test/verify/yosupo-lca-2.test.cpp

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• Last update: 2026-08-10 11:00:59+00:00
• Problem: https://judge.yosupo.jp/problem/lca

Depends on

• Graph Template (グラフテンプレート) (graph/graph-template.hpp)
• RMQ Lowest Common Ancestor (最小共通祖先) (graph/tree/rmq-lowest-common-ancestor.hpp)
• Printer(高速出力) (other/printer.hpp)
• Scanner(高速入力) (other/scanner.hpp)
• Sparse Table (スパーステーブル) (structure/others/sparse-table.hpp)

Code

// clang-format off
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/lca
// clang-format on

#include <cstdio>

#include "../../graph/tree/rmq-lowest-common-ancestor.hpp"
#include "../../other/printer.hpp"
#include "../../other/scanner.hpp"

using namespace std;

int main() {
  Scanner in(stdin);
  Printer out(stdout);
  int N, Q;
  in.read(N, Q);
  RMQLowestCommonAncestor<int> g(N);
  for (int i = 1; i < N; i++) {
    int x;
    in.read(x);
    g.add_directed_edge(x, i);
  }
  g.build();
  for (int i = 0; i < Q; i++) {
    int u, v;
    in.read(u, v);
    out.writeln(g.lca(u, v));
  }
}

#line 1 "test/verify/yosupo-lca-2.test.cpp"
// clang-format off
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/lca
// clang-format on

#include <cstdio>

#line 2 "graph/tree/rmq-lowest-common-ancestor.hpp"

#include <functional>
#include <iterator>
#include <numeric>
#include <utility>
#include <vector>

#line 2 "structure/others/sparse-table.hpp"

#line 4 "structure/others/sparse-table.hpp"

/**
 * @brief Sparse-Table(スパーステーブル)
 *
 */
template <typename T, typename F>
struct SparseTable {
  F f;
  std::vector<std::vector<T>> st;
  std::vector<int> lookup;

  SparseTable() = default;

  explicit SparseTable(const std::vector<T>& v, const F& f) : f(f) {
    const int n = (int)v.size();
    const int b = 32 - __builtin_clz(n);
    st.assign(b, std::vector<T>(n));
    for (int i = 0; i < n; i++) {
      st[0][i] = v[i];
    }
    for (int i = 1; i < b; i++) {
      for (int j = 0; j + (1 << i) <= n; j++) {
        st[i][j] = f(st[i - 1][j], st[i - 1][j + (1 << (i - 1))]);
      }
    }
    lookup.resize(v.size() + 1);
    for (int i = 2; i <= n; i++) {
      lookup[i] = lookup[i >> 1] + 1;
    }
  }

  inline T fold(int l, int r) const {
    int b = lookup[r - l];
    return f(st[b][l], st[b][r - (1 << b)]);
  }
};

template <typename T, typename F>
SparseTable<T, F> get_sparse_table(const std::vector<T>& v, const F& f) {
  return SparseTable<T, F>(v, f);
}
#line 2 "graph/graph-template.hpp"

#include <cstddef>
#include <iostream>
#line 6 "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 {
  std::vector<std::vector<Edge<T> > > g;
  int es;

  Graph() = default;

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

  std::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;
      std::cin >> a >> b;
      a += padding;
      b += padding;
      T c = T(1);
      if (weighted) std::cin >> c;
      if (directed)
        add_directed_edge(a, b, c);
      else
        add_edge(a, b, c);
    }
  }

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

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

template <typename T = int>
using Edges = std::vector<Edge<T> >;
#line 11 "graph/tree/rmq-lowest-common-ancestor.hpp"

