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

二重辺連結成分分解

使い方

tuple(vector<vector<int>>, vector<int>, vector<vector<int>>) two_edge_connected_components(vector<vector<int>> g) $G$ の二重辺連結成分分解をした

を返す。

Depends on

Verified with

Code

#pragma once

#include "../data_structure/union_find.hpp"
#include "./lowlink.hpp"

#include<cassert>
#include<tuple>

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 2 "graph/two_edge_connected_components.hpp"

#line 2 "data_structure/union_find.hpp"

#include<cassert>
#include<vector>

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 4 "graph/lowlink.hpp"
#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 5 "graph/two_edge_connected_components.hpp"

#line 7 "graph/two_edge_connected_components.hpp"
#include<tuple>

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);
}
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