library_for_cpp

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:heavy_check_mark: Graph/Graph/Two_Edge_Connected_Components.hpp

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#pragma once

#include"Lowlink.hpp"

namespace graph {
    class Two_Edge_Connected_Components {
        public:
        vector<vector<int>> components;
        vector<int> component_ids;

        Two_Edge_Connected_Components(const Graph &G) {
            calculate(G);
        }

        private:
        vector<bool> bridges;
        void calculate(const Graph &G) {
            bridges = Lowlink(G).bridge;

            components.clear();
            component_ids.assign(G.order(), -1);

            for (int x = 0; x < G.order(); x++) {
                unless(component_ids[x] == -1) { continue; }
                dfs(G, x);
            }
        }

        void dfs(const Graph &G, int start) {
            int component_id = components.size();

            components.emplace_back();
            component_ids[start] = component_id;

            stack<int> st;
            st.emplace(start);
            components[component_id].emplace_back(start);

            while(!st.empty()) {
                int x = st.top(); st.pop();
                for (auto [edge_id, y]: G.incidence(x)) {
                    if (bridges[edge_id]) { continue; }
                    unless (component_ids[y] == -1) { continue; }

                    component_ids[y] = component_id;
                    components[component_id].emplace_back(y);
                    st.emplace(y);
                }
            }
        }
    };
}
#line 2 "Graph/Graph/Two_Edge_Connected_Components.hpp"

#line 2 "Graph/Graph/Lowlink.hpp"

#line 2 "Graph/Graph/Graph.hpp"

#line 2 "template/template.hpp"

using namespace std;

// intrinstic
#include <immintrin.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

// utility
#line 2 "template/utility.hpp"

using ll = long long;

// a ← max(a, b) を実行する. a が更新されたら, 返り値が true.
template<typename T, typename U>
inline bool chmax(T &a, const U b){
    return (a < b ? a = b, 1: 0);
}

// a ← min(a, b) を実行する. a が更新されたら, 返り値が true.
template<typename T, typename U>
inline bool chmin(T &a, const U b){
    return (a > b ? a = b, 1: 0);
}
#line 59 "template/template.hpp"

// math
#line 2 "template/math.hpp"

// 除算に関する関数

// floor(x / y) を求める.
template<typename T, typename U>
T div_floor(T x, U y){ return (x > 0 ? x / y: (x - y + 1) / y); }

// ceil(x / y) を求める.
template<typename T, typename U>
T div_ceil(T x, U y){ return (x > 0 ? (x + y - 1) / y: x / y) ;}

// x を y で割った余りを求める.
template<typename T, typename U>
T mod(T x, U y){
    T q = div_floor(x, y);
    return x - q * y ;
}

// x を y で割った商と余りを求める.
template<typename T, typename U>
pair<T, T> divmod(T x, U y){
    T q = div_floor(x, y);
    return {q, x - q * y};
}

// 四捨五入を求める.
template<typename T, typename U>
T round(T x, U y){
    T q, r;
    tie (q, r) = divmod(x, y);
    return (r >= div_ceil(y, 2)) ? q + 1 : q;
}

// 指数に関する関数

// x の y 乗を求める.
ll intpow(ll x, ll y){
    ll a = 1;
    while (y){
        if (y & 1) { a *= x; }
        x *= x;
        y >>= 1;
    }
    return a;
}

// x の y 乗を z で割った余りを求める.
ll modpow(ll x, ll y, ll z){
    ll a = 1;
    while (y){
        if (y & 1) { (a *= x) %= z; }
        (x *= x) %= z;
        y >>= 1;
    }
    return a;
}

// x の y 乗を z で割った余りを求める.
template<typename T, typename U>
T modpow(T x, U y, T z) {
    T a = 1;
    while (y) {
        if (y & 1) { (a *= x) %= z; }

        (x *= x) %= z;
        y >>= 1;
    }

    return a;
}

// vector の要素の総和を求める.
ll sum(vector<ll> &X){
    ll y = 0;
    for (auto &&x: X) { y+=x; }
    return y;
}

// vector の要素の総和を求める.
template<typename T>
T sum(vector<T> &X){
    T y = T(0);
    for (auto &&x: X) { y += x; }
    return y;
}

