test/verify/yosupo-lca-4.test.cpp

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• Last update: 2024-04-27 01:27:28+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)
• Offline LCA(オフライン最小共通祖先) (graph/tree/offline-lca.hpp)
• Printer(高速出力) (other/printer.hpp)
• Scanner(高速入力) (other/scanner.hpp)
• Union Find (structure/union-find/union-find.hpp)
• template/template.hpp

Code

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

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

#include "../../graph/tree/offline-lca.hpp"

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

int main() {
  Scanner in(stdin);
  Printer out(stdout);
  int N, Q;
  in.read(N, Q);
  Graph< int > g(N);
  for(int i = 1; i < N; i++) {
    int x;
    in.read(x);
    g.add_directed_edge(x, i);
  }
  vector< pair< int, int > > qs(Q);
  for(auto&[l, r]: qs) in.read(l, r);
  auto ans = offline_lca(g, qs);
  for(auto &p: ans) out.writeln(p);
}

#line 1 "test/verify/yosupo-lca-4.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-4.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 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 3 "graph/tree/offline-lca.hpp"

/**
 * @brief Offline LCA(オフライン最小共通祖先)
 **/
template <typename T>
vector<int> offline_lca(const Graph<T> &g, vector<pair<int, int> > &qs,
                        int root = 0) {
  int n = (int)g.size();
  UnionFind uf(n);
  vector<int> st(n), mark(n), ptr(n), ans(qs.size(), -1);
  int top = 0;
  st[top] = root;
  for (auto &[l, r] : qs) mark[l]++, mark[r]++;
  vector<vector<pair<int, int> > > q(n);
  for (int i = 0; i < n; i++) {
    q[i].reserve(mark[i]);
    mark[i] = -1;
    ptr[i] = (int)g[i].size();
  }
  for (int i = 0; i < qs.size(); i++) {
    q[qs[i].first].emplace_back(qs[i].second, i);
    q[qs[i].second].emplace_back(qs[i].first, i);
  }
  auto run = [&](int u) -> bool {
    while (ptr[u]) {
      int v = g[u][--ptr[u]];
      if (mark[v] == -1) {
        st[++top] = v;
        return true;
      }
    }
    return false;
  };
  while (~top) {
    int u = st[top];
    if (mark[u] == -1) {
      mark[u] = u;
    } else {
      uf.unite(u, g[u][ptr[u]]);
      mark[uf.find(u)] = u;
    }
    if (not run(u)) {
      for (auto &[v, i] : q[u]) {
        if (~mark[v] and ans[i] == -1) {
          ans[i] = mark[uf.find(v)];
        }
      }
      --top;
    }
  }
  return ans;
}
#line 6 "test/verify/yosupo-lca-4.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 9 "test/verify/yosupo-lca-4.test.cpp"

int main() {
  Scanner in(stdin);
  Printer out(stdout);
  int N, Q;
  in.read(N, Q);
  Graph< int > g(N);
  for(int i = 1; i < N; i++) {
    int x;
    in.read(x);
    g.add_directed_edge(x, i);
  }
  vector< pair< int, int > > qs(Q);
  for(auto&[l, r]: qs) in.read(l, r);
  auto ans = offline_lca(g, qs);
  for(auto &p: ans) out.writeln(p);
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	binary_00	AC	254 ms	67 MB
g++	binary_01	AC	260 ms	67 MB
g++	binary_02	AC	239 ms	67 MB
g++	example_00	AC	7 ms	4 MB
g++	line_00	AC	87 ms	57 MB
g++	line_01	AC	100 ms	65 MB
g++	line_02	AC	39 ms	20 MB
g++	line_03	AC	47 ms	46 MB
g++	line_04	AC	47 ms	35 MB
g++	max_line_00	AC	114 ms	71 MB
g++	max_line_01	AC	112 ms	71 MB
g++	max_line_02	AC	110 ms	71 MB
g++	max_random_00	AC	249 ms	68 MB
g++	max_random_01	AC	244 ms	68 MB
g++	max_random_02	AC	283 ms	68 MB
g++	path_graph_root_centroid_00	AC	101 ms	71 MB
g++	path_graph_root_centroid_01	AC	103 ms	71 MB
g++	path_graph_root_centroid_02	AC	112 ms	71 MB
g++	random_00	AC	202 ms	54 MB
g++	random_01	AC	255 ms	62 MB
g++	random_02	AC	46 ms	19 MB
g++	random_03	AC	108 ms	43 MB
g++	random_04	AC	79 ms	34 MB
clang++	binary_00	AC	259 ms	67 MB
clang++	binary_01	AC	267 ms	67 MB
clang++	binary_02	AC	279 ms	67 MB
clang++	example_00	AC	7 ms	4 MB
clang++	line_00	AC	97 ms	57 MB
clang++	line_01	AC	108 ms	65 MB
clang++	line_02	AC	43 ms	20 MB
clang++	line_03	AC	53 ms	46 MB
clang++	line_04	AC	50 ms	35 MB
clang++	max_line_00	AC	117 ms	71 MB
clang++	max_line_01	AC	118 ms	71 MB
clang++	max_line_02	AC	116 ms	71 MB
clang++	max_random_00	AC	253 ms	68 MB
clang++	max_random_01	AC	277 ms	68 MB
clang++	max_random_02	AC	264 ms	68 MB
clang++	path_graph_root_centroid_00	AC	111 ms	71 MB
clang++	path_graph_root_centroid_01	AC	109 ms	71 MB
clang++	path_graph_root_centroid_02	AC	108 ms	71 MB
clang++	random_00	AC	201 ms	54 MB
clang++	random_01	AC	232 ms	62 MB
clang++	random_02	AC	46 ms	19 MB
clang++	random_03	AC	143 ms	43 MB
clang++	random_04	AC	86 ms	34 MB

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