graph/find_cycle.hpp

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• Last update: 2023-11-07 22:29:27+09:00
• Include: #include "graph/find_cycle.hpp"

Depends on

• graph/base.hpp

Verified with

• test/library_checker/graph/cycle_detection.test.cpp
• test/library_checker/graph/cycle_detection_undirected.test.cpp

Code

#include "graph/base.hpp"

// {vs, es} or empty. minimal.

template <typename GT>
pair<vc<int>, vc<int>> find_cycle_directed(GT& G) {
  static_assert(GT::is_directed);
  assert(G.is_prepared());

  int N = G.N;
  vc<int> used(N);
  vc<pair<int, int>> par(N);
  vector<int> es, vs;

  auto dfs = [&](auto self, int v) -> void {
    used[v] = 1;
    for (auto&& e: G[v]) {
      if (len(es)) return;
      if (!used[e.to]) {
        par[e.to] = {v, e.id};
        self(self, e.to);
      }
      elif (used[e.to] == 1) {
        es = {e.id};
        int cur = v;
        while (cur != e.to) {
          es.eb(par[cur].se);
          cur = par[cur].fi;
        }
        reverse(all(es));
        return;
      }
    }
    used[v] = 2;
  };
  FOR(v, N) if (!used[v]) dfs(dfs, v);
  if (es.empty()) return {vs, es};

  // minimal cycle

  vc<int> nxt(N, -1);
  for (auto&& eid: es) nxt[G.edges[eid].frm] = eid;

  for (auto&& e: G.edges) {
    int a = e.frm, b = e.to;
    if (nxt[a] == -1 || nxt[b] == -1) continue;
    if (G.edges[nxt[a]].to == e.to) continue;
    while (a != b) {
      int t = G.edges[nxt[a]].to;
      nxt[a] = -1;
      a = t;
    }
    nxt[e.frm] = e.id;
  }
  es.clear();
  FOR(v, N) {
    if (nxt[v] == -1) continue;
    int x = v;
    while (1) {
      vs.eb(x);
      es.eb(nxt[x]);
      x = G.edges[nxt[x]].to;
      if (x == v) break;
    }
    break;
  }
  return {vs, es};
}

// {vs, es} or empty. minimal.

template <typename GT>
pair<vc<int>, vc<int>> find_cycle_undirected(GT& G) {
  assert(!GT::is_directed);
  assert(G.is_prepared());
  const int N = G.N;
  const int M = G.M;
  vc<int> dep(N, -1);
  vc<bool> used_e(M);
  vc<int> par(N, -1); // edge idx


  auto dfs = [&](auto& dfs, int v, int d) -> int {
    dep[v] = d;
    for (auto&& e: G[v]) {
      if (used_e[e.id]) continue;
      if (dep[e.to] != -1) return v;
      used_e[e.id] = 1;
      par[e.to] = e.id;
      int res = dfs(dfs, e.to, d + 1);
      if (res != -1) return res;
    }
    return -1;
  };

  vc<int> vs, es;
  FOR(v, N) {
    if (dep[v] != -1) continue;
    // w has back edge

    int w = dfs(dfs, v, 0);
    if (w == -1) continue;
    int b = -1, back_e = -1;
    while (1) {
      for (auto&& e: G[w]) {
        if (used_e[e.id]) continue;
        if (dep[e.to] > dep[w] || dep[e.to] == -1) continue;
        b = w, back_e = e.id;
      }
      if (w == v) break;
      auto& e = G.edges[par[w]];
      w = e.frm + e.to - w;
    }
    int a = G.edges[back_e].frm + G.edges[back_e].to - b;
    es.eb(back_e), vs.eb(a);
    while (1) {
      int x = vs.back();
      auto& e = G.edges[es.back()];
      int y = e.frm + e.to - x;
      if (y == a) break;
      vs.eb(y);
      es.eb(par[y]);
    }
    return {vs, es};
  }
  return {vs, es};
}

