graph/connected-components/strongly-connected-components.hpp

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• Last update: 2024-10-04 14:05:18+02:00
• Include: #include "graph/connected-components/strongly-connected-components.hpp"

Depends on

• graph/graph-template.hpp

Verified with

• test/aoj-grl-3-c.test.cpp
• test/yosupo-scc.test.cpp

Code

#pragma once

/*
Kosaraju 算法
复杂度 O(E + V)
强联通分量：一个强联通分量里的任意两个点两两互达
*/

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

template <typename T = int>
struct StronglyConnectedComponents : Graph<T> {
   public:
    using Graph<T>::Graph;
    using Graph<T>::g;
    vector<int> comp;           // comp[i] i 点在的组 id
    Graph<T> dag;               // 缩点后的图
    vector<vector<int>> group;  // group[i] 表示第 i 组有的点

    void build() {
        int n = g.size();
        rg = Graph<T>(n);
        for (int i = 0; i < n; i++) {
            for (auto &e : g[i]) {
                int u = e.from, v = e.to;
                rg.add_directed_edge(v, u, e.cost);
            }
        }

        used = vector<int>(n, 0);
        comp = vector<int>(n, -1);

        for (int i = 0; i < n; i++) {
            if (used[i] == 0) {
                dfs(i);
            }
        }
        reverse(order.begin(), order.end());

        int cnt = 0;
        for (int i = 0; i < n; i++) {
            int u = order[i];
            if (comp[u] == -1) {
                rdfs(u, cnt);
                cnt++;
            }
        }

        dag = Graph<T>(cnt);
        group.resize(cnt);
        for (int i = 0; i < n; i++) {
            for (auto &e : g[i]) {
                int u = comp[e.from], v = comp[e.to];
                if (u == v) continue;
                dag.add_directed_edge(u, v, e.cost);
            }
            group[comp[i]].push_back(i);
        }
    }

    int operator[](int k) const {
        return comp[k];
    }

   private:
    vector<int> order, used;
    Graph<T> rg;

    void dfs(int idx) {
        used[idx] = 1;
        for (auto &e : g[idx]) {
            int v = e.to;
            if (used[v] == 0) {
                dfs(v);
            }
        }
        order.push_back(idx);
    }

    void rdfs(int idx, int cnt) {
        comp[idx] = cnt;
        for (auto &e : rg[idx]) {
            int v = e.to;
            if (comp[v] == -1) {
                rdfs(v, cnt);
            }
        }
    }
};

#line 2 "graph/connected-components/strongly-connected-components.hpp"

/*
Kosaraju 算法
复杂度 O(E + V)
强联通分量：一个强联通分量里的任意两个点两两互达
*/

#line 2 "graph/graph-template.hpp"
#include <bits/stdc++.h>
using namespace std;

template <typename T = int>
struct Edge {
    int from, to;
    T cost;
    int idx;

    Edge() = default;

    Edge(int from, int to, T cost = 1, int idx = -1)
        : from(from), to(to), cost(cost), idx(idx) {}

    operator int() const { return to; }
};

template <typename T = int>
struct Graph {
    vector<vector<Edge<T> > > g;
    int es;

    Graph() = default;

    explicit Graph(int n) : g(n), es(0) {}

    size_t size() const { return g.size(); }

    virtual void add_directed_edge(int from, int to, T cost = 1) {
        g[from].emplace_back(from, to, cost, es++);
    }

    // virtual 可以被重载，实现多态
    virtual void add_edge(int from, int to, T cost = 1) {
        g[from].emplace_back(from, to, cost, es);
        g[to].emplace_back(to, from, cost, es++);
    }

    void read(int M, int padding = -1, bool weighted = false,
              bool directed = false) {
        for (int i = 0; i < M; i++) {
            int a, b;
            cin >> a >> b;
            a += padding;
            b += padding;
            T c = T(1);
            if (weighted) cin >> c;
            if (directed)
                add_directed_edge(a, b, c);
            else
                add_edge(a, b, c);
        }
    }

    inline vector<Edge<T> > &operator[](const int &k) { return g[k]; }

    inline const vector<Edge<T> > &operator[](const int &k) const { return g[k]; }
};

template <typename T = int>
using Edges = vector<Edge<T> >;
#line 10 "graph/connected-components/strongly-connected-components.hpp"

template <typename T = int>
struct StronglyConnectedComponents : Graph<T> {
   public:
    using Graph<T>::Graph;
    using Graph<T>::g;
    vector<int> comp;           // comp[i] i 点在的组 id
    Graph<T> dag;               // 缩点后的图
    vector<vector<int>> group;  // group[i] 表示第 i 组有的点

    void build() {
        int n = g.size();
        rg = Graph<T>(n);
        for (int i = 0; i < n; i++) {
            for (auto &e : g[i]) {
                int u = e.from, v = e.to;
                rg.add_directed_edge(v, u, e.cost);
            }
        }

        used = vector<int>(n, 0);
        comp = vector<int>(n, -1);

        for (int i = 0; i < n; i++) {
            if (used[i] == 0) {
                dfs(i);
            }
        }
        reverse(order.begin(), order.end());

        int cnt = 0;
        for (int i = 0; i < n; i++) {
            int u = order[i];
            if (comp[u] == -1) {
                rdfs(u, cnt);
                cnt++;
            }
        }

        dag = Graph<T>(cnt);
        group.resize(cnt);
        for (int i = 0; i < n; i++) {
            for (auto &e : g[i]) {
                int u = comp[e.from], v = comp[e.to];
                if (u == v) continue;
                dag.add_directed_edge(u, v, e.cost);
            }
            group[comp[i]].push_back(i);
        }
    }

    int operator[](int k) const {
        return comp[k];
    }

   private:
    vector<int> order, used;
    Graph<T> rg;

    void dfs(int idx) {
        used[idx] = 1;
        for (auto &e : g[idx]) {
            int v = e.to;
            if (used[v] == 0) {
                dfs(v);
            }
        }
        order.push_back(idx);
    }

    void rdfs(int idx, int cnt) {
        comp[idx] = cnt;
        for (auto &e : rg[idx]) {
            int v = e.to;
            if (comp[v] == -1) {
                rdfs(v, cnt);
            }
        }
    }
};

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