graph/eulerwalk.hpp

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• Last update: 2024-04-19 02:20:22+09:00
• Include: #include "graph/eulerwalk.hpp"

Depends on

• ds/hashmap.hpp
• ds/unionfind/unionfind.hpp
• graph/base.hpp
• graph/vs_to_es.hpp

Verified with

• test/library_checker/graph/eulerwalk_d.test.cpp
• test/library_checker/graph/eulerwalk_ud.test.cpp
• test_atcoder/arc157a.test.cpp

Code

#include "ds/unionfind/unionfind.hpp"

#include "graph/base.hpp"

#include "graph/vs_to_es.hpp"


// (vs, es) or empty

template <typename GT>
pair<vc<int>, vc<int>> euler_walk(GT& G, int s = -1) {
  const int N = G.N, M = G.M;
  assert(G.is_prepared());
  assert(N > 0);

  if (s == -1) {
    vc<int> deg(N);
    for (auto&& e: G.edges) {
      if constexpr (GT::is_directed) {
        deg[e.frm]++, deg[e.to]--;
      } else {
        deg[e.frm]++, deg[e.to]++;
      }
    }
    if constexpr (GT::is_directed) {
      s = max_element(all(deg)) - deg.begin();
      if (deg[s] == 0) s = (M == 0 ? 0 : G.edges[0].frm);
    } else {
      s = [&]() -> int {
        FOR(v, N) if (deg[v] & 1) return v;
        return (M == 0 ? 0 : G.edges[0].frm);
      }();
    }
  }

  if (M == 0) return {{s}, {}};
  vc<int> D(N), its(N), eu(M), vs, st = {s};
  FOR(v, N) its[v] = G.indptr[v];
  ++D[s];
  while (!st.empty()) {
    int x = st.back(), y, e, &it = its[x], end = G.indptr[x + 1];
    if (it == end) {
      vs.eb(x);
      st.pop_back();
      continue;
    }
    auto& ee = G.csr_edges[it++];
    y = ee.to, e = ee.id;
    if (!eu[e]) {
      D[x]--, D[y]++;
      eu[e] = 1;
      st.eb(y);
    }
  }
  for (auto&& x: D)
    if (x < 0) return {{}, {}};
  if (len(vs) != M + 1) return {{}, {}};
  reverse(all(vs));
  auto es = vs_to_es(G, vs, false);
  return {vs, es};
}

template <typename GT>
bool has_euler_walk(GT& G, int s = -1) {
  int N = G.N, M = G.M;
  if (M == 0) return true;
  if constexpr (!GT::is_directed) {
    vc<int> odd(N);
    for (auto& e: G.edges) odd[e.frm] ^= 1, odd[e.to] ^= 1;
    int n_odd = 0;
    for (auto x: odd) n_odd += x;

    if (n_odd >= 4) return false;
    if (s != -1 && n_odd == 2 && !odd[s]) return false;
    UnionFind uf(N);
    for (auto& e: G.edges) uf.merge(e.frm, e.to);
    vector<int> cnt_edge(N);
    for (auto& e: G.edges) cnt_edge[uf[e.frm]]++;
    if (s != -1 && cnt_edge[uf[s]] == 0) return false;
    // 辺がある成分を数える

    int nc = 0;
    for (int v = 0; v < N; ++v) {
      if (uf[v] == v && cnt_edge[v] >= 1) ++nc;
    }
    return nc <= 1;
  } else {
    int N = G.N;
    vc<int> in(N), out(N);
    for (auto& e: G.edges) out[e.frm]++, in[e.to]++;

    int ng = 0;
    FOR(v, N) ng += abs(out[v] - in[v]);
    if (ng >= 4) return false;
    if (s != -1 && ng == 2 && out[s] != in[s] + 1) return false;

