cycle.hpp

#include "noya/cycle.hpp"

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#ifndef NOYA_CYCLE_HPP
#define NOYA_CYCLE_HPP 1

#include "atcoder/dsu.hpp"
#include <numeric>
#include <vector>

namespace noya {
/// @brief Detect whether a directed graph contains a cycle.
bool cycle_detection_directed(const std::vector<std::vector<int>> &g) {
  int N = int(g.size());
  std::vector<int> deg(N);
  for (auto &gi : g) {
    for (auto &v : gi) {
      deg[v] += 1;
    }
  }
  std::vector<int> que;
  for (int i = 0; i < N; i++) {
    if (deg[i] == 0) {
      que.push_back(i);
    }
  }

  for (int i = 0; i < int(que.size()); i++) {
    int u = que[i];
    for (auto v : g[u]) {
      deg[v] -= 1;
      if (!deg[v]) {
        que.push_back(v);
      }
    }
  }
  return std::accumulate(deg.begin(), deg.end(), 0) > 0;
}

/// @brief Detect whether an undirected edge list contains a cycle.
bool cycle_detection_undirected(const std::vector<std::pair<int, int>> &edge) {
  int N = 0;
  for (auto &[a, b] : edge) {
    N = std::max(N, a);
    N = std::max(N, b);
  }
  N++;
  atcoder::dsu f(N);
  for (auto &[a, b] : edge) {
    if (f.same(a, b)) {
      return true;
    }
    f.merge(a, b);
  }
  return false;
}
}


#endif // NOYA_CYCLE_HPP

#include <algorithm>
#include <cassert>
#include <numeric>
#include <vector>

namespace atcoder {

// Implement (union by size) + (path compression)
// Reference:
// Zvi Galil and Giuseppe F. Italiano,
// Data structures and algorithms for disjoint set union problems
struct dsu {
  public:
    dsu() : _n(0) {}
    explicit dsu(int n) : _n(n), parent_or_size(n, -1) {}

    int merge(int a, int b) {
        assert(0 <= a && a < _n);
        assert(0 <= b && b < _n);
        int x = leader(a), y = leader(b);
        if (x == y) return x;
        if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y);
        parent_or_size[x] += parent_or_size[y];
        parent_or_size[y] = x;
        return x;
    }

    bool same(int a, int b) {
        assert(0 <= a && a < _n);
        assert(0 <= b && b < _n);
        return leader(a) == leader(b);
    }

    int leader(int a) {
        assert(0 <= a && a < _n);
        return _leader(a);
    }

    int size(int a) {
        assert(0 <= a && a < _n);
        return -parent_or_size[leader(a)];
    }

    std::vector<std::vector<int>> groups() {
        std::vector<int> leader_buf(_n), group_size(_n);
        for (int i = 0; i < _n; i++) {
            leader_buf[i] = leader(i);
            group_size[leader_buf[i]]++;
        }
        std::vector<std::vector<int>> result(_n);
        for (int i = 0; i < _n; i++) {
            result[i].reserve(group_size[i]);
        }
        for (int i = 0; i < _n; i++) {
            result[leader_buf[i]].push_back(i);
        }
        result.erase(
            std::remove_if(result.begin(), result.end(),
                           [&](const std::vector<int>& v) { return v.empty(); }),
            result.end());
        return result;
    }

  private:
    int _n;
    // root node: -1 * component size
    // otherwise: parent
    std::vector<int> parent_or_size;

    int _leader(int a) {
        if (parent_or_size[a] < 0) return a;
        return parent_or_size[a] = _leader(parent_or_size[a]);
    }
};

}  // namespace atcoder

namespace noya {
/// @brief Detect whether a directed graph contains a cycle.
bool cycle_detection_directed(const std::vector<std::vector<int>> &g) {
  int N = int(g.size());
  std::vector<int> deg(N);
  for (auto &gi : g) {
    for (auto &v : gi) {
      deg[v] += 1;
    }
  }
  std::vector<int> que;
  for (int i = 0; i < N; i++) {
    if (deg[i] == 0) {
      que.push_back(i);
    }
  }

  for (int i = 0; i < int(que.size()); i++) {
    int u = que[i];
    for (auto v : g[u]) {
      deg[v] -= 1;
      if (!deg[v]) {
        que.push_back(v);
      }
    }
  }
  return std::accumulate(deg.begin(), deg.end(), 0) > 0;
}

/// @brief Detect whether an undirected edge list contains a cycle.
bool cycle_detection_undirected(const std::vector<std::pair<int, int>> &edge) {
  int N = 0;
  for (auto &[a, b] : edge) {
    N = std::max(N, a);
    N = std::max(N, b);
  }
  N++;
  atcoder::dsu f(N);
  for (auto &[a, b] : edge) {
    if (f.same(a, b)) {
      return true;
    }
    f.merge(a, b);
  }
  return false;
}
}