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:heavy_check_mark: graph/connected-components/three-edge-connected-components.hpp

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Code

#pragma once

#include "../graph-template.hpp"
#include "incremental-bridge-connectivity.hpp"

template <typename T = int>
struct ThreeEdgeConnectedComponents : Graph<T> {
 public:
  using Graph<T>::Graph;
  using Graph<T>::g;
  vector<vector<int> > group;

  void build() {
    uf = UnionFind(g.size());
    bcc = IncrementalBridgeConnectivity(g.size());
    used.assign(g.size(), 0);
    in.assign(g.size(), 0);
    out.assign(g.size(), 0);
    deg.assign(g.size(), 0);
    low.assign(g.size(), g.size());
    for (size_t from = 0; from < g.size(); from++) {
      for (auto &to : g[from]) {
        if ((T)from < to) bcc.add_edge(from, to);
      }
    }
    int cnt = 0;
    for (size_t i = 0; i < g.size(); i++) {
      if (used[i]) continue;
      vector<int> tmp;
      dfs(i, -1, tmp, cnt);
      cnt++;
    }
    vector<int> id(g.size(), -1);
    cnt = 0;
    for (size_t i = 0; i < g.size(); i++) {
      if (id[uf.find(i)] == -1) id[uf.find(i)] = cnt++;
    }
    group.resize(cnt);
    for (size_t i = 0; i < g.size(); i++) {
      group[id[uf.find(i)]].emplace_back(i);
    }
  }

  int operator[](const int &k) { return uf.find(k); }

 private:
  vector<int> used;
  vector<int> in, out, low, deg;
  IncrementalBridgeConnectivity bcc;
  UnionFind uf;

  void absorb(vector<int> &path, int v, int w = -1) {
    while (!path.empty()) {
      int x = path.back();
      if (w != -1 && (in[x] > in[w] or in[w] >= out[x])) break;
      path.pop_back();
      uf.unite(v, x);
      deg[v] += deg[x] - 2;
    }
  }

  void dfs(int idx, int p, vector<int> &path, int &k) {
    used[idx] = 1;
    in[idx] = low[idx] = k++;
    for (auto &to : g[idx]) {
      if (idx == to || bcc.find(idx) != bcc.find(to)) continue;
      deg[idx]++;
      if (to == p) {
        p = -1;
        continue;
      }
      if (used[to]) {
        if (in[idx] > in[to]) {
          if (in[to] < low[idx]) {
            low[idx] = in[to];
            absorb(path, idx);
          }
        } else {
          deg[idx] -= 2;
          absorb(path, idx, to);
        }
      } else {
        vector<int> ps;
        dfs(to, idx, ps, k);
        if (deg[to] == 2) ps.pop_back();
        if (low[to] < low[idx]) {
          low[idx] = low[to];
          absorb(path, idx);
          path = ps;
        } else {
          absorb(ps, idx);
        }
      }
    }
    out[idx] = k;
    path.push_back(idx);
  }
};

#line 2 "graph/connected-components/three-edge-connected-components.hpp"

#line 2 "graph/graph-template.hpp"

/**
 * @brief Graph Template(グラフテンプレート)
 */
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(); }

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

  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 2 "graph/connected-components/incremental-bridge-connectivity.hpp"

#line 2 "structure/union-find/union-find.hpp"

struct UnionFind {
  vector<int> data;

  UnionFind() = default;

  explicit UnionFind(size_t sz) : data(sz, -1) {}

  bool unite(int x, int y) {
    x = find(x), y = find(y);
    if (x == y) return false;
    if (data[x] > data[y]) swap(x, y);
    data[x] += data[y];
    data[y] = x;
    return true;
  }

  int find(int k) {
    if (data[k] < 0) return (k);
    return data[k] = find(data[k]);
  }

  int size(int k) { return -data[find(k)]; }

  bool same(int x, int y) { return find(x) == find(y); }

  vector<vector<int> > groups() {
    int n = (int)data.size();
    vector<vector<int> > ret(n);
    for (int i = 0; i < n; i++) {
      ret[find(i)].emplace_back(i);
    }
    ret.erase(remove_if(begin(ret), end(ret),
                        [&](const vector<int> &v) { return v.empty(); }),
              end(ret));
    return ret;
  }
};
#line 4 "graph/connected-components/incremental-bridge-connectivity.hpp"

struct IncrementalBridgeConnectivity {
 private:
  UnionFind cc, bcc;
  vector<int> bbf;
  size_t bridge;

  int size() { return bbf.size(); }

  int par(int x) { return bbf[x] == size() ? size() : bcc.find(bbf[x]); }

  int lca(int x, int y) {
    unordered_set<int> used;
    for (;;) {
      if (x != size()) {
        if (!used.insert(x).second) return x;
        x = par(x);
      }
      swap(x, y);
    }
  }

  void compress(int x, int y) {
    while (bcc.find(x) != bcc.find(y)) {
      int nxt = par(x);
      bbf[x] = bbf[y];
      bcc.unite(x, y);
      x = nxt;
      --bridge;
    }
  }

  void link(int x, int y) {
    int v = x, pre = y;
    while (v != size()) {
      int nxt = par(v);
      bbf[v] = pre;
      pre = v;
      v = nxt;
    }
  }

 public:
  IncrementalBridgeConnectivity() = default;

  explicit IncrementalBridgeConnectivity(int sz)
      : cc(sz), bcc(sz), bbf(sz, sz), bridge(0) {}

  int find(int k) { return bcc.find(k); }

  size_t bridge_size() const { return bridge; }

  void add_edge(int x, int y) {
    x = bcc.find(x);
    y = bcc.find(y);
    if (cc.find(x) == cc.find(y)) {
      int w = lca(x, y);
      compress(x, w);
      compress(y, w);
    } else {
      if (cc.size(x) > cc.size(y)) swap(x, y);
      link(x, y);
      cc.unite(x, y);
      ++bridge;
    }
  }
};
#line 5 "graph/connected-components/three-edge-connected-components.hpp"

template <typename T = int>
struct ThreeEdgeConnectedComponents : Graph<T> {
 public:
  using Graph<T>::Graph;
  using Graph<T>::g;
  vector<vector<int> > group;

  void build() {
    uf = UnionFind(g.size());
    bcc = IncrementalBridgeConnectivity(g.size());
    used.assign(g.size(), 0);
    in.assign(g.size(), 0);
    out.assign(g.size(), 0);
    deg.assign(g.size(), 0);
    low.assign(g.size(), g.size());
    for (size_t from = 0; from < g.size(); from++) {
      for (auto &to : g[from]) {
        if ((T)from < to) bcc.add_edge(from, to);
      }
    }
    int cnt = 0;
    for (size_t i = 0; i < g.size(); i++) {
      if (used[i]) continue;
      vector<int> tmp;
      dfs(i, -1, tmp, cnt);
      cnt++;
    }
    vector<int> id(g.size(), -1);
    cnt = 0;
    for (size_t i = 0; i < g.size(); i++) {
      if (id[uf.find(i)] == -1) id[uf.find(i)] = cnt++;
    }
    group.resize(cnt);
    for (size_t i = 0; i < g.size(); i++) {
      group[id[uf.find(i)]].emplace_back(i);
    }
  }

  int operator[](const int &k) { return uf.find(k); }

 private:
  vector<int> used;
  vector<int> in, out, low, deg;
  IncrementalBridgeConnectivity bcc;
  UnionFind uf;

  void absorb(vector<int> &path, int v, int w = -1) {
    while (!path.empty()) {
      int x = path.back();
      if (w != -1 && (in[x] > in[w] or in[w] >= out[x])) break;
      path.pop_back();
      uf.unite(v, x);
      deg[v] += deg[x] - 2;
    }
  }

  void dfs(int idx, int p, vector<int> &path, int &k) {
    used[idx] = 1;
    in[idx] = low[idx] = k++;
    for (auto &to : g[idx]) {
      if (idx == to || bcc.find(idx) != bcc.find(to)) continue;
      deg[idx]++;
      if (to == p) {
        p = -1;
        continue;
      }
      if (used[to]) {
        if (in[idx] > in[to]) {
          if (in[to] < low[idx]) {
            low[idx] = in[to];
            absorb(path, idx);
          }
        } else {
          deg[idx] -= 2;
          absorb(path, idx, to);
        }
      } else {
        vector<int> ps;
        dfs(to, idx, ps, k);
        if (deg[to] == 2) ps.pop_back();
        if (low[to] < low[idx]) {
          low[idx] = low[to];
          absorb(path, idx);
          path = ps;
        } else {
          absorb(ps, idx);
        }
      }
    }
    out[idx] = k;
    path.push_back(idx);
  }
};
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