mmrz::solve();
}
#line 2 "graph/two_edge_connected_components.hpp"

#line 2 "data_structure/union_find.hpp"

#line 5 "data_structure/union_find.hpp"

struct union_find {
	std::vector<int> v;
	int g_size;
	int n;

	union_find(size_t size) : v(size, -1), g_size(size), n(size) {}

	int root(int x){
		assert(x < n);
		return (v[x] < 0 ? x : v[x] = root(v[x]));
	}

	bool is_root(int x){
		assert(x < n);
		return root(x) == x;
	}

	bool unite(int x, int y){
		assert(x < n && y < n);
		x = root(x);
		y = root(y);
		if(x != y){
			if(v[x] > v[y])std::swap(x, y);
			v[x] += v[y];
			v[y] = x;
			g_size--;
			return true;
		}
		return false;
	}

	bool is_same(int x,int y){
		assert(x < n && y < n);
		return root(x) == root(y);
	}

	int get_size(int x){
		assert(x < n);
		x = root(x);
		return -v[x];
	}

	int groups_size(){
		return g_size;
	}

	std::vector<std::vector<int>> groups(){
		std::vector<std::vector<int>> member(n);
		for(int i = 0;i < n;i++){
			member[root(i)].push_back(i);
		}

		std::vector<std::vector<int>> ret;
		for(int i = 0;i < n;i++){
			if(member[i].empty())continue;
			ret.push_back(member[i]);
		}
		return ret;
	}
};
#line 2 "graph/lowlink.hpp"

#line 5 "graph/lowlink.hpp"

class lowlink{
	std::vector<std::vector<int>> g;
	std::vector<int> order, low;
	std::vector<bool> __is_articulation;

	void dfs(int cur, int pre, int &time){
		int count_child = 0;
		low[cur] = order[cur] = time++;
		bool first_parent = true;
		for(int to : g[cur]){
			if(to == pre && std::exchange(first_parent, false))continue;
			if(order[to] == -1){
				dfs(to, cur, time);
				count_child++;
				if(pre != -1){
					if(not __is_articulation[cur]) __is_articulation[cur] = (low[to] >= order[cur]);
				}
				low[cur] = std::min(low[cur], low[to]);
			}else{
				low[cur] = std::min(low[cur], order[to]);
			}
		}
		if(pre == -1){
			__is_articulation[cur] = (count_child >= 2);
		}
	}

public:

	lowlink(const std::vector<std::vector<int>> &_g) : g(_g), order(g.size(), -1), low(g.size()), __is_articulation(g.size(), false){
		int time = 0;
		for(int v = 0;v < (int)g.size();v++){
			if(order[v] == -1){
				dfs(v, -1, time);
			}
		}
	}

	bool is_bridge(int u, int v) const {
		if(order[u] > order[v]){
			std::swap(u, v);
		}
		return order[u] < low[v];
	}

	bool is_articulation(int v) const {
		return __is_articulation[v];
	}
};
#line 5 "graph/two_edge_connected_components.hpp"

#line 8 "graph/two_edge_connected_components.hpp"

auto two_edge_connected_components(std::vector<std::vector<int>> &g){
	lowlink l(g);
	union_find uf((int)g.size());
	for(int i = 0;i < (int)g.size();i++){
		for(int to : g[i]){
			if(not l.is_bridge(i, to)){
				uf.unite(i, to);
			}
		}
	}

	std::vector<std::vector<int>> group = uf.groups();
	std::vector<int> comp((int)g.size());
	for(int i = 0;i < (int)group.size();i++){
		for(int v : group[i]){
			comp[v] = i;
		}
	}

	std::vector<std::vector<int>> tree((int)group.size());
	for(int i = 0;i < (int)g.size();i++){
		for(int to : g[i]){
			if(comp[i] != comp[to]){
				tree[comp[i]].push_back(comp[to]);
			}
		}
	}

	return make_tuple(group, comp, tree);
}
#line 5 "verify/yosupo/two_edge_connected_components.test.cpp"

void mmrz::solve(){
	int n, m;
	cin >> n >> m;
	vector<vector<int>> g(n);
	while(m--){
		int a, b;
		cin >> a >> b;
		g[a].pb(b);
		g[b].pb(a);
	}

	auto [groups, comp, tree] = two_edge_connected_components(g);

	cout << len(groups) << '\n';
	for(auto v : groups){
		cout << len(v);
		for(auto c : v){
			cout << " " << c;
		}
		cout << '\n';
	}
}

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