Biconnected components
(Mylib/Graph/GraphUtils/biconnected_components.cpp)

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• Last update: 2021-04-23 23:44:44+09:00

Operations

Requirements

Notes

Problems

• ARC062 F - AtCoDeerくんとグラフ色塗り

References

• http://www.prefield.com/algorithm/graph/articulation_point.html
• https://ei1333.github.io/luzhiled/snippets/graph/bi-connected-components.html

Depends on

• Basic graph (Mylib/Graph/Template/graph.cpp)

Code

#pragma once
#include <algorithm>
#include <stack>
#include <vector>
#include "Mylib/Graph/Template/graph.cpp"

namespace haar_lib {
  namespace biconnected_components_impl {
    template <typename T>
    void dfs(
        const graph<T> &g,
        int cur,
        int par,
        std::vector<bool> &check,
        std::vector<int> &low,
        std::vector<int> &ord,
        std::vector<std::vector<edge<T>>> &ret,
        std::stack<edge<T>> &st,
        int &t) {
      check[cur] = true;
      ord[cur]   = t;
      low[cur]   = t;
      ++t;

      for (auto &e : g[cur]) {
        if (e.to == par) continue;

        if (ord[e.to] < ord[cur]) {
          auto f = e;
          if (f.from > f.to) std::swap(f.from, f.to);
          st.push(f);
        }
        if (not check[e.to]) {
          dfs(g, e.to, cur, check, low, ord, ret, st, t);
          low[cur] = std::min(low[cur], low[e.to]);
          if (low[e.to] >= ord[cur]) {
            ret.emplace_back();
            while (true) {
              auto f = st.top();
              st.pop();
              ret.back().push_back(f);
              if (f.from == std::min(e.from, e.to) and f.to == std::max(e.from, e.to)) break;
            }
          }
        } else {
          low[cur] = std::min(low[cur], ord[e.to]);
        }
      }
    }
  }  // namespace biconnected_components_impl

  template <typename T>
  auto biconnected_components(const graph<T> &g) {
    const int n = g.size();

    std::vector<bool> check(n);
    std::vector<int> low(n, -1), ord(n, -1);
    std::vector<std::vector<edge<T>>> ret;
    std::stack<edge<T>> st;
    int t = 0;

    for (int i = 0; i < n; ++i) {
      if (not check[i]) biconnected_components_impl::dfs(g, i, -1, check, low, ord, ret, st, t);
    }

    return ret;
  }
}  // namespace haar_lib

#line 2 "Mylib/Graph/GraphUtils/biconnected_components.cpp"
#include <algorithm>
#include <stack>
#include <vector>
#line 2 "Mylib/Graph/Template/graph.cpp"
#include <iostream>
#line 4 "Mylib/Graph/Template/graph.cpp"

namespace haar_lib {
  template <typename T>
  struct edge {
    int from, to;
    T cost;
    int index = -1;
    edge() {}
    edge(int from, int to, T cost) : from(from), to(to), cost(cost) {}
    edge(int from, int to, T cost, int index) : from(from), to(to), cost(cost), index(index) {}
  };

  template <typename T>
  struct graph {
    using weight_type = T;
    using edge_type   = edge<T>;

    std::vector<std::vector<edge<T>>> data;

    auto& operator[](size_t i) { return data[i]; }
    const auto& operator[](size_t i) const { return data[i]; }

    auto begin() const { return data.begin(); }
    auto end() const { return data.end(); }

    graph() {}
    graph(int N) : data(N) {}

    bool empty() const { return data.empty(); }
    int size() const { return data.size(); }

    void add_edge(int i, int j, T w, int index = -1) {
      data[i].emplace_back(i, j, w, index);
    }

    void add_undirected(int i, int j, T w, int index = -1) {
      add_edge(i, j, w, index);
      add_edge(j, i, w, index);
    }

    template <size_t I, bool DIRECTED = true, bool WEIGHTED = true>
    void read(int M) {
      for (int i = 0; i < M; ++i) {
        int u, v;
        std::cin >> u >> v;
        u -= I;
        v -= I;
        T w = 1;
        if (WEIGHTED) std::cin >> w;
        if (DIRECTED)
          add_edge(u, v, w, i);
        else
          add_undirected(u, v, w, i);
      }
    }
  };

  template <typename T>
  using tree = graph<T>;
}  // namespace haar_lib
#line 6 "Mylib/Graph/GraphUtils/biconnected_components.cpp"

namespace haar_lib {
  namespace biconnected_components_impl {
    template <typename T>
    void dfs(
        const graph<T> &g,
        int cur,
        int par,
        std::vector<bool> &check,
        std::vector<int> &low,
        std::vector<int> &ord,
        std::vector<std::vector<edge<T>>> &ret,
        std::stack<edge<T>> &st,
        int &t) {
      check[cur] = true;
      ord[cur]   = t;
      low[cur]   = t;
      ++t;

      for (auto &e : g[cur]) {
        if (e.to == par) continue;

        if (ord[e.to] < ord[cur]) {
          auto f = e;
          if (f.from > f.to) std::swap(f.from, f.to);
          st.push(f);
        }
        if (not check[e.to]) {
          dfs(g, e.to, cur, check, low, ord, ret, st, t);
          low[cur] = std::min(low[cur], low[e.to]);
          if (low[e.to] >= ord[cur]) {
            ret.emplace_back();
            while (true) {
              auto f = st.top();
              st.pop();
              ret.back().push_back(f);
              if (f.from == std::min(e.from, e.to) and f.to == std::max(e.from, e.to)) break;
            }
          }
        } else {
          low[cur] = std::min(low[cur], ord[e.to]);
        }
      }
    }
  }  // namespace biconnected_components_impl

  template <typename T>
  auto biconnected_components(const graph<T> &g) {
    const int n = g.size();

    std::vector<bool> check(n);
    std::vector<int> low(n, -1), ord(n, -1);
    std::vector<std::vector<edge<T>>> ret;
    std::stack<edge<T>> st;
    int t = 0;

    for (int i = 0; i < n; ++i) {
      if (not check[i]) biconnected_components_impl::dfs(g, i, -1, check, low, ord, ret, st, t);
    }

    return ret;
  }
}  // namespace haar_lib

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