test/verify/yosupo-range-kth-smallest-2.test.cpp

• View this file on GitHub
• Last update: 2026-08-10 15:44:16+00:00
• Problem: https://judge.yosupo.jp/problem/range_kth_smallest

Depends on

• Succinct Indexable Dictionary (完備辞書) (structure/wavelet/succinct-indexable-dictionary.hpp)
• Wavelet Tree (ウェーブレット木) (structure/wavelet/wavelet-tree.hpp)

Code

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

#include <iostream>
#include <vector>

#include "../../structure/wavelet/wavelet-tree.hpp"

using namespace std;

int main() {
  int N, Q;
  cin >> N >> Q;
  vector<int> A(N);
  for (int& a : A) cin >> a;
  CompressedWaveletTree<int, 18> mat(A);
  for (int i = 0; i < Q; i++) {
    int a, b, c;
    cin >> a >> b >> c;
    cout << mat.kth_smallest(a, b, c) << "\n";
  }
}

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

#include <iostream>
#include <vector>

#line 2 "structure/wavelet/wavelet-tree.hpp"

#include <algorithm>
#include <cassert>
#include <cstddef>
#include <iterator>
#include <set>
#line 9 "structure/wavelet/wavelet-tree.hpp"

#line 2 "structure/wavelet/succinct-indexable-dictionary.hpp"

#line 5 "structure/wavelet/succinct-indexable-dictionary.hpp"

/**
 * @brief Succinct Indexable Dictionary(完備辞書)
 */
struct SuccinctIndexableDictionary {
  std::size_t length;
  std::size_t blocks;
  std::vector<unsigned> bit, sum;

  SuccinctIndexableDictionary() = default;

  SuccinctIndexableDictionary(std::size_t length)
      : length(length), blocks((length + 31) >> 5) {
    bit.assign(blocks, 0U);
    sum.assign(blocks, 0U);
  }

  void set(int k) { bit[k >> 5] |= 1U << (k & 31); }

  void build() {
    sum[0] = 0U;
    for (int i = 1; i < blocks; i++) {
      sum[i] = sum[i - 1] + __builtin_popcount(bit[i - 1]);
    }
  }

  bool operator[](int k) { return (bool((bit[k >> 5] >> (k & 31)) & 1)); }

  int rank(int k) {
    return (sum[k >> 5] +
            __builtin_popcount(bit[k >> 5] & ((1U << (k & 31)) - 1)));
  }

  int rank(bool val, int k) { return (val ? rank(k) : k - rank(k)); }
};
#line 11 "structure/wavelet/wavelet-tree.hpp"

/*
 * @brief Wavelet Tree(ウェーブレット木)
 *
 */
template <typename T, int MAXLOG>
struct WaveletTree {
  struct Node {
    SuccinctIndexableDictionary sid;
    Node* ch[2];

    Node() = default;

    Node(std::size_t length) : sid(length + 1), ch{nullptr} {}
  };

  Node* root;

  Node* build(std::vector<T>& v, std::vector<T>& rbuff, int bit, int l, int r) {
    if (l >= r || bit == -1) return nullptr;
    Node* node = new Node(r - l);
    int left = 0, right = 0;
    for (int k = l; k < r; k++) {
      if (((v[k] >> bit) & 1)) {
        rbuff[right++] = v[k];
        node->sid.set(k - l);
      } else {
        v[l + left++] = v[k];
      }
    }
    for (int k = 0; k < right; k++) {
      v[l + left + k] = rbuff[k];
    }
    node->sid.build();
    node->ch[0] = build(v, rbuff, bit - 1, l, l + left);
    node->ch[1] = build(v, rbuff, bit - 1, l + left, r);
    return node;
  }

  WaveletTree() = default;

  WaveletTree(std::vector<T> v) {
    std::vector<T> rbuff(v.size());
    root = build(v, rbuff, MAXLOG - 1, 0, v.size());
  }

  int rank(Node* t, int l, int r, const T& x, int level) {
    if (l >= r || t == