test/verify/aoj-2821.test.cpp

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• Last update: 2024-07-28 19:56:12+09:00
• Problem: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2821

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)
• Tree-Isomorphism(木の同型性判定) (graph/tree/tree-isomorphism.hpp)
• Union Find (structure/union-find/union-find.hpp)
• template/template.hpp

Code

// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2821

#include "../../template/template.hpp"

#include "../../structure/union-find/union-find.hpp"

#include "../../graph/tree/tree-isomorphism.hpp"

int main() {
  int N, M;
  cin >> N >> M;
  vector< int > U(M), V(M);
  UnionFind uf(N);
  for(int i = 0; i < M; i++) {
    cin >> U[i] >> V[i];
    --U[i], --V[i];
    uf.unite(U[i], V[i]);
  }
  vector< vector< int > > belong_v(N), belong_e(N);
  for(int i = 0; i < N; i++) {
    belong_v[uf.find(i)].emplace_back(i);
  }
  for(int i = 0; i < M; i++) {
    belong_e[uf.find(U[i])].emplace_back(i);
  }

  cin >> N;
  Graph<> t(N);
  t.read(N - 1);

  int ret = 0;
  vector< int > id(belong_v.size());
  for(int i = 0; i < (int) belong_v.size(); i++) {
    if(uf.find(i) == i) {
      Graph<> g(belong_v[i].size());
      int ptr = 0;
      for(auto &p : belong_v[i]) id[p] = ptr++;
      for(auto &j : belong_e[i]) {
        g.add_edge(id[U[j]], id[V[j]]);
      }
      ret += tree_isomorphism(t, g);
    }
  }
  cout << ret << endl;
}

#line 1 "test/verify/aoj-2821.test.cpp"
// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2821

#line 1 "template/template.hpp"
#include <bits/stdc++.h>
#if __has_include(<atcoder/all>)
#include <atcoder/all>
#endif

using namespace std;

using int64 = long long;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << p.first << " " << p.second;
  return os;
}

template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  for (int i = 0; i < (int)v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (T &in : v) is >> in;
  return is;
}

template <typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {
  return a < b && (a = b, true);
}

template <typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {
  return a > b && (a = b, true);
}

template <typename T = int64>
vector<T> make_v(size_t a) {
  return vector<T>(a);
}

template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
  t = v;
}

template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
  for (auto &e : t) fill_v(e, v);
}

template <typename F>
struct FixPoint : F {
  explicit FixPoint(F &&f) : F(std::forward<F>(f)) {}

  template <typename... Args>
  decltype(auto) operator()(Args &&...args) const {
    return F::operator()(*this, std::forward<Args>(args)...);
  }
};

template <typename F>
inline decltype(auto) MFP(F &&f) {
  return FixPoint<F>{std::forward<F>(f)};
}
#line 4 "test/verify/aoj-2821.test.cpp"

#line 2 "structure/union-find/union-find.hpp"

struct UnionFind {
  vector<int> data;

  UnionFind() = default;

  explicit UnionFind(size_t sz) : data(sz, -1) {}

  bool unite(int x, int y) {
    x = find(x), y = find(y);
    if (x == y) return false;
    if (data[x] > data[y]) swap(x, y);
    data[x] += data[y];
    data[y] = x;
    return true;
  }

  int find(int k) {
    if (data[k] < 0) return (k);
    return data[k] = find(data[k]);
  }

  int size(int k) { return -data[find(k)]; }

  bool same(int x, int y) { return find(x) == find(y); }

  vector<vector<int> > groups() {
    int n = (int)data.size();
    vector<vector<int> > ret(n);
    for (int i = 0; i < n; i++) {
      ret[find(i)].emplace_back(i);
    }
    ret.erase(remove_if(begin(ret), end(ret),
                        [&](const vector<int> &v) { return v.empty(); }),
              end(ret));
    return ret;
  }
};
#line 6 "test/verify/aoj-2821.test.cpp"