// a x + b y = gcd(a, b) を満たす整数の組 (a, b) に対して, (x, y, gcd(a, b)) を求める.
tuple<ll, ll, ll> Extended_Euclid(ll a, ll b) {
    ll s = 1, t = 0, u = 0, v = 1;
    while (b) {
        ll q;
        tie(q, a, b) = make_tuple(div_floor(a, b), b, mod(a, b));
        tie(s, t) = make_pair(t, s - q * t);
        tie(u, v) = make_pair(v, u - q * v);
    }

    return make_tuple(s, u, a);
}

// floor(sqrt(N)) を求める (N < 0 のときは, 0 とする).
ll isqrt(const ll &N) { 
    if (N <= 0) { return 0; }

    ll x = sqrt(N);
    while ((x + 1) * (x + 1) <= N) { x++; }
    while (x * x > N) { x--; }

    return x;
}

// floor(sqrt(N)) を求める (N < 0 のときは, 0 とする).
ll floor_sqrt(const ll &N) { return isqrt(N); }

// ceil(sqrt(N)) を求める (N < 0 のときは, 0 とする).
ll ceil_sqrt(const ll &N) {
    ll x = isqrt(N);
    return x * x == N ? x : x + 1;
}
#line 62 "template/template.hpp"

// inout
#line 1 "template/inout.hpp"
// 入出力
template<class... T>
void input(T&... a){ (cin >> ... >> a); }

void print(){ cout << "\n"; }

template<class T, class... Ts>
void print(const T& a, const Ts&... b){
    cout << a;
    (cout << ... << (cout << " ", b));
    cout << "\n";
}

template<typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &P){
    is >> P.first >> P.second;
    return is;
}

template<typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &P){
    os << P.first << " " << P.second;
    return os;
}

template<typename T>
vector<T> vector_input(int N, int index){
    vector<T> X(N+index);
    for (int i=index; i<index+N; i++) cin >> X[i];
    return X;
}

template<typename T>
istream &operator>>(istream &is, vector<T> &X){
    for (auto &x: X) { is >> x; }
    return is;
}

template<typename T>
ostream &operator<<(ostream &os, const vector<T> &X){
    int s = (int)X.size();
    for (int i = 0; i < s; i++) { os << (i ? " " : "") << X[i]; }
    return os;
}

template<typename T>
ostream &operator<<(ostream &os, const unordered_set<T> &S){
    int i = 0;
    for (T a: S) {os << (i ? " ": "") << a; i++;}
    return os;
}

template<typename T>
ostream &operator<<(ostream &os, const set<T> &S){
    int i = 0;
    for (T a: S) { os << (i ? " ": "") << a; i++; }
    return os;
}

template<typename T>
ostream &operator<<(ostream &os, const unordered_multiset<T> &S){
    int i = 0;
    for (T a: S) { os << (i ? " ": "") << a; i++; }
    return os;
}

template<typename T>
ostream &operator<<(ostream &os, const multiset<T> &S){
    int i = 0;
    for (T a: S) { os << (i ? " ": "") << a; i++; }
    return os;
}
#line 65 "template/template.hpp"

// macro
#line 2 "template/macro.hpp"

// マクロの定義
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if
#define unless(cond) if (!(cond))
#define until(cond) while (!(cond))
#define loop while (true)

// オーバーロードマクロ
#define overload2(_1, _2, name, ...) name
#define overload3(_1, _2, _3, name, ...) name
#define overload4(_1, _2, _3, _4, name, ...) name
#define overload5(_1, _2, _3, _4, _5, name, ...) name

// 繰り返し系
#define rep1(n) for (ll i = 0; i < n; i++)
#define rep2(i, n) for (ll i = 0; i < n; i++)
#define rep3(i, a, b) for (ll i = a; i < b; i++)
#define rep4(i, a, b, c) for (ll i = a; i < b; i += c)
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)

#define foreach1(x, a) for (auto &&x: a)
#define foreach2(x, y, a) for (auto &&[x, y]: a)
#define foreach3(x, y, z, a) for (auto &&[x, y, z]: a)
#define foreach4(x, y, z, w, a) for (auto &&[x, y, z, w]: a)
#define foreach(...) overload5(__VA_ARGS__, foreach4, foreach3, foreach2, foreach1)(__VA_ARGS__)
#line 68 "template/template.hpp"

// bitop
#line 2 "template/bitop.hpp"

// 非負整数 x の bit legnth を求める.
ll bit_length(ll x) {
    if (x == 0) { return 0; }
    return (sizeof(long) * CHAR_BIT) - __builtin_clzll(x);
}

// 非負整数 x の popcount を求める.
ll popcount(ll x) { return __builtin_popcountll(x); }

// 正の整数 x に対して, floor(log2(x)) を求める.
ll floor_log2(ll x) { return bit_length(x) - 1; }

// 正の整数 x に対して, ceil(log2(x)) を求める.
ll ceil_log2(ll x) { return bit_length(x - 1); }

