test/verify/aoj-grl-5-c-2.test.cpp

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• Last update: 2024-05-01 23:44:47+09:00
• Problem: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_5_C

Depends on

• Graph Template(グラフテンプレート) (graph/graph-template.hpp)
• Heavy-Light-Decomposition(HL分解) (graph/tree/heavy-light-decomposition.hpp)
• template/template.hpp

Code

// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_5_C

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

#include "../../graph/tree/heavy-light-decomposition.hpp"

int main() {
  int N, Q;
  cin >> N;
  HeavyLightDecomposition< int > hld(N);
  for(int i = 0; i < N; i++) {
    int k;
    cin >> k;
    for(int j = 0; j < k; j++) {
      int c;
      cin >> c;
      hld.add_edge(i, c);
    }
  }
  hld.build();
  cin >> Q;
  for(int i = 0; i < Q; i++) {
    int u, v;
    cin >> u >> v;
    cout << hld.lca(u, v) << "\n";
  }
}

#line 1 "test/verify/aoj-grl-5-c-2.test.cpp"
// competitive-verifier: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_5_C

#line 1 "template/template.hpp"
#include <bits/stdc++.h>

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(forward<F>(f)) {}

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

template <typename F>
inline decltype(auto) MFP(F &&f) {
  return FixPoint<F>{forward<F>(f)};
}
#line 4 "test/verify/aoj-grl-5-c-2.test.cpp"

#line 2 "graph/tree/heavy-light-decomposition.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 4 "graph/tree/heavy-light-decomposition.hpp"

/**
 * @brief Heavy-Light-Decomposition(HL分解)
 * @see https://smijake3.hatenablog.com/entry/2019/09/15/200200
 */
template <typename T = int>
struct HeavyLightDecomposition : Graph<T> {
 public:
  using Graph<T>::Graph;
  using Graph<T>::g;
  vector<int> sz, in, out, head, rev, par, dep;

  void build() {
    sz.assign(g.size(), 0);
    in.assign(g.size(), 0);
    out.assign(g.size(), 0);
    head.assign(g.size(), 0);
    rev.assign(g.size(), 0);
    par.assign(g.size(), 0);
    dep.assign(g.size(), 0);
    dfs_sz(0, -1, 0);
    int t = 0;
    dfs_hld(0, -1, t);
  }

  /* k: 0-indexed */
  int la(int v, int k) {
    while (1) {
      int u = head[v];
      if (in[v] - k >= in[u]) return rev[in[v] - k];
      k -= in[v] - in[u] + 1;
      v = par[u];
    }
  }

  int lca(int u, int v) const {
    for (;; v = par[head[v]]) {
      if (in[u] > in[v]) swap(u, v);
      if (head[u] == head[v]) return u;
    }
  }

  int dist(int u, int v) const { return dep[u] + dep[v] - 2 * dep[lca(u, v)]; }

  template <typename E, typename Q, typename F, typename S>
  E query(int u, int v, const E &ti, const Q &q, const F &f, const S &s,
          bool edge = false) {
    E l = ti, r = ti;
    for (;; v = par[head[v]]) {
      if (in[u] > in[v]) swap(u, v), swap(l, r);
      if (head[u] == head[v]) break;
      l = f(q(in[head[v]], in[v] + 1), l);
    }
    return s(f(q(in[u] + edge, in[v] + 1), l), r);
  }

  template <typename E, typename Q, typename F>
  E query(int u, int v, const E &ti, const Q &q, const F &f,
          bool edge = false) {
    return query(u, v, ti, q, f, f, edge);
  }

  template <typename Q>
  void add(int u, int v, const Q &q, bool edge = false) {
    for (;; v = par[head[v]]) {
      if (in[u] > in[v]) swap(u, v);
      if (head[u] == head[v]) break;
      q(in[head[v]], in[v] + 1);
    }
    q(in[u] + edge, in[v] + 1);
  }

  /* {parent, child} */
  vector<pair<int, int> > compress(vector<int> &remark) {
    auto cmp = [&](int a, int b) { return in[a] < in[b]; };
    sort(begin(remark), end(remark), cmp);
    remark.erase(unique(begin(remark), end(remark)), end(remark));
    int K = (int)remark.size();
    for (int k = 1; k < K; k++)
      remark.emplace_back(lca(remark[k - 1], remark[k]));
    sort(begin(remark), end(remark), cmp);
    remark.erase(unique(begin(remark), end(remark)), end(remark));
    vector<pair<int, int> > es;
    stack<int> st;
    for (auto &k : remark) {
      while (!st.empty() && out[st.top()] <= in[k]) st.pop();
      if (!st.empty()) es.emplace_back(st.top(), k);
      st.emplace(k);
    }
    return es;
  }

  explicit HeavyLightDecomposition(const Graph<T> &g) : Graph<T>(g) {}

 private:
  void dfs_sz(int idx, int p, int d) {
    dep[idx] = d;
    par[idx] = p;
    sz[idx] = 1;
    if (g[idx].size() && g[idx][0] == p) swap(g[idx][0], g[idx].back());
    for (auto &to : g[idx]) {
      if (to == p) continue;
      dfs_sz(to, idx, d + 1);
      sz[idx] += sz[to];
      if (sz[g[idx][0]] < sz[to]) swap(g[idx][0], to);
    }
  }