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

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

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);
}
#line 8 "test/verify/aoj-2821.test.cpp"

int main() {
  int N, M;
  cin >> N >> M;
  vector< int > U(M), V(M);
  UnionFind uf(N);
  for(int i = 0; i < M; i++) {
    cin >> U[i] >> V[i];
    --U[i], --V[i];
    uf.unite(U[i], V[i]);
  }
  vector< vector< int > > belong_v(N), belong_e(N);
  for(int i = 0; i < N; i++) {
    belong_v[uf.find(i)].emplace_back(i);
  }
  for(int i = 0; i < M; i++) {
    belong_e[uf.find(U[i])].emplace_back(i);
  }

  cin >> N;
  Graph<> t(N);
  t.read(N - 1);

  int ret = 0;
  vector< int > id(belong_v.size());
  for(int i = 0; i < (int) belong_v.size(); i++) {
    if(uf.find(i) == i) {
      Graph<> g(belong_v[i].size());
      int ptr = 0;
      for(auto &p : belong_v[i]) id[p] = ptr++;
      for(auto &j : belong_e[i]) {
        g.add_edge(id[U[j]], id[V[j]]);
      }
      ret += tree_isomorphism(t, g);
    }
  }
  cout << ret << endl;
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	00_sample_00.in	AC	5 ms	3 MB
g++	00_sample_01.in	AC	4 ms	3 MB
g++	10_small_0.in	AC	4 ms	3 MB
g++	10_small_1.in	AC	4 ms	3 MB
g++	10_small_2.in	AC	4 ms	3 MB
g++	10_small_3.in	AC	4 ms	3 MB
g++	10_small_4.in	AC	4 ms	3 MB
g++	10_small_5.in	AC	4 ms	3 MB
g++	10_small_6.in	AC	4 ms	3 MB
g++	10_small_7.in	AC	4 ms	3 MB
g++	10_small_8.in	AC	4 ms	3 MB
g++	10_small_9.in	AC	4 ms	3 MB
g++	11_large_0.in	AC	154 ms	31 MB
g++	11_large_1.in	AC	147 ms	30 MB
g++	11_large_2.in	AC	124 ms	49 MB
g++	11_large_3.in	AC	109 ms	49 MB
g++	11_large_4.in	AC	147 ms	30 MB
g++	11_large_5.in	AC	140 ms	28 MB
g++	11_large_6.in	AC	121 ms	48 MB
g++	11_large_7.in	AC	103 ms	46 MB
g++	11_large_8.in	AC	154 ms	31 MB
g++	11_large_9.in	AC	152 ms	31 MB
g++	20_line0_0.in	AC	124 ms	51 MB
g++	20_line0_1.in	AC	40 ms	15 MB
g++	20_line0_2.in	AC	34 ms	10 MB
g++	20_line0_3.in	AC	31 ms	9 MB
g++	21_line1_0.in	AC	122 ms	53 MB
g++	21_line1_1.in	AC	38 ms	14 MB
g++	21_line1_2.in	AC	31 ms	10 MB
g++	21_line1_3.in	AC	28 ms	8 MB
g++	22_line2_0.in	AC	113 ms	50 MB
g++	22_line2_1.in	AC	34 ms	13 MB
g++	22_line2_2.in	AC	28 ms	9 MB
g++	22_line2_3.in	AC	25 ms	8 MB
g++	23_line5_0.in	AC	112 ms	51 MB
g++	23_line5_1.in	AC	30 ms	13 MB
g++	23_line5_2.in	AC	25 ms	9 MB
g++	23_line5_3.in	AC	23 ms	8 MB
g++	30_linear2_10.in	AC	155 ms	27 MB
g++	30_linear2_20.in	AC	133 ms	27 MB
g++	30_linear2_3.in	AC	170 ms	26 MB
g++	30_linear2_4.in	AC	163 ms	26 MB
g++	30_linear2_5.in	AC	181 ms	26 MB
g++	31_linear3_10.in	AC	159 ms	27 MB
g++	31_linear3_20.in	AC	159 ms	26 MB
g++	31_linear3_3.in	AC	172 ms	26 MB
g++	31_linear3_4.in	AC	162 ms	26 MB
g++	31_linear3_5.in	AC	162 ms	26 MB
g++	40_line_0.in	AC	40 ms	15 MB
g++	40_line_1.in	AC	37 ms	14 MB