#line 2 "graph/base.hpp"

template <typename T>
struct Edge {
  int frm, to;
  T cost;
  int id;
};

template <typename T = int, bool directed = false>
struct Graph {
  static constexpr bool is_directed = directed;
  int N, M;
  using cost_type = T;
  using edge_type = Edge<T>;
  vector<edge_type> edges;
  vector<int> indptr;
  vector<edge_type> csr_edges;
  vc<int> vc_deg, vc_indeg, vc_outdeg;
  bool prepared;

  class OutgoingEdges {
  public:
    OutgoingEdges(const Graph* G, int l, int r) : G(G), l(l), r(r) {}

    const edge_type* begin() const {
      if (l == r) { return 0; }
      return &G->csr_edges[l];
    }

    const edge_type* end() const {
      if (l == r) { return 0; }
      return &G->csr_edges[r];
    }

  private:
    const Graph* G;
    int l, r;
  };

  bool is_prepared() { return prepared; }

  Graph() : N(0), M(0), prepared(0) {}
  Graph(int N) : N(N), M(0), prepared(0) {}

  void build(int n) {
    N = n, M = 0;
    prepared = 0;
    edges.clear();
    indptr.clear();
    csr_edges.clear();
    vc_deg.clear();
    vc_indeg.clear();
    vc_outdeg.clear();
  }

  void add(int frm, int to, T cost = 1, int i = -1) {
    assert(!prepared);
    assert(0 <= frm && 0 <= to && to < N);
    if (i == -1) i = M;
    auto e = edge_type({frm, to, cost, i});
    edges.eb(e);
    ++M;
  }

#ifdef FASTIO
  // wt, off
  void read_tree(bool wt = false, int off = 1) { read_graph(N - 1, wt, off); }

  void read_graph(int M, bool wt = false, int off = 1) {
    for (int m = 0; m < M; ++m) {
      INT(a, b);
      a -= off, b -= off;
      if (!wt) {
        add(a, b);
      } else {
        T c;
        read(c);
        add(a, b, c);
      }
    }
    build();
  }
#endif

  void build() {
    assert(!prepared);
    prepared = true;
    indptr.assign(N + 1, 0);
    for (auto&& e: edges) {
      indptr[e.frm + 1]++;
      if (!directed) indptr[e.to + 1]++;
    }
    for (int v = 0; v < N; ++v) { indptr[v + 1] += indptr[v]; }
    auto counter = indptr;
    csr_edges.resize(indptr.back() + 1);
    for (auto&& e: edges) {
      csr_edges[counter[e.frm]++] = e;
      if (!directed)
        csr_edges[counter[e.to]++] = edge_type({e.to, e.frm, e.cost, e.id});
    }
  }

  OutgoingEdges operator[](int v) const {
    assert(prepared);
    return {this, indptr[v], indptr[v + 1]};
  }

  vc<int> deg_array() {
    if (vc_deg.empty()) calc_deg();
    return vc_deg;
  }

  pair<vc<int>, vc<int>> deg_array_inout() {
    if (vc_indeg.empty()) calc_deg_inout();
    return {vc_indeg, vc_outdeg};
  }

  int deg(int v) {
    if (vc_deg.empty()) calc_deg();
    return vc_deg[v];
  }

  int in_deg(int v) {
    if (vc_indeg.empty()) calc_deg_inout();
    return vc_indeg[v];
  }

  int out_deg(int v) {
    if (vc_outdeg.empty()) calc_deg_inout();
    return vc_outdeg[v];
  }

#ifdef FASTIO
  void debug() {
    print("Graph");
    if (!prepared) {
      print("frm to cost id");
      for (auto&& e: edges) print(e.frm, e.to, e.cost, e.id);
    } else {
      print("indptr", indptr);
      print("frm to cost id");
      FOR(v, N) for (auto&& e: (*this)[v]) print(e.frm, e.to, e.cost, e.id);
    }
  }
#endif

  vc<int> new_idx;
  vc<bool> used_e;

  // G における頂点 V[i] が、新しいグラフで i になるようにする
  // {G, es}
  Graph<T, directed> rearrange(vc<int> V, bool keep_eid = 0) {
    if (len(new_idx) != N) new_idx.assign(N, -1);
    if (len(used_e) != M) used_e.assign(M, 0);
    int n = len(V);
    FOR(i, n) new_idx[V[i]] = i;
    Graph<T, directed> G(n);
    vc<int> history;
    FOR(i, n) {
      for (auto&& e: (*this)[V[i]]) {
        if (used_e[e.id]) continue;
        int a = e.frm, b = e.to;
        if (new_idx[a] != -1 && new_idx[b] != -1) {
          history.eb(e.id);
          used_e[e.id] = 1;
          int eid = (keep_eid ? e.id : -1);
          G.add(new_idx[a], new_idx[b], e.cost, eid);
        }
      }
    }
    FOR(i, n) new_idx[V[i]] = -1;
    for (auto&& eid: history) used_e[eid] = 0;
    G.build();
    return G;
  }