// x の第 k ビットを取得する
int get_bit(ll x, int k) { return (x >> k) & 1; }

// x のビット列を取得する.
// k はビット列の長さとする.
vector<int> get_bits(ll x, int k) {
    vector<int> bits(k);
    rep(i, k) {
        bits[i] = x & 1;
        x >>= 1;
    }

    return bits;
}

// x のビット列を取得する.
vector<int> get_bits(ll x) { return get_bits(x, bit_length(x)); }
#line 4 "Graph/Graph/Graph.hpp"

namespace graph {
    struct Edge {
        int id, u, v;

        Edge() = default;
        Edge(int id, int u, int v): id(id), u(u), v(v) {}
    };

    class Graph {
        private:
        vector<vector<pair<int, int>>> incidences; // { edge_id, neighbor_vertex }
        vector<Edge> edges;

        public:
        int edge_id_offset;

        public:
        Graph(int n, int edge_id_offset = 0): edge_id_offset(edge_id_offset) {
            incidences.assign(n, {});
            edges.resize(edge_id_offset, Edge());
        }
        
        inline int order() const { return int(incidences.size()); }

        inline int size() const { return int(edges.size()) - edge_id_offset; }

        // 頂点 u から頂点 v への辺を追加する.
        int add_edge(int u, int v) {
            int id = int(edges.size());

            incidences[u].emplace_back(id, v);
            incidences[v].emplace_back(id, u);
            edges.emplace_back(Edge(id, u, v));

            return id;
        }

        // 頂点 u に接続する辺 ID と隣接頂点 v のペア { ID, v } のリストを取得
        inline const vector<pair<int, int>>& incidence (int u) const { return incidences[u]; }

        // 辺 ID が id であり, source が u である辺を取得する.
        inline const Edge& get_edge(int id) const { return edges[id]; }

        // 辺 ID が id であり, source が u である辺を取得する.
        inline Edge& get_edge(int id) { return edges[id]; }
    };
}
#line 4 "Graph/Graph/Lowlink.hpp"

namespace graph {
    class Lowlink {
        private:
        vector<bool> used;

        public:
        vector<bool> bridge, articulation;
        vector<int> ord, low;

        Lowlink(const Graph &G) {
            int N = G.order(), M = G.size();
            used.assign(N, false);
            ord.assign(N, -1);
            low.assign(N, -1);

            bridge.assign(M + G.edge_id_offset, false);
            articulation.assign(N, false);

            int k = 0;
            for (int i = 0; i < N; i++) {
                unless(used[i]) { k = dfs(G, i, k, -1); }
            }
        }

        private:
        int dfs(const Graph &G, int v, int k, int parent) {
            used[v] = true;
            ord[v] = k++;
            low[v] = ord[v];

            bool is_articulation = false;
            int children_number = 0;

            for (auto [edge_id, target]: G.incidence(v)) {
                if (used[target]) {
                    unless (target == parent) {
                        low[v] = min(low[v], ord[target]);
                    }
                    continue;
                }

                children_number++;
                k = dfs(G, target, k, v);
                low[v] = min(low[v], low[target]);

                if (parent != -1 && ord[v] <= low[target]) { is_articulation = true; }
                if (ord[v] < low[target]) { bridge[edge_id] = true; }
            }

            if (parent == -1 && children_number >= 2) { is_articulation = true; }
            if (is_articulation) { articulation[v] = true; }

            return k;
        }
    };
}
#line 4 "Graph/Graph/Two_Edge_Connected_Components.hpp"

namespace graph {
    class Two_Edge_Connected_Components {
        public:
        vector<vector<int>> components;
        vector<int> component_ids;

        Two_Edge_Connected_Components(const Graph &G) {
            calculate(G);
        }

        private:
        vector<bool> bridges;
        void calculate(const Graph &G) {
            bridges = Lowlink(G).bridge;

            components.clear();
            component_ids.assign(G.order(), -1);

            for (int x = 0; x < G.order(); x++) {
                unless(component_ids[x] == -1) { continue; }
                dfs(G, x);
            }
        }

        void dfs(const Graph &G, int start) {
            int component_id = components.size();

            components.emplace_back();
            component_ids[start] = component_id;

            stack<int> st;
            st.emplace(start);
            components[component_id].emplace_back(start);

            while(!st.empty()) {
                int x = st.top(); st.pop();
                for (auto [edge_id, y]: G.incidence(x)) {
                    if (bridges[edge_id]) { continue; }
                    unless (component_ids[y] == -1) { continue; }

                    component_ids[y] = component_id;
                    components[component_id].emplace_back(y);
                    st.emplace(y);
                }
            }
        }
    };
}
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