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

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• Last update: 2024-04-24 02:34:04+09:00
• 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)
• template/template.hpp

Code

// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/lca

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

#include "../../graph/graph-template.hpp"
#include "../../graph/tree/rmq-lowest-common-ancestor.hpp"

#include "../../other/scanner.hpp"
#include "../../other/printer.hpp"


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"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/lca

#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/yosupo-lca-2.test.cpp"

#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/rmq-lowest-common-ancestor.hpp"

#line 1 "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;
  vector< vector< T > > st;
  vector< int > lookup;

  SparseTable() = default;

  explicit SparseTable(const vector< T > &v, const F &f) : f(f) {
    const int n = (int) v.size();
    const int b = 32 - __builtin_clz(n);
    st.assign(b, vector< T >(n));
    for(int i = 0; i < v.size(); 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 < lookup.size(); 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 vector< T > &v, const F &f) {
  return SparseTable< T, F >(v, f);
}
#line 5 "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 = 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);
    vector< int > vs(g.size() * 2 - 1);
    iota(begin(vs), 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]) swap(x, y);
    return x == y ? x : ord[st.fold(in[x], in[y])];
  }

private:
  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 7 "test/verify/yosupo-lca-2.test.cpp"

#line 1 "other/scanner.hpp"
/**
 * @brief Scanner(高速入力)
 */
struct Scanner {
public:

  explicit Scanner(FILE *fp) : fp(fp) {}

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

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

  void read() {}

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

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

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

  template< typename T >
  void read_single(vector< T > &s) {
    for(auto &d : s) read(d);
  }
};
#line 1 "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 size_t line_size = 1 << 16;
  static constexpr 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, enable_if_t< is_integral< T >::value, int > = 0 >
  void write_single(T s) {
    if(st + int_digits >= line + line_size) flush();
    st += to_chars(st, st + int_digits, s).ptr - st;
  }

  void write_single(const 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 vector< T > &s) {
    for(size_t i = 0; i < s.size(); i++) {
      if(i) write_single(' ');
      write_single(s[i]);
    }
  }
};
#line 10 "test/verify/yosupo-lca-2.test.cpp"


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++	binary_00	AC	245 ms	123 MB
g++	binary_01	AC	234 ms	123 MB
g++	binary_02	AC	232 ms	123 MB
g++	example_00	AC	6 ms	4 MB
g++	line_00	AC	206 ms	136 MB
g++	line_01	AC	232 ms	161 MB
g++	line_02	AC	58 ms	20 MB
g++	line_03	AC	166 ms	149 MB
g++	line_04	AC	125 ms	98 MB
g++	max_line_00	AC	257 ms	173 MB
g++	max_line_01	AC	257 ms	173 MB
g++	max_line_02	AC	255 ms	174 MB
g++	max_random_00	AC	236 ms	124 MB
g++	max_random_01	AC	233 ms	124 MB
g++	max_random_02	AC	241 ms	124 MB
g++	path_graph_root_centroid_00	AC	197 ms	150 MB
g++	path_graph_root_centroid_01	AC	198 ms	150 MB
g++	path_graph_root_centroid_02	AC	196 ms	150 MB
g++	random_00	AC	169 ms	97 MB
g++	random_01	AC	201 ms	115 MB
g++	random_02	AC	49 ms	15 MB
g++	random_03	AC	156 ms	107 MB
g++	random_04	AC	110 ms	70 MB
clang++	binary_00	AC	236 ms	123 MB
clang++	binary_01	AC	243 ms	123 MB
clang++	binary_02	AC	244 ms	123 MB
clang++	example_00	AC	6 ms	4 MB
clang++	line_00	AC	202 ms	136 MB
clang++	line_01	AC	229 ms	161 MB
clang++	line_02	AC	61 ms	20 MB
clang++	line_03	AC	168 ms	149 MB
clang++	line_04	AC	125 ms	98 MB
clang++	max_line_00	AC	259 ms	174 MB
clang++	max_line_01	AC	267 ms	173 MB
clang++	max_line_02	AC	255 ms	173 MB
clang++	max_random_00	AC	244 ms	124 MB
clang++	max_random_01	AC	239 ms	124 MB
clang++	max_random_02	AC	235 ms	124 MB
clang++	path_graph_root_centroid_00	AC	204 ms	150 MB
clang++	path_graph_root_centroid_01	AC	207 ms	150 MB
clang++	path_graph_root_centroid_02	AC	204 ms	150 MB
clang++	random_00	AC	191 ms	97 MB
clang++	random_01	AC	218 ms	115 MB
clang++	random_02	AC	55 ms	15 MB
clang++	random_03	AC	192 ms	107 MB
clang++	random_04	AC	112 ms	70 MB

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