/**
 * @brief RMQ-Lowest-Common-Ancestor(最小共通祖先)
 *
 **/
template <typename T = int>
struct RMQLowestCommonAncestor : Graph<T> {
 public:
  using Graph<T>::Graph;
  using Graph<T>::g;
  using F = std::function<int(int, int)>;

  void build(int root = 0) {
    ord.reserve(g.size() * 2 - 1);
    dep.reserve(g.size() * 2 - 1);
    in.resize(g.size());
    dfs(root, -1, 0);
    std::vector<int> vs(g.size() * 2 - 1);
    std::iota(std::begin(vs), std::end(vs), 0);
    F f = [&](int a, int b) { return dep[a] < dep[b] ? a : b; };
    st = get_sparse_table(vs, f);
  }

  int lca(int x, int y) const {
    if (in[x] > in[y]) std::swap(x, y);
    return x == y ? x : ord[st.fold(in[x], in[y])];
  }

 private:
  std::vector<int> ord, dep, in;
  SparseTable<int, F> st;

  void dfs(int idx, int par, int d) {
    in[idx] = (int)ord.size();
    ord.emplace_back(idx);
    dep.emplace_back(d);
    for (auto& to : g[idx]) {
      if (to != par) {
        dfs(to, idx, d + 1);
        ord.emplace_back(idx);
        dep.emplace_back(d);
      }
    }
  }
};
#line 2 "other/printer.hpp"

#include <charconv>
#line 6 "other/printer.hpp"
#include <string>
#include <type_traits>
#line 9 "other/printer.hpp"

/**
 * @brief Printer(高速出力)
 */
struct Printer {
 public:
  explicit Printer(FILE* fp) : fp(fp) {}

  ~Printer() { flush(); }

  template <bool f = false, typename T, typename... E>
  void write(const T& t, const E&... e) {
    if (f) write_single(' ');
    write_single(t);
    write<true>(e...);
  }

  template <typename... T>
  void writeln(const T&... t) {
    write(t...);
    write_single('\n');
  }

  void flush() {
    fwrite(line, 1, st - line, fp);
    st = line;
  }

 private:
  FILE* fp = nullptr;
  static constexpr std::size_t line_size = 1 << 16;
  static constexpr std::size_t int_digits = 20;
  char line[line_size + 1] = {};
  char* st = line;

  template <bool f = false>
  void write() {}

  void write_single(const char& t) {
    if (st + 1 >= line + line_size) flush();
    *st++ = t;
  }

  template <typename T, std::enable_if_t<std::is_integral<T>::value, int> = 0>
  void write_single(T s) {
    if (st + int_digits >= line + line_size) flush();
    st += std::to_chars(st, st + int_digits, s).ptr - st;
  }

  void write_single(const std::string& s) {
    for (auto& c : s) write_single(c);
  }

  void write_single(const char* s) {
    while (*s != 0) write_single(*s++);
  }

  template <typename T>
  void write_single(const std::vector<T>& s) {
    for (std::size_t i = 0; i < s.size(); i++) {
      if (i) write_single(' ');
      write_single(s[i]);
    }
  }
};
#line 2 "other/scanner.hpp"

#line 5 "other/scanner.hpp"
#include <cstring>
#line 9 "other/scanner.hpp"

/**
 * @brief Scanner(高速入力)
 */
struct Scanner {
 public:
  explicit Scanner(std::FILE* fp) : fp(fp) {}

  template <typename T, typename... E>
  void read(T& t, E&... e) {
    read_single(t);
    read(e...);
  }

 private:
  static constexpr std::size_t line_size = 1 << 16;
  static constexpr std::size_t int_digits = 20;
  char line[line_size + 1] = {};
  std::FILE* fp = nullptr;
  char* st = line;
  char* ed = line;

  void read() {}

  static inline bool is_space(char c) { return c <= ' '; }

  void reread() {
    std::ptrdiff_t len = ed - st;
    std::memmove(line, st, len);
    char* tmp = line + len;
    ed = tmp + std::fread(tmp, 1, line_size - len, fp);
    *ed = 0;
    st = line;
  }

  void skip_space() {
    while (true) {
      if (st == ed) reread();
      while (*st && is_space(*st)) ++st;
      if (st != ed) return;
    }
  }

  template <typename T, std::enable_if_t<std::is_integral<T>::value, int> = 0>
  void read_single(T& s) {
    skip_space();
    if (st + int_digits >= ed) reread();
    bool neg = false;
    if (std::is_signed<T>::value && *st == '-') {
      neg = true;
      ++st;
    }
    typename std::make_unsigned<T>::type y = *st++ - '0';
    while (*st >= '0') {
      y = 10 * y + *st++ - '0';
    }
    s = (neg ? -y : y);
  }