private:
  void calc_deg() {
    assert(vc_deg.empty());
    vc_deg.resize(N);
    for (auto&& e: edges) vc_deg[e.frm]++, vc_deg[e.to]++;
  }

  void calc_deg_inout() {
    assert(vc_indeg.empty());
    vc_indeg.resize(N);
    vc_outdeg.resize(N);
    for (auto&& e: edges) { vc_indeg[e.to]++, vc_outdeg[e.frm]++; }
  }
};
#line 2 "graph/find_cycle.hpp"

// {vs, es} or empty. minimal.

template <typename GT>
pair<vc<int>, vc<int>> find_cycle_directed(GT& G) {
  static_assert(GT::is_directed);
  assert(G.is_prepared());

  int N = G.N;
  vc<int> used(N);
  vc<pair<int, int>> par(N);
  vector<int> es, vs;

  auto dfs = [&](auto self, int v) -> void {
    used[v] = 1;
    for (auto&& e: G[v]) {
      if (len(es)) return;
      if (!used[e.to]) {
        par[e.to] = {v, e.id};
        self(self, e.to);
      }
      elif (used[e.to] == 1) {
        es = {e.id};
        int cur = v;
        while (cur != e.to) {
          es.eb(par[cur].se);
          cur = par[cur].fi;
        }
        reverse(all(es));
        return;
      }
    }
    used[v] = 2;
  };
  FOR(v, N) if (!used[v]) dfs(dfs, v);
  if (es.empty()) return {vs, es};

  // minimal cycle

  vc<int> nxt(N, -1);
  for (auto&& eid: es) nxt[G.edges[eid].frm] = eid;

  for (auto&& e: G.edges) {
    int a = e.frm, b = e.to;
    if (nxt[a] == -1 || nxt[b] == -1) continue;
    if (G.edges[nxt[a]].to == e.to) continue;
    while (a != b) {
      int t = G.edges[nxt[a]].to;
      nxt[a] = -1;
      a = t;
    }
    nxt[e.frm] = e.id;
  }
  es.clear();
  FOR(v, N) {
    if (nxt[v] == -1) continue;
    int x = v;
    while (1) {
      vs.eb(x);
      es.eb(nxt[x]);
      x = G.edges[nxt[x]].to;
      if (x == v) break;
    }
    break;
  }
  return {vs, es};
}

// {vs, es} or empty. minimal.

template <typename GT>
pair<vc<int>, vc<int>> find_cycle_undirected(GT& G) {
  assert(!GT::is_directed);
  assert(G.is_prepared());
  const int N = G.N;
  const int M = G.M;
  vc<int> dep(N, -1);
  vc<bool> used_e(M);
  vc<int> par(N, -1); // edge idx


  auto dfs = [&](auto& dfs, int v, int d) -> int {
    dep[v] = d;
    for (auto&& e: G[v]) {
      if (used_e[e.id]) continue;
      if (dep[e.to] != -1) return v;
      used_e[e.id] = 1;
      par[e.to] = e.id;
      int res = dfs(dfs, e.to, d + 1);
      if (res != -1) return res;
    }
    return -1;
  };

  vc<int> vs, es;
  FOR(v, N) {
    if (dep[v] != -1) continue;
    // w has back edge

    int w = dfs(dfs, v, 0);
    if (w == -1) continue;
    int b = -1, back_e = -1;
    while (1) {
      for (auto&& e: G[w]) {
        if (used_e[e.id]) continue;
        if (dep[e.to] > dep[w] || dep[e.to] == -1) continue;
        b = w, back_e = e.id;
      }
      if (w == v) break;
      auto& e = G.edges[par[w]];
      w = e.frm + e.to - w;
    }
    int a = G.edges[back_e].frm + G.edges[back_e].to - b;
    es.eb(back_e), vs.eb(a);
    while (1) {
      int x = vs.back();
      auto& e = G.edges[es.back()];
      int y = e.frm + e.to - x;
      if (y == a) break;
      vs.eb(y);
      es.eb(par[y]);
    }
    return {vs, es};
  }
  return {vs, es};
}

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