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lowlinkを用いた橋・関節点の検出
(graph/lowlink.hpp)

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• Last update: 2025-07-01 03:22:56+09:00
• Include: #include "graph/lowlink.hpp"

lowlinkを用いた橋・関節点の検出

使い方

• lowlink(vector<vector<int>> g) : グラフ $G$ に関する lowlink を求めるコンストラクタ。 $O(N)$
• is_bridge(int u, int v) : 辺 $(u, v)$ が橋かどうかを返す。 $O(1)$
• is_articulation(int v) : 頂点 $v$ が関節点かどうかを返す。 $O(1)$

Required by

• 二重辺連結成分分解 (graph/two_edge_connected_components.hpp)

Verified with

• verify/aoj/grl/3_A.test.cpp
• verify/aoj/grl/3_B.test.cpp
• verify/yosupo/two_edge_connected_components.test.cpp

Code

#pragma once

#include<vector>
#include<utility>

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 2 "graph/lowlink.hpp"

#include<vector>
#include<utility>

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];
	}
};

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