Articulation points
(Mylib/Graph/GraphUtils/articulation_points.cpp)

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

Requirements

Notes

Problems

References

Depends on

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

Verified with

• test/aoj/GRL_3_A/main.test.cpp

Code

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

namespace haar_lib {
  namespace articulation_points_impl {
    template <typename T>
    int dfs(
        const graph<T> &g,
        int root,
        int cur,
        std::vector<int> &visit,
        std::vector<int> &low,
        std::vector<int> &ret,
        int &v) {
      if (visit[cur] != -1) return visit[cur];
      visit[cur] = v;

      int temp = v;
      std::vector<int> children;
      ++v;

      for (auto &e : g[cur]) {
        if (visit[e.to] == -1) children.push_back(e.to);
        int t = dfs(g, root, e.to, visit, low, ret, v);
        temp  = std::min(temp, t);
      }

      low[cur] = temp;

      if (cur != root or children.size() >= 2) {
        for (auto x : children) {
          if (low[x] >= visit[cur]) {
            ret.push_back(cur);
            break;
          }
        }
      }

      return low[cur];
    };
  }  // namespace articulation_points_impl

  template <typename T>
  std::vector<int> articulation_points(const graph<T> &g) {
    const int n = g.size();
    std::vector<int> visit(n, -1), low(n, -1), ret;
    int v = 0;

    for (int i = 0; i < n; ++i) {
      if (visit[i] == -1) {
        articulation_points_impl::dfs(g, i, i, visit, low, ret, v);
      }
    }

    return ret;
  }
}  // namespace haar_lib

#line 2 "Mylib/Graph/GraphUtils/articulation_points.cpp"
#include <algorithm>
#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 5 "Mylib/Graph/GraphUtils/articulation_points.cpp"

namespace haar_lib {
  namespace articulation_points_impl {
    template <typename T>
    int dfs(
        const graph<T> &g,
        int root,
        int cur,
        std::vector<int> &visit,
        std::vector<int> &low,
        std::vector<int> &ret,
        int &v) {
      if (visit[cur] != -1) return visit[cur];
      visit[cur] = v;

      int temp = v;
      std::vector<int> children;
      ++v;

      for (auto &e : g[cur]) {
        if (visit[e.to] == -1) children.push_back(e.to);
        int t = dfs(g, root, e.to, visit, low, ret, v);
        temp  = std::min(temp, t);
      }

      low[cur] = temp;

      if (cur != root or children.size() >= 2) {
        for (auto x : children) {
          if (low[x] >= visit[cur]) {
            ret.push_back(cur);
            break;
          }
        }
      }

      return low[cur];
    };
  }  // namespace articulation_points_impl

  template <typename T>
  std::vector<int> articulation_points(const graph<T> &g) {
    const int n = g.size();
    std::vector<int> visit(n, -1), low(n, -1), ret;
    int v = 0;

    for (int i = 0; i < n; ++i) {
      if (visit[i] == -1) {
        articulation_points_impl::dfs(g, i, i, visit, low, ret, v);
      }
    }

    return ret;
  }
}  // namespace haar_lib

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