cplib-cpp

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:heavy_check_mark: graph/test/two-edge-connected-components.test.cpp

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/two_edge_connected_components"
#include "../lowlink.hpp"
#include <iostream>
#include <vector>
using namespace std;

int main() {
    cin.tie(nullptr), ios::sync_with_stdio(false);

    int V, E;
    cin >> V >> E;
    lowlink graph(V);
    while (E--) {
        int s, t;
        cin >> s >> t;
        graph.add_edge(s, t);
    }

    auto ret = graph.two_edge_connected_components();
    cout << ret.size() << '\n';
    for (const auto &vec : ret) {
        cout << vec.size();
        for (auto x : vec) cout << ' ' << x;
        cout << '\n';
    }
}
#line 1 "graph/test/two-edge-connected-components.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/two_edge_connected_components"
#line 2 "graph/lowlink.hpp"
#include <algorithm>
#include <cassert>
#include <queue>
#include <utility>
#include <vector>

struct lowlink {
    int V; // # of vertices
    int E; // # of edges
    int k;
    std::vector<std::vector<std::pair<int, int>>> to;
    std::vector<std::pair<int, int>> edges;
    std::vector<int> root_ids; // DFS forestの構築で根になった頂点

    std::vector<int> is_bridge;       // Whether edge i is bridge or not, size = E
    std::vector<int> is_articulation; // whether vertex i is articulation point or not, size = V

    // lowlink
    std::vector<int> order;           // visiting order of DFS tree, size = V
    std::vector<int> lowlink_;        // size = V
    std::vector<int> is_dfstree_edge; // size = E

    int tecc_num;             // 二重辺連結成分数
    std::vector<int> tecc_id; // 各頂点が何個目の二重辺連結成分か

    int tvcc_num;             // 二重頂点連結成分数
    std::vector<int> tvcc_id; // 各辺が何個目の二重頂点連結成分か

    lowlink(int V)
        : V(V), E(0), k(0), to(V), is_articulation(V, 0), order(V, -1), lowlink_(V, -1),
          tecc_num(0), tvcc_num(0) {}

    void add_edge(int v1, int v2) {
        assert(v1 >= 0 and v1 < V);
        assert(v2 >= 0 and v2 < V);
        to[v1].emplace_back(v2, E);
        to[v2].emplace_back(v1, E);
        edges.emplace_back(v1, v2);
        is_bridge.push_back(0);
        is_dfstree_edge.push_back(0);
        tvcc_id.push_back(-1);
        E++;
    }

    std::vector<int> _edge_stack;
    int _root_now;

    // Build DFS tree
    // Complexity: O(V + E)
    void dfs_lowlink(int now, int prv_eid = -1) {
        if (prv_eid < 0) _root_now = k;
        if (prv_eid == -1) root_ids.push_back(now);
        order[now] = lowlink_[now] = k++;
        for (const auto &nxt : to[now]) {
            if (nxt.second == prv_eid) continue;
            if (order[nxt.first] < order[now]) _edge_stack.push_back(nxt.second);
            if (order[nxt.first] >= 0) {
                lowlink_[now] = std::min(lowlink_[now], order[nxt.first]);
            } else {
                is_dfstree_edge[nxt.second] = 1;
                dfs_lowlink(nxt.first, nxt.second);
                lowlink_[now] = std::min(lowlink_[now], lowlink_[nxt.first]);

                if ((order[now] == _root_now and order[nxt.first] != _root_now + 1) or
                    (order[now] != _root_now and lowlink_[nxt.first] >= order[now])) {
                    is_articulation[now] = 1;
                }
                if (lowlink_[nxt.first] >= order[now]) {
                    while (true) {
                        int e = _edge_stack.back();
                        tvcc_id[e] = tvcc_num;
                        _edge_stack.pop_back();
                        if (e == nxt.second) break;
                    }
                    tvcc_num++;
                }
            }
        }
    }

    void build() {
        for (int v = 0; v < V; ++v) {
            if (order[v] < 0) dfs_lowlink(v);
        }

        // Find all bridges
        // Complexity: O(V + E)
        for (int i = 0; i < E; i++) {
            int v1 = edges[i].first, v2 = edges[i].second;
            if (order[v1] > order[v2]) std::swap(v1, v2);
            is_bridge[i] = order[v1] < lowlink_[v2];
        }
    }

    // Find two-edge-connected components and classify all vertices
    // Complexity: O(V + E)
    std::vector<std::vector<int>> two_edge_connected_components() {
        build();
        tecc_num = 0;
        tecc_id.assign(V, -1);

        std::vector<int> st;
        for (int i = 0; i < V; i++) {
            if (tecc_id[i] != -1) continue;
            tecc_id[i] = tecc_num;
            st.push_back(i);
            while (!st.empty()) {
                int now = st.back();
                st.pop_back();
                for (const auto &edge : to[now]) {
                    int nxt = edge.first;
                    if (tecc_id[nxt] >= 0 or is_bridge[edge.second]) continue;
                    tecc_id[nxt] = tecc_num;
                    st.push_back(nxt);
                }
            }
            ++tecc_num;
        }
        std::vector<std::vector<int>> ret(tecc_num);
        for (int i = 0; i < V; ++i) ret[tecc_id[i]].push_back(i);
        return ret;
    }

    // Find biconnected components and enumerate vertices for each component.
    // Complexity: O(V \log V + E)
    std::vector<std::vector<int>> biconnected_components_by_vertices() {
        build();
        std::vector<std::vector<int>> ret(tvcc_num);
        for (int i = 0; i < E; ++i) {
            ret[tvcc_id[i]].push_back(edges[i].first);
            ret[tvcc_id[i]].push_back(edges[i].second);
        }

        for (auto &vec : ret) {
            std::sort(vec.begin(), vec.end());
            vec.erase(std::unique(vec.begin(), vec.end()), vec.end());
        }

        for (int i = 0; i < V; ++i) {
            if (to[i].empty()) ret.push_back({i});
        }

        return ret;
    }

    // Find biconnected components and classify all edges
    // Complexity: O(V + E)
    std::vector<std::vector<int>> biconnected_components_by_edges() {
        build();
        std::vector<std::vector<int>> ret(tvcc_num);
        for (int i = 0; i < E; ++i) ret[tvcc_id[i]].push_back(i);
        return ret;
    }
};
#line 3 "graph/test/two-edge-connected-components.test.cpp"
#include <iostream>
#line 5 "graph/test/two-edge-connected-components.test.cpp"
using namespace std;

int main() {
    cin.tie(nullptr), ios::sync_with_stdio(false);

    int V, E;
    cin >> V >> E;
    lowlink graph(V);
    while (E--) {
        int s, t;
        cin >> s >> t;
        graph.add_edge(s, t);
    }

    auto ret = graph.two_edge_connected_components();
    cout << ret.size() << '\n';
    for (const auto &vec : ret) {
        cout << vec.size();
        for (auto x : vec) cout << ' ' << x;
        cout << '\n';
    }
}
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