閉路の検出
(graph/cycle-detection.hpp)

• View this file on GitHub
• Last update: 2023-09-05 21:46:27+09:00
• Include: #include "graph/cycle-detection.hpp"

Depends on

• グラフテンプレート (graph/graph-template.hpp)

Verified with

• verify/verify-yosupo-graph/yosupo-cycle-detection.test.cpp

Code

#pragma once

#include <utility>
#include <vector>
using namespace std;

#include "./graph-template.hpp"

template <typename G>
vector<pair<int, int>> CycleDetection(const G& g, bool directed = true) {
  for (int i = 0; i < (int)g.size(); i++) {
    for (auto j : g[i]) {
      if (i == j) {
        vector<pair<int, int>> res;
        res.emplace_back(i, i);
        return res;
      }
    }
  }

  vector<int> pidx(g.size(), -1), vis(g.size(), 0);

  vector<pair<int, int>> cycle;
  int finish = 0;
  auto dfs = [&](auto rec, int cur, int pval, int par) -> int {
    pidx[cur] = pval;
    vis[cur] = 1;
    for (auto& dst : g[cur]) {
      if (finish) return -1;
      if (!directed && dst == par) continue;
      if (pidx[dst] == pidx[cur]) {
        cycle.emplace_back(cur, dst);
        return dst;
      }
      if (vis[dst]) continue;
      int nx = rec(rec, dst, pval, cur);
      if (nx != -1) {
        cycle.emplace_back(cur, dst);
        if (cur == nx) {
          finish = 1;
          return -1;
        }
        return nx;
      }
    }
    pidx[cur] = -1;
    return -1;
  };

  for (int i = 0; i < (int)g.size(); i++) {
    if (vis[i]) continue;
    dfs(dfs, i, i, -1);

    if (finish) {
      reverse(begin(cycle), end(cycle));
      return cycle;
    }
  }
  return vector<pair<int, int>>{};
}

/**
 * @brief 閉路の検出
 */

#line 2 "graph/cycle-detection.hpp"

#include <utility>
#include <vector>
using namespace std;

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

template <typename T>
struct edge {
  int src, to;
  T cost;

  edge(int _to, T _cost) : src(-1), to(_to), cost(_cost) {}
  edge(int _src, int _to, T _cost) : src(_src), to(_to), cost(_cost) {}

  edge &operator=(const int &x) {
    to = x;
    return *this;
  }

  operator int() const { return to; }
};
template <typename T>
using Edges = vector<edge<T>>;
template <typename T>
using WeightedGraph = vector<Edges<T>>;
using UnweightedGraph = vector<vector<int>>;

// Input of (Unweighted) Graph
UnweightedGraph graph(int N, int M = -1, bool is_directed = false,
                      bool is_1origin = true) {
  UnweightedGraph g(N);
  if (M == -1) M = N - 1;
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    if (is_1origin) x--, y--;
    g[x].push_back(y);
    if (!is_directed) g[y].push_back(x);
  }
  return g;
}

// Input of Weighted Graph
template <typename T>
WeightedGraph<T> wgraph(int N, int M = -1, bool is_directed = false,
                        bool is_1origin = true) {
  WeightedGraph<T> g(N);
  if (M == -1) M = N - 1;
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    T c;
    cin >> c;
    if (is_1origin) x--, y--;
    g[x].emplace_back(x, y, c);
    if (!is_directed) g[y].emplace_back(y, x, c);
  }
  return g;
}

// Input of Edges
template <typename T>
Edges<T> esgraph(int N, int M, int is_weighted = true, bool is_1origin = true) {
  Edges<T> es;
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    T c;
    if (is_weighted)
      cin >> c;
    else
      c = 1;
    if (is_1origin) x--, y--;
    es.emplace_back(x, y, c);
  }
  return es;
}

// Input of Adjacency Matrix
template <typename T>
vector<vector<T>> adjgraph(int N, int M, T INF, int is_weighted = true,
                           bool is_directed = false, bool is_1origin = true) {
  vector<vector<T>> d(N, vector<T>(N, INF));
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    T c;
    if (is_weighted)
      cin >> c;
    else
      c = 1;
    if (is_1origin) x--, y--;
    d[x][y] = c;
    if (!is_directed) d[y][x] = c;
  }
  return d;
}

/**
 * @brief グラフテンプレート
 * @docs docs/graph/graph-template.md
 */
#line 8 "graph/cycle-detection.hpp"

template <typename G>
vector<pair<int, int>> CycleDetection(const G& g, bool directed = true) {
  for (int i = 0; i < (int)g.size(); i++) {
    for (auto j : g[i]) {
      if (i == j) {
        vector<pair<int, int>> res;
        res.emplace_back(i, i);
        return res;
      }
    }
  }

  vector<int> pidx(g.size(), -1), vis(g.size(), 0);

  vector<pair<int, int>> cycle;
  int finish = 0;
  auto dfs = [&](auto rec, int cur, int pval, int par) -> int {
    pidx[cur] = pval;
    vis[cur] = 1;
    for (auto& dst : g[cur]) {
      if (finish) return -1;
      if (!directed && dst == par) continue;
      if (pidx[dst] == pidx[cur]) {
        cycle.emplace_back(cur, dst);
        return dst;
      }
      if (vis[dst]) continue;
      int nx = rec(rec, dst, pval, cur);
      if (nx != -1) {
        cycle.emplace_back(cur, dst);
        if (cur == nx) {
          finish = 1;
          return -1;
        }
        return nx;
      }
    }
    pidx[cur] = -1;
    return -1;
  };

  for (int i = 0; i < (int)g.size(); i++) {
    if (vis[i]) continue;
    dfs(dfs, i, i, -1);

    if (finish) {
      reverse(begin(cycle), end(cycle));
      return cycle;
    }
  }
  return vector<pair<int, int>>{};
}

/**
 * @brief 閉路の検出
 */

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