Undirected shortest cycle
(Mylib/Graph/Cycle/undirected_shortest_cycle.cpp)

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

Operations

• shortest_cycle(g, src)
  • src始点の最小閉路を検出する。
  • Time complexity $O(E)$

Requirements

Notes

Problems

• Codeforces Round #628 (Div. 2) E. Ehab’s REAL Number Theory Problem

References

Depends on

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

Code

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

namespace haar_lib {
  template <typename T>
  std::optional<int> shortest_cycle(const graph<T> &g, const int src) {
    for (auto &e : g[src]) {
      if (e.to == src) return 1;  // self loop
    }

    if (g[src].size() <= 1) return {};

    const int N = g.size();
    std::vector<int> visit(N);
    std::vector<int> dist(N);

    visit[src] = -1;

    std::queue<int> q;
    for (int i = 0; i < (int) g[src].size(); ++i) {
      int j = g[src][i].to;
      if (visit[j]) return 2;  // multiple edges
      q.push(j);
      visit[j] = i + 1;
      dist[j]  = 1;
    }

    while (not q.empty()) {
      int i = q.front();
      q.pop();

      for (auto &e : g[i]) {
        if (not visit[e.to]) {
          visit[e.to] = visit[i];
          dist[e.to]  = dist[i] + 1;
          q.push(e.to);
        } else {
          if (e.to != src and visit[e.from] != visit[e.to]) {
            return dist[e.from] + dist[e.to] + 1;
          }
        }
      }
    }

    return {};
  }
}  // namespace haar_lib

#line 2 "Mylib/Graph/Cycle/undirected_shortest_cycle.cpp"
#include <optional>
#include <queue>
#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/Cycle/undirected_shortest_cycle.cpp"

namespace haar_lib {
  template <typename T>
  std::optional<int> shortest_cycle(const graph<T> &g, const int src) {
    for (auto &e : g[src]) {
      if (e.to == src) return 1;  // self loop
    }

    if (g[src].size() <= 1) return {};

    const int N = g.size();
    std::vector<int> visit(N);
    std::vector<int> dist(N);

    visit[src] = -1;

    std::queue<int> q;
    for (int i = 0; i < (int) g[src].size(); ++i) {
      int j = g[src][i].to;
      if (visit[j]) return 2;  // multiple edges
      q.push(j);
      visit[j] = i + 1;
      dist[j]  = 1;
    }

    while (not q.empty()) {
      int i = q.front();
      q.pop();

      for (auto &e : g[i]) {
        if (not visit[e.to]) {
          visit[e.to] = visit[i];
          dist[e.to]  = dist[i] + 1;
          q.push(e.to);
        } else {
          if (e.to != src and visit[e.from] != visit[e.to]) {
            return dist[e.from] + dist[e.to] + 1;
          }
        }
      }
    }

    return {};
  }
}  // namespace haar_lib

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