    UnionFind uf(N);
    for (auto& e: G.edges) uf.merge(e.frm, e.to);
    vector<int> cnt_edge(N);
    for (auto& e: G.edges) cnt_edge[uf[e.frm]]++;
    if (s != -1 && cnt_edge[uf[s]] == 0) return false;
    // 辺がある成分を数える

    int nc = 0;
    for (int v = 0; v < N; ++v) {
      if (uf[v] == v && cnt_edge[v] >= 1) ++nc;
    }
    return nc <= 1;
  }
}

#line 2 "ds/unionfind/unionfind.hpp"

struct UnionFind {
  int n, n_comp;
  vc<int> dat; // par or (-size)
  UnionFind(int n = 0) { build(n); }

  void build(int m) {
    n = m, n_comp = m;
    dat.assign(n, -1);
  }

  void reset() { build(n); }

  int operator[](int x) {
    while (dat[x] >= 0) {
      int pp = dat[dat[x]];
      if (pp < 0) { return dat[x]; }
      x = dat[x] = pp;
    }
    return x;
  }

  ll size(int x) {
    x = (*this)[x];
    return -dat[x];
  }

  bool merge(int x, int y) {
    x = (*this)[x], y = (*this)[y];
    if (x == y) return false;
    if (-dat[x] < -dat[y]) swap(x, y);
    dat[x] += dat[y], dat[y] = x, n_comp--;
    return true;
  }

  vc<int> get_all() {
    vc<int> A(n);
    FOR(i, n) A[i] = (*this)[i];
    return A;
  }
};
#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);
    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 (len(used_e) <= e.id) used_e.resize(e.id + 1);
        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/vs_to_es.hpp"

#line 2 "ds/hashmap.hpp"

// u64 -> Val

template <typename Val>
struct HashMap {
  HashMap(u32 n = 0) { build(n); }
  void build(u32 n) {
    u32 k = 8;
    while (k < n * 2) k *= 2;
    cap = k / 2, mask = k - 1;
    key.resize(k), val.resize(k), used.assign(k, 0);
  }
  void clear() { build(0); }
  int size() { return len(used) - cap; }

  int index(const u64& k) {
    int i = 0;
    for (i = hash(k); used[i] && key[i] != k; i = (i + 1) & mask) {}
    return i;
  }

  Val& operator[](const u64& k) {
    if (cap == 0) extend();
    int i = index(k);
    if (!used[i]) { used[i] = 1, key[i] = k, val[i] = Val{}, --cap; }
    return val[i];
  }

  Val get(const u64& k, Val default_value) {
    int i = index(k);
    return (used[i] ? val[i] : default_value);
  }

  bool count(const u64& k) {
    int i = index(k);
    return used[i] && key[i] == k;
  }

  // f(key, val)

  template <typename F>
  void enumerate_all(F f) {
    FOR(i, len(used)) if (used[i]) f(key[i], val[i]);
  }

private:
  u32 cap, mask;
  vc<u64> key;
  vc<Val> val;
  vc<bool> used;

  u64 hash(u64 x) {
    static const u64 FIXED_RANDOM
        = std::chrono::steady_clock::now().time_since_epoch().count();
    x += FIXED_RANDOM;
    x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
    x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
    return (x ^ (x >> 31)) & mask;
  }

  void extend() {
    vc<pair<u64, Val>> dat;
    dat.reserve(len(used) - cap);
    FOR(i, len(used)) {
      if (used[i]) dat.eb(key[i], val[i]);
    }
    build(2 * len(dat));
    for (auto& [a, b]: dat) (*this)[a] = b;
  }
};
#line 4 "graph/vs_to_es.hpp"

template <typename GT>
vc<int> vs_to_es(GT& G, vc<int>& vs, bool allow_use_twice = false) {
  assert(!vs.empty());

  HashMap<int> MP(G.M);
  vc<int> nxt(G.M, -1);

  auto get = [&](ll a, ll b) -> u64 {
    if (!GT::is_directed && a > b) swap(a, b);
    return a * G.N + b;
  };

