Two Edge Connected Components
(graph/connected-components/TwoEdgeConnectedComponents.hpp)

• View this file on GitHub
• Last update: 2024-12-02 00:38:27+09:00
• Include: #include "graph/connected-components/TwoEdgeConnectedComponents.hpp"

概要

todo

計算量

todo

Depends on

• Low Link (graph/others/LowLink.hpp)

Verified with

• verify/LibraryChecker/graph/connected-components/TwoEdgeConnectedComponents.test.cpp

Code

#include "../others/LowLink.hpp"

class TwoEdgeConnectedComponents {
   private:
    int n;
    int m;
    int eid;
    vector<pair<int, int>> edges;
    LowLink l;

    void dfs(int v, int prev, int prev_eid, const vector<bool> &is_bridge, int cid) {
        cmp[v] = cid;
        for (auto &[nex, eid] : l.g[v]) {
            if (cmp[nex] == -1 and !is_bridge[eid]) {
                dfs(nex, v, eid, is_bridge, cid);
            }
        }
    }

   public:
    vector<int> cmp;
    vector<vector<int>> components;

    TwoEdgeConnectedComponents(int _n) : n(_n), l(_n), eid(0) {
        cmp.assign(n, -1);
    }

    void add_edge(int u, int v) {
        l.add_edge(u, v, eid);
        edges.emplace_back(u, v);
        eid++;
    }

    void build() {
        l.build();
        vector<bool> is_bridge(eid, false);
        for (int id : l.bridge) is_bridge[id] = true;

        int cid = 0;
        for (int i = 0; i < n; i++) {
            if (cmp[i] == -1) {
                dfs(i, -1, -1, is_bridge, cid++);
            }
        }
        components.resize(cid);
        for (int i = 0; i < n; i++) {
            components[cmp[i]].push_back(i);
        }
    }
};

#line 1 "graph/others/LowLink.hpp"
class LowLink {
   public:
    int n, time;
    vector<vector<pair<int, int>>> g;
    vector<bool> seen;
    vector<int> order, low;
    vector<int> articulation;
    vector<int> bridge;

    LowLink(int _n) : n(_n), time(0) {
        g.resize(n);
        seen.assign(n, false);
        order.assign(n, -1);
        low.assign(n, 0);
    }

    void add_edge(int u, int v, int eid) {
        g[u].emplace_back(v, eid);
        g[v].emplace_back(u, eid);
    }

    void dfs(int cur, int prev, int prev_eid) {
        seen[cur] = true;
        order[cur] = low[cur] = time++;
        int child = 0;
        bool is_articulation = false;
        for (auto &[nex, eid] : g[cur]) {
            if (!seen[nex]) {
                child++;
                dfs(nex, cur, eid);
                low[cur] = min(low[cur], low[nex]);
                if (prev != -1 and order[cur] <= low[nex]) is_articulation = true;
                if (order[cur] < low[nex]) bridge.push_back(eid);
            } else if (eid != prev_eid) {
                low[cur] = min(low[cur], order[nex]);
            }
        }
        if (prev == -1 and child > 1) is_articulation = true;
        if (is_articulation) articulation.push_back(cur);
    }

    void build() {
        for (int i = 0; i < n; i++) {
            if (!seen[i]) dfs(i, -1, -1);
        }
    }
};
#line 2 "graph/connected-components/TwoEdgeConnectedComponents.hpp"

class TwoEdgeConnectedComponents {
   private:
    int n;
    int m;
    int eid;
    vector<pair<int, int>> edges;
    LowLink l;

    void dfs(int v, int prev, int prev_eid, const vector<bool> &is_bridge, int cid) {
        cmp[v] = cid;
        for (auto &[nex, eid] : l.g[v]) {
            if (cmp[nex] == -1 and !is_bridge[eid]) {
                dfs(nex, v, eid, is_bridge, cid);
            }
        }
    }

   public:
    vector<int> cmp;
    vector<vector<int>> components;

    TwoEdgeConnectedComponents(int _n) : n(_n), l(_n), eid(0) {
        cmp.assign(n, -1);
    }

    void add_edge(int u, int v) {
        l.add_edge(u, v, eid);
        edges.emplace_back(u, v);
        eid++;
    }

    void build() {
        l.build();
        vector<bool> is_bridge(eid, false);
        for (int id : l.bridge) is_bridge[id] = true;

        int cid = 0;
        for (int i = 0; i < n; i++) {
            if (cmp[i] == -1) {
                dfs(i, -1, -1, is_bridge, cid++);
            }
        }
        components.resize(cid);
        for (int i = 0; i < n; i++) {
            components[cmp[i]].push_back(i);
        }
    }
};

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