  template <typename T,
            std::enable_if_t<std::is_same<T, std::string>::value, int> = 0>
  void read_single(T& s) {
    s = "";
    skip_space();
    while (true) {
      char* base = st;
      while (*st && !is_space(*st)) ++st;
      s += std::string(base, st);
      if (st != ed) return;
      reread();
    }
  }

  template <typename T>
  void read_single(std::vector<T>& s) {
    for (auto& d : s) read(d);
  }
};
#line 10 "test/verify/yosupo-lca-2.test.cpp"

using namespace std;

int main() {
  Scanner in(stdin);
  Printer out(stdout);
  int N, Q;
  in.read(N, Q);
  RMQLowestCommonAncestor<int> g(N);
  for (int i = 1; i < N; i++) {
    int x;
    in.read(x);
    g.add_directed_edge(x, i);
  }
  g.build();
  for (int i = 0; i < Q; i++) {
    int u, v;
    in.read(u, v);
    out.writeln(g.lca(u, v));
  }
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	almost_line_00	AC	247 ms	135 MB
g++	almost_line_01	AC	232 ms	135 MB
g++	binary_00	AC	222 ms	123 MB
g++	binary_01	AC	217 ms	123 MB
g++	binary_02	AC	243 ms	123 MB
g++	example_00	AC	2 ms	4 MB
g++	line_00	AC	176 ms	117 MB
g++	line_01	AC	188 ms	138 MB
g++	line_02	AC	53 ms	18 MB
g++	line_03	AC	127 ms	128 MB
g++	line_04	AC	98 ms	84 MB
g++	max_line_00	AC	210 ms	149 MB
g++	max_line_01	AC	219 ms	149 MB
g++	max_line_02	AC	211 ms	149 MB
g++	max_random_00	AC	240 ms	124 MB
g++	max_random_01	AC	207 ms	124 MB
g++	max_random_02	AC	209 ms	124 MB
g++	path_graph_root_centroid_00	AC	163 ms	138 MB
g++	path_graph_root_centroid_01	AC	164 ms	138 MB
g++	path_graph_root_centroid_02	AC	165 ms	138 MB
g++	random_00	AC	167 ms	97 MB
g++	random_01	AC	193 ms	115 MB
g++	random_02	AC	45 ms	15 MB
g++	random_03	AC	150 ms	107 MB
g++	random_04	AC	107 ms	70 MB
clang++	almost_line_00	AC	254 ms	148 MB
clang++	almost_line_01	AC	251 ms	148 MB
clang++	binary_00	AC	222 ms	123 MB
clang++	binary_01	AC	238 ms	123 MB
clang++	binary_02	AC	238 ms	123 MB
clang++	example_00	AC	2 ms	4 MB
clang++	line_00	AC	187 ms	136 MB
clang++	line_01	AC	216 ms	161 MB
clang++	line_02	AC	57 ms	20 MB
clang++	line_03	AC	152 ms	149 MB
clang++	line_04	AC	113 ms	98 MB
clang++	max_line_00	AC	238 ms	173 MB
clang++	max_line_01	AC	251 ms	173 MB
clang++	max_line_02	AC	240 ms	173 MB
clang++	max_random_00	AC	223 ms	124 MB
clang++	max_random_01	AC	222 ms	124 MB
clang++	max_random_02	AC	244 ms	124 MB
clang++	path_graph_root_centroid_00	AC	192 ms	150 MB
clang++	path_graph_root_centroid_01	AC	193 ms	150 MB
clang++	path_graph_root_centroid_02	AC	191 ms	150 MB
clang++	random_00	AC	168 ms	97 MB
clang++	random_01	AC	212 ms	115 MB
clang++	random_02	AC	50 ms	15 MB
clang++	random_03	AC	151 ms	107 MB
clang++	random_04	AC	105 ms	70 MB

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