Graph/DfsTree/StronglyConnected.h

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• Last update: 2024-06-02 18:23:02+08:00
• Link: https://cses.fi/problemset/task/1686/
• Link: https://judge.yosupo.jp/problem/scc
• Link: https://oj.vnoi.info/problem/bedao_g16_b

Required by

• Graph/2sat.h

Verified with

• Graph/tests/aizu_grl_3_c_strongly_connected.test.cpp
• Graph/tests/aizu_grl_4_a_strongly_connected_cycle_check.test.cpp
• Graph/tests/strongly_connected.test.cpp
• Graph/tests/two_sat.test.cpp

Code

// Index from 0
// Usage:
// DirectedDfs tree;
// Now you can use tree.scc
//
// Note: reverse(tree.scc) is topo sorted
//
// Tested:
// - (requires scc to be topo sorted) https://judge.yosupo.jp/problem/scc
// - https://cses.fi/problemset/task/1686/
// - (edges have costs) https://oj.vnoi.info/problem/bedao_g16_b
struct DirectedDfs {
    vector<vector<int>> g;
    int n;
    vector<int> num, low, current, S;
    int counter;
    vector<int> comp_ids;
    vector< vector<int> > scc;

    DirectedDfs(const vector<vector<int>>& _g) : g(_g), n(g.size()),
            num(n, -1), low(n, 0), current(n, 0), counter(0), comp_ids(n, -1) {
        for (int i = 0; i < n; i++) {
            if (num[i] == -1) dfs(i);
        }
    }

    void dfs(int u) {
        low[u] = num[u] = counter++;
        S.push_back(u);
        current[u] = 1;
        for (auto v : g[u]) {
            if (num[v] == -1) dfs(v);
            if (current[v]) low[u] = min(low[u], low[v]);
        }
        if (low[u] == num[u]) {
            scc.push_back(vector<int>());
            while (1) {
                int v = S.back(); S.pop_back(); current[v] = 0;
                scc.back().push_back(v);
                comp_ids[v] = ((int) scc.size()) - 1;
                if (u == v) break;
            }
        }
    }

    // build DAG of strongly connected components
    // Returns: adjacency list of DAG
    std::vector<std::vector<int>> build_scc_dag() {
        std::vector<std::vector<int>> dag(scc.size());
        for (int u = 0; u < n; u++) {
            int x = comp_ids[u];
            for (int v : g[u]) {
                int y = comp_ids[v];
                if (x != y) {
                    dag[x].push_back(y);
                }
            }
        }
        return dag;
    }
};

#line 1 "Graph/DfsTree/StronglyConnected.h"
// Index from 0
// Usage:
// DirectedDfs tree;
// Now you can use tree.scc
//
// Note: reverse(tree.scc) is topo sorted
//
// Tested:
// - (requires scc to be topo sorted) https://judge.yosupo.jp/problem/scc
// - https://cses.fi/problemset/task/1686/
// - (edges have costs) https://oj.vnoi.info/problem/bedao_g16_b
struct DirectedDfs {
    vector<vector<int>> g;
    int n;
    vector<int> num, low, current, S;
    int counter;
    vector<int> comp_ids;
    vector< vector<int> > scc;

    DirectedDfs(const vector<vector<int>>& _g) : g(_g), n(g.size()),
            num(n, -1), low(n, 0), current(n, 0), counter(0), comp_ids(n, -1) {
        for (int i = 0; i < n; i++) {
            if (num[i] == -1) dfs(i);
        }
    }

    void dfs(int u) {
        low[u] = num[u] = counter++;
        S.push_back(u);
        current[u] = 1;
        for (auto v : g[u]) {
            if (num[v] == -1) dfs(v);
            if (current[v]) low[u] = min(low[u], low[v]);
        }
        if (low[u] == num[u]) {
            scc.push_back(vector<int>());
            while (1) {
                int v = S.back(); S.pop_back(); current[v] = 0;
                scc.back().push_back(v);
                comp_ids[v] = ((int) scc.size()) - 1;
                if (u == v) break;
            }
        }
    }

    // build DAG of strongly connected components
    // Returns: adjacency list of DAG
    std::vector<std::vector<int>> build_scc_dag() {
        std::vector<std::vector<int>> dag(scc.size());
        for (int u = 0; u < n; u++) {
            int x = comp_ids[u];
            for (int v : g[u]) {
                int y = comp_ids[v];
                if (x != y) {
                    dag[x].push_back(y);
                }
            }
        }
        return dag;
    }
};

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