  FOR(eid, G.M) {
    u64 k = get(G.edges[eid].frm, G.edges[eid].to);
    int x = MP.get(k, -1);
    nxt[eid] = x, MP[k] = eid;
  }
  int n = len(vs);
  vc<int> es(n - 1);
  FOR(i, n - 1) {
    u64 k = get(vs[i], vs[i + 1]);
    int eid = MP.get(k, -1);
    assert(eid != -1);
    es[i] = eid;
    if (!allow_use_twice) { MP[k] = nxt[eid]; }
  }
  return es;
}
#line 4 "graph/eulerwalk.hpp"

// (vs, es) or empty

template <typename GT>
pair<vc<int>, vc<int>> euler_walk(GT& G, int s = -1) {
  const int N = G.N, M = G.M;
  assert(G.is_prepared());
  assert(N > 0);

  if (s == -1) {
    vc<int> deg(N);
    for (auto&& e: G.edges) {
      if constexpr (GT::is_directed) {
        deg[e.frm]++, deg[e.to]--;
      } else {
        deg[e.frm]++, deg[e.to]++;
      }
    }
    if constexpr (GT::is_directed) {
      s = max_element(all(deg)) - deg.begin();
      if (deg[s] == 0) s = (M == 0 ? 0 : G.edges[0].frm);
    } else {
      s = [&]() -> int {
        FOR(v, N) if (deg[v] & 1) return v;
        return (M == 0 ? 0 : G.edges[0].frm);
      }();
    }
  }

  if (M == 0) return {{s}, {}};
  vc<int> D(N), its(N), eu(M), vs, st = {s};
  FOR(v, N) its[v] = G.indptr[v];
  ++D[s];
  while (!st.empty()) {
    int x = st.back(), y, e, &it = its[x], end = G.indptr[x + 1];
    if (it == end) {
      vs.eb(x);
      st.pop_back();
      continue;
    }
    auto& ee = G.csr_edges[it++];
    y = ee.to, e = ee.id;
    if (!eu[e]) {
      D[x]--, D[y]++;
      eu[e] = 1;
      st.eb(y);
    }
  }
  for (auto&& x: D)
    if (x < 0) return {{}, {}};
  if (len(vs) != M + 1) return {{}, {}};
  reverse(all(vs));
  auto es = vs_to_es(G, vs, false);
  return {vs, es};
}

template <typename GT>
bool has_euler_walk(GT& G, int s = -1) {
  int N = G.N, M = G.M;
  if (M == 0) return true;
  if constexpr (!GT::is_directed) {
    vc<int> odd(N);
    for (auto& e: G.edges) odd[e.frm] ^= 1, odd[e.to] ^= 1;
    int n_odd = 0;
    for (auto x: odd) n_odd += x;

    if (n_odd >= 4) return false;
    if (s != -1 && n_odd == 2 && !odd[s]) return false;
    UnionFind uf(N);
    for (auto& e: G.edges) uf.merge(e.frm, e.to);
    vector<int> cnt_edge(N);
    for (auto& e: G.edges) cnt_edge[uf[e.frm]]++;
    if (s != -1 && cnt_edge[uf[s]] == 0) return false;
    // 辺がある成分を数える

    int nc = 0;
    for (int v = 0; v < N; ++v) {
      if (uf[v] == v && cnt_edge[v] >= 1) ++nc;
    }
    return nc <= 1;
  } else {
    int N = G.N;
    vc<int> in(N), out(N);
    for (auto& e: G.edges) out[e.frm]++, in[e.to]++;

    int ng = 0;
    FOR(v, N) ng += abs(out[v] - in[v]);
    if (ng >= 4) return false;
    if (s != -1 && ng == 2 && out[s] != in[s] + 1) return false;

    UnionFind uf(N);
    for (auto& e: G.edges) uf.merge(e.frm, e.to);
    vector<int> cnt_edge(N);
    for (auto& e: G.edges) cnt_edge[uf[e.frm]]++;
    if (s != -1 && cnt_edge[uf[s]] == 0) return false;
    // 辺がある成分を数える

    int nc = 0;
    for (int v = 0; v < N; ++v) {
      if (uf[v] == v && cnt_edge[v] >= 1) ++nc;
    }
    return nc <= 1;
  }
}

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