Tree-Isomorphism(木の同型性判定) (graph/tree/tree-isomorphism.hpp)

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• Last update: 2024-04-27 01:27:28+09:00
• Include: #include "graph/tree/tree-isomorphism.hpp"

Depends on

• Graph Template(グラフテンプレート) (graph/graph-template.hpp)
• Centroid(木の重心) (graph/tree/centroid.hpp)

Verified with

• test/verify/aoj-2821.test.cpp

Code

#pragma once

#include "../graph-template.hpp"
#include "./centroid.hpp"

/**
 * @brief Tree-Isomorphism(木の同型性判定)
 */
template <typename T>
bool tree_isomorphism(const Graph<T> &a, const Graph<T> &b) {
  if (a.size() != b.size()) return false;

  const int N = (int)a.size();
  using pvi = pair<vector<int>, vector<int> >;

  auto get_uku = [&](const Graph<T> &t, int e) {
    stack<pair<int, int> > st;
    st.emplace(e, -1);
    vector<int> dep(N, -1), par(N);
    while (!st.empty()) {
      auto p = st.top();
      if (dep[p.first] == -1) {
        dep[p.first] = p.second == -1 ? 0 : dep[p.second] + 1;
        for (auto &to : t[p.first])
          if (to != p.second) st.emplace(to, p.first);
      } else {
        par[p.first] = p.second;
        st.pop();
      }
    }
    return make_pair(dep, par);
  };

  auto solve = [&](const pvi &latte, const pvi &malta) {
    int d = *max_element(begin(latte.first), end(latte.first));
    if (d != *max_element(begin(malta.first), end(malta.first))) return false;

    vector<vector<int> > latte_d(d + 1), malta_d(d + 1), latte_key(N),
        malta_key(N);

    for (int i = 0; i < N; i++) latte_d[latte.first[i]].emplace_back(i);
    for (int i = 0; i < N; i++) malta_d[malta.first[i]].emplace_back(i);

    for (int i = d; i >= 0; i--) {
      map<vector<int>, int> ord;
      for (auto &idx : latte_d[i]) {
        sort(begin(latte_key[idx]), end(latte_key[idx]));
        ord[latte_key[idx]]++;
      }
      for (auto &idx : malta_d[i]) {
        sort(begin(malta_key[idx]), end(malta_key[idx]));
        if (--ord[malta_key[idx]] < 0) return false;
      }
      if (i == 0) return ord.size() == 1;

      int ptr = 0;
      for (auto &p : ord) {
        if (p.second != 0) return false;
        p.second = ptr++;
      }
      for (auto &idx : latte_d[i]) {
        latte_key[latte.second[idx]].emplace_back(ord[latte_key[idx]]);
      }
      for (auto &idx : malta_d[i]) {
        malta_key[malta.second[idx]].emplace_back(ord[malta_key[idx]]);
      }
    }
    assert(0);
  };
  auto p = centroid(a), q = centroid(b);
  if (p.size() != q.size()) return false;
  auto a1 = get_uku(a, p[0]);
  auto b1 = get_uku(b, q[0]);
  if (solve(a1, b1)) return true;
  if (p.size() == 1) return false;
  auto a2 = get_uku(a, p[1]);
  return solve(a2, b1);
}

#line 2 "graph/tree/tree-isomorphism.hpp"

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

/**
 * @brief Graph Template(グラフテンプレート)
 */
template <typename T = int>
struct Edge {
  int from, to;
  T cost;
  int idx;

  Edge() = default;

  Edge(int from, int to, T cost = 1, int idx = -1)
      : from(from), to(to), cost(cost), idx(idx) {}

  operator int() const { return to; }
};

template <typename T = int>
struct Graph {
  vector<vector<Edge<T> > > g;
  int es;

  Graph() = default;

  explicit Graph(int n) : g(n), es(0) {}

  size_t size() const { return g.size(); }

  void add_directed_edge(int from, int to, T cost = 1) {
    g[from].emplace_back(from, to, cost, es++);
  }

  void add_edge(int from, int to, T cost = 1) {
    g[from].emplace_back(from, to, cost, es);
    g[to].emplace_back(to, from, cost, es++);
  }

  void read(int M, int padding = -1, bool weighted = false,
            bool directed = false) {
    for (int i = 0; i < M; i++) {
      int a, b;
      cin >> a >> b;
      a += padding;
      b += padding;
      T c = T(1);
      if (weighted) cin >> c;
      if (directed)
        add_directed_edge(a, b, c);
      else
        add_edge(a, b, c);
    }
  }

  inline vector<Edge<T> > &operator[](const int &k) { return g[k]; }

  inline const vector<Edge<T> > &operator[](const int &k) const { return g[k]; }
};

template <typename T = int>
using Edges = vector<Edge<T> >;
#line 2 "graph/tree/centroid.hpp"

#line 4 "graph/tree/centroid.hpp"

/**
 * @brief Centroid(木の重心)
 *
 */
template <typename T>
vector<int> centroid(const Graph<T> &g) {
  const int N = (int)g.size();

  stack<pair<int, int> > st;
  st.emplace(0, -1);
  vector<int> sz(N), par(N);
  while (!st.empty()) {
    auto p = st.top();
    if (sz[p.first] == 0) {
      sz[p.first] = 1;
      for (auto &to : g[p.first])
        if (to != p.second) st.emplace(to, p.first);
    } else {
      for (auto &to : g[p.first])
        if (to != p.second) sz[p.first] += sz[to];
      par[p.first] = p.second;
      st.pop();
    }
  }

  vector<int> ret;
  int size = N;
  for (int i = 0; i < N; i++) {
    int val = N - sz[i];
    for (auto &to : g[i])
      if (to != par[i]) val = max(val, sz[to]);
    if (val < size) size = val, ret.clear();
    if (val == size) ret.emplace_back(i);
  }

  return ret;
}
#line 5 "graph/tree/tree-isomorphism.hpp"

/**
 * @brief Tree-Isomorphism(木の同型性判定)
 */
template <typename T>
bool tree_isomorphism(const Graph<T> &a, const Graph<T> &b) {
  if (a.size() != b.size()) return false;

  const int N = (int)a.size();
  using pvi = pair<vector<int>, vector<int> >;

  auto get_uku = [&](const Graph<T> &t, int e) {
    stack<pair<int, int> > st;
    st.emplace(e, -1);
    vector<int> dep(N, -1), par(N);
    while (!st.empty()) {
      auto p = st.top();
      if (dep[p.first] == -1) {
        dep[p.first] = p.second == -1 ? 0 : dep[p.second] + 1;
        for (auto &to : t[p.first])
          if (to != p.second) st.emplace(to, p.first);
      } else {
        par[p.first] = p.second;
        st.pop();
      }
    }
    return make_pair(dep, par);
  };

  auto solve = [&](const pvi &latte, const pvi &malta) {
    int d = *max_element(begin(latte.first), end(latte.first));
    if (d != *max_element(begin(malta.first), end(malta.first))) return false;

    vector<vector<int> > latte_d(d + 1), malta_d(d + 1), latte_key(N),
        malta_key(N);

    for (int i = 0; i < N; i++) latte_d[latte.first[i]].emplace_back(i);
    for (int i = 0; i < N; i++) malta_d[malta.first[i]].emplace_back(i);

    for (int i = d; i >= 0; i--) {
      map<vector<int>, int> ord;
      for (auto &idx : latte_d[i]) {
        sort(begin(latte_key[idx]), end(latte_key[idx]));
        ord[latte_key[idx]]++;
      }
      for (auto &idx : malta_d[i]) {
        sort(begin(malta_key[idx]), end(malta_key[idx]));
        if (--ord[malta_key[idx]] < 0) return false;
      }
      if (i == 0) return ord.size() == 1;

      int ptr = 0;
      for (auto &p : ord) {
        if (p.second != 0) return false;
        p.second = ptr++;
      }
      for (auto &idx : latte_d[i]) {
        latte_key[latte.second[idx]].emplace_back(ord[latte_key[idx]]);
      }
      for (auto &idx : malta_d[i]) {
        malta_key[malta.second[idx]].emplace_back(ord[malta_key[idx]]);
      }
    }
    assert(0);
  };
  auto p = centroid(a), q = centroid(b);
  if (p.size() != q.size()) return false;
  auto a1 = get_uku(a, p[0]);
  auto b1 = get_uku(b, q[0]);
  if (solve(a1, b1)) return true;
  if (p.size() == 1) return false;
  auto a2 = get_uku(a, p[1]);
  return solve(a2, b1);
}

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