  void dfs_hld(int idx, int p, int &times) {
    in[idx] = times++;
    rev[in[idx]] = idx;
    for (auto &to : g[idx]) {
      if (to == p) continue;
      head[to] = (g[idx][0] == to ? head[idx] : to);
      dfs_hld(to, idx, times);
    }
    out[idx] = times;
  }
};
#line 6 "test/verify/aoj-grl-5-c-2.test.cpp"

int main() {
  int N, Q;
  cin >> N;
  HeavyLightDecomposition< int > hld(N);
  for(int i = 0; i < N; i++) {
    int k;
    cin >> k;
    for(int j = 0; j < k; j++) {
      int c;
      cin >> c;
      hld.add_edge(i, c);
    }
  }
  hld.build();
  cin >> Q;
  for(int i = 0; i < Q; i++) {
    int u, v;
    cin >> u >> v;
    cout << hld.lca(u, v) << "\n";
  }
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	00_sample_00.in	AC	6 ms	4 MB
g++	01_small_00.in	AC	6 ms	4 MB
g++	02_middle_00.in	AC	6 ms	4 MB
g++	02_middle_01.in	AC	6 ms	4 MB
g++	02_middle_02.in	AC	6 ms	4 MB
g++	02_middle_03.in	AC	6 ms	4 MB
g++	03_corner_00.in	AC	5 ms	4 MB
g++	03_corner_01.in	AC	6 ms	4 MB
g++	04_rand_00.in	AC	6 ms	4 MB
g++	04_rand_01.in	AC	6 ms	4 MB
g++	04_rand_02.in	AC	6 ms	4 MB
g++	04_rand_03.in	AC	6 ms	4 MB
g++	04_rand_04.in	AC	6 ms	4 MB
g++	04_rand_05.in	AC	6 ms	4 MB
g++	04_rand_06.in	AC	6 ms	4 MB
g++	04_rand_07.in	AC	6 ms	4 MB
g++	05_complete_00.in	AC	6 ms	4 MB
g++	05_complete_01.in	AC	5 ms	4 MB
g++	05_complete_02.in	AC	6 ms	4 MB
g++	05_complete_03.in	AC	6 ms	4 MB
g++	05_complete_04.in	AC	6 ms	4 MB
g++	05_complete_05.in	AC	7 ms	4 MB
g++	05_complete_06.in	AC	11 ms	4 MB
g++	05_complete_07.in	AC	17 ms	9 MB
g++	06_biased_00.in	AC	19 ms	5 MB
g++	06_biased_01.in	AC	43 ms	18 MB
g++	06_biased_02.in	AC	38 ms	13 MB
g++	06_biased_03.in	AC	39 ms	16 MB
g++	07_large_00.in	AC	50 ms	14 MB
g++	07_large_01.in	AC	49 ms	14 MB
g++	07_large_02.in	AC	53 ms	14 MB
g++	07_large_03.in	AC	52 ms	14 MB
clang++	00_sample_00.in	AC	6 ms	4 MB
clang++	01_small_00.in	AC	6 ms	4 MB
clang++	02_middle_00.in	AC	6 ms	4 MB
clang++	02_middle_01.in	AC	6 ms	4 MB
clang++	02_middle_02.in	AC	6 ms	4 MB
clang++	02_middle_03.in	AC	6 ms	4 MB
clang++	03_corner_00.in	AC	6 ms	4 MB
clang++	03_corner_01.in	AC	6 ms	4 MB
clang++	04_rand_00.in	AC	6 ms	4 MB
clang++	04_rand_01.in	AC	6 ms	4 MB
clang++	04_rand_02.in	AC	6 ms	4 MB
clang++	04_rand_03.in	AC	6 ms	4 MB
clang++	04_rand_04.in	AC	6 ms	4 MB
clang++	04_rand_05.in	AC	6 ms	4 MB
clang++	04_rand_06.in	AC	6 ms	4 MB
clang++	04_rand_07.in	AC	6 ms	4 MB
clang++	05_complete_00.in	AC	6 ms	4 MB
clang++	05_complete_01.in	AC	6 ms	4 MB
clang++	05_complete_02.in	AC	6 ms	4 MB
clang++	05_complete_03.in	AC	6 ms	4 MB
clang++	05_complete_04.in	AC	6 ms	4 MB
clang++	05_complete_05.in	AC	7 ms	4 MB
clang++	05_complete_06.in	AC	9 ms	4 MB
clang++	05_complete_07.in	AC	18 ms	9 MB
clang++	06_biased_00.in	AC	20 ms	5 MB
clang++	06_biased_01.in	AC	45 ms	23 MB
clang++	06_biased_02.in	AC	41 ms	13 MB
clang++	06_biased_03.in	AC	41 ms	18 MB
clang++	07_large_00.in	AC	60 ms	14 MB
clang++	07_large_01.in	AC	61 ms	14 MB
clang++	07_large_02.in	AC	59 ms	14 MB
clang++	07_large_03.in	AC	58 ms	14 MB

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