g++	40_line_10.in	AC	28 ms	13 MB
g++	40_line_14999.in	AC	22 ms	12 MB
g++	40_line_173.in	AC	24 ms	13 MB
g++	40_line_2.in	AC	33 ms	13 MB
g++	40_line_29999.in	AC	21 ms	12 MB
g++	40_line_5.in	AC	30 ms	13 MB
g++	40_line_9999.in	AC	22 ms	12 MB
g++	50_pie_0.in	AC	33 ms	13 MB
g++	50_pie_1.in	AC	25 ms	10 MB
g++	50_pie_2.in	AC	30 ms	11 MB
g++	50_pie_3.in	AC	25 ms	10 MB
g++	50_pie_4.in	AC	25 ms	10 MB
clang++	00_sample_00.in	AC	5 ms	3 MB
clang++	00_sample_01.in	AC	4 ms	3 MB
clang++	10_small_0.in	AC	4 ms	3 MB
clang++	10_small_1.in	AC	4 ms	3 MB
clang++	10_small_2.in	AC	4 ms	3 MB
clang++	10_small_3.in	AC	4 ms	3 MB
clang++	10_small_4.in	AC	4 ms	3 MB
clang++	10_small_5.in	AC	4 ms	3 MB
clang++	10_small_6.in	AC	4 ms	3 MB
clang++	10_small_7.in	AC	4 ms	3 MB
clang++	10_small_8.in	AC	4 ms	3 MB
clang++	10_small_9.in	AC	4 ms	3 MB
clang++	11_large_0.in	AC	159 ms	31 MB
clang++	11_large_1.in	AC	151 ms	30 MB
clang++	11_large_2.in	AC	128 ms	49 MB
clang++	11_large_3.in	AC	112 ms	49 MB
clang++	11_large_4.in	AC	151 ms	30 MB
clang++	11_large_5.in	AC	146 ms	28 MB
clang++	11_large_6.in	AC	123 ms	48 MB
clang++	11_large_7.in	AC	104 ms	46 MB
clang++	11_large_8.in	AC	159 ms	31 MB
clang++	11_large_9.in	AC	155 ms	31 MB
clang++	20_line0_0.in	AC	128 ms	51 MB
clang++	20_line0_1.in	AC	41 ms	15 MB
clang++	20_line0_2.in	AC	34 ms	10 MB
clang++	20_line0_3.in	AC	30 ms	9 MB
clang++	21_line1_0.in	AC	125 ms	53 MB
clang++	21_line1_1.in	AC	37 ms	14 MB
clang++	21_line1_2.in	AC	32 ms	10 MB
clang++	21_line1_3.in	AC	29 ms	8 MB
clang++	22_line2_0.in	AC	118 ms	50 MB
clang++	22_line2_1.in	AC	35 ms	13 MB
clang++	22_line2_2.in	AC	28 ms	9 MB
clang++	22_line2_3.in	AC	26 ms	8 MB
clang++	23_line5_0.in	AC	114 ms	51 MB
clang++	23_line5_1.in	AC	31 ms	13 MB
clang++	23_line5_2.in	AC	26 ms	9 MB
clang++	23_line5_3.in	AC	23 ms	8 MB
clang++	30_linear2_10.in	AC	157 ms	27 MB
clang++	30_linear2_20.in	AC	134 ms	27 MB
clang++	30_linear2_3.in	AC	172 ms	26 MB
clang++	30_linear2_4.in	AC	164 ms	26 MB
clang++	30_linear2_5.in	AC	178 ms	26 MB
clang++	31_linear3_10.in	AC	161 ms	27 MB
clang++	31_linear3_20.in	AC	163 ms	26 MB
clang++	31_linear3_3.in	AC	169 ms	26 MB
clang++	31_linear3_4.in	AC	164 ms	26 MB
clang++	31_linear3_5.in	AC	164 ms	26 MB
clang++	40_line_0.in	AC	41 ms	15 MB
clang++	40_line_1.in	AC	37 ms	14 MB
clang++	40_line_10.in	AC	28 ms	13 MB
clang++	40_line_14999.in	AC	23 ms	12 MB
clang++	40_line_173.in	AC	24 ms	13 MB
clang++	40_line_2.in	AC	34 ms	13 MB
clang++	40_line_29999.in	AC	22 ms	12 MB
clang++	40_line_5.in	AC	30 ms	13 MB
clang++	40_line_9999.in	AC	23 ms	12 MB
clang++	50_pie_0.in	AC	33 ms	13 MB
clang++	50_pie_1.in	AC	26 ms	10 MB
clang++	50_pie_2.in	AC	30 ms	11 MB
clang++	50_pie_3.in	AC	26 ms	10 MB
clang++	50_pie_4.in	AC	26 ms	10 MB

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