Fu_L's Library

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:heavy_check_mark: TwoEdgeConnectedComponents
(src/graph/two_edge_connected_components.hpp)

TwoEdgeConnectedComponents

無向グラフの二重辺連結成分分解を行います．

二重辺連結成分とは，無向グラフから橋を全て削除したときの連結成分です．

異なる $2$ つの二重辺連結成分 $A, B$ について，以下の性質が成り立ちます．

コンストラクタ

TwoEdgeConnectedComponents<T> tecc(Graph<T> g)

$n$ 頂点 $m$ 辺の無向グラフ g を二重辺連結成分分解します．

計算量

operator []

int tecc[int i]

頂点 i が何番目の二重辺連結成分に属するかを返します．

制約

計算量

メンバ変数

(1) vector<vector<int>> tecc.groups
(2) vector<vector<int>> tecc.tree

Depends on

Verified with

Code

#pragma once
#include "../template/template.hpp"
#include "./graph_template.hpp"
#include "./low_link.hpp"
template <typename T>
struct TwoEdgeConnectedComponents {
    vector<vector<int>> groups, tree;
    TwoEdgeConnectedComponents(const Graph<T>& g)
        : n(g.size()), k(0), low(g), comp(n, -1) {
        for(int i = 0; i < n; ++i) {
            if(comp[i] == -1) dfs(g, i, -1);
        }
        groups.resize(k);
        tree.resize(k);
        for(int i = 0; i < n; ++i) {
            groups[comp[i]].emplace_back(i);
        }
        for(const pair<int, int>& e : low.bridge) {
            int u = comp[e.first], v = comp[e.second];
            tree[u].emplace_back(v);
            tree[v].emplace_back(u);
        }
    }
    inline int operator[](const int& i) const {
        assert(0 <= i and i < n);
        return comp[i];
    }

   private:
    int n, k;
    LowLink<T> low;
    vector<int> comp;
    void dfs(const Graph<T>& g, const int i, const int p) {
        if(p >= 0 and low.ord[p] >= low.low[i]) comp[i] = comp[p];
        else comp[i] = k++;
        for(const Edge<T>& e : g[i]) {
            if(comp[e.to] == -1) dfs(g, e.to, i);
        }
    }
};
#line 2 "src/template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using P = pair<long long, long long>;
#define rep(i, a, b) for(long long i = (a); i < (b); ++i)
#define rrep(i, a, b) for(long long i = (a); i >= (b); --i)
constexpr long long inf = 4e18;
struct SetupIO {
    SetupIO() {
        ios::sync_with_stdio(0);
        cin.tie(0);
        cout << fixed << setprecision(30);
    }
} setup_io;
#line 3 "src/graph/graph_template.hpp"
template <typename T>
struct Edge {
    int from, to;
    T cost;
    int idx;
    Edge()
        : from(-1), to(-1), cost(-1), idx(-1) {}
    Edge(const int from, const int to, const T& cost = 1, const int idx = -1)
        : from(from), to(to), cost(cost), idx(idx) {}
    operator int() const {
        return to;
    }
};
template <typename T>
struct Graph {
    Graph(const int N)
        : n(N), es(0), g(N) {}
    int size() const {
        return n;
    }
    int edge_size() const {
        return es;
    }
    void add_edge(const int from, const int to, const T& cost = 1) {
        assert(0 <= from and from < n);
        assert(0 <= to and to < n);
        g[from].emplace_back(from, to, cost, es);
        g[to].emplace_back(to, from, cost, es++);
    }
    void add_directed_edge(const int from, const int to, const T& cost = 1) {
        assert(0 <= from and from < n);
        assert(0 <= to and to < n);
        g[from].emplace_back(from, to, cost, es++);
    }
    inline vector<Edge<T>>& operator[](const int& k) {
        assert(0 <= k and k < n);
        return g[k];
    }
    inline const vector<Edge<T>>& operator[](const int& k) const {
        assert(0 <= k and k < n);
        return g[k];
    }

   private:
    int n, es;
    vector<vector<Edge<T>>> g;
};
template <typename T>
using Edges = vector<Edge<T>>;
#line 4 "src/graph/low_link.hpp"
template <typename T>
struct LowLink {
    vector<int> ord, low, articulation;
    vector<pair<int, int>> bridge;
    LowLink(const Graph<T>& g)
        : ord(g.size(), -1), low(g.size(), -1) {
        for(int i = 0, k = 0; i < g.size(); ++i) {
            if(ord[i] == -1) k = dfs(g, i, k, -1);
        }
    }

   private:
    int dfs(const Graph<T>& g, const int idx, int k, const int par) {
        low[idx] = (ord[idx] = k++);
        int cnt = 0;
        bool arti = false, second = false;
        for(const Edge<T>& e : g[idx]) {
            const int to = e.to;
            if(ord[to] == -1) {
                ++cnt;
                k = dfs(g, to, k, idx);
                low[idx] = min(low[idx], low[to]);
                arti |= (par != -1) and (low[to] >= ord[idx]);
                if(ord[idx] < low[to]) {
                    bridge.emplace_back(minmax(idx, to));
                }
            } else if(to != par or second) {
                low[idx] = min(low[idx], ord[to]);
            } else {
                second = true;
            }
        }
        arti |= (par == -1) and (cnt > 1);
        if(arti) articulation.emplace_back(idx);
        return k;
    }
};
#line 5 "src/graph/two_edge_connected_components.hpp"
template <typename T>
struct TwoEdgeConnectedComponents {
    vector<vector<int>> groups, tree;
    TwoEdgeConnectedComponents(const Graph<T>& g)
        : n(g.size()), k(0), low(g), comp(n, -1) {
        for(int i = 0; i < n; ++i) {
            if(comp[i] == -1) dfs(g, i, -1);
        }
        groups.resize(k);
        tree.resize(k);
        for(int i = 0; i < n; ++i) {
            groups[comp[i]].emplace_back(i);
        }
        for(const pair<int, int>& e : low.bridge) {
            int u = comp[e.first], v = comp[e.second];
            tree[u].emplace_back(v);
            tree[v].emplace_back(u);
        }
    }
    inline int operator[](const int& i) const {
        assert(0 <= i and i < n);
        return comp[i];
    }

   private:
    int n, k;
    LowLink<T> low;
    vector<int> comp;
    void dfs(const Graph<T>& g, const int i, const int p) {
        if(p >= 0 and low.ord[p] >= low.low[i]) comp[i] = comp[p];
        else comp[i] = k++;
        for(const Edge<T>& e : g[i]) {
            if(comp[e.to] == -1) dfs(g, e.to, i);
        }
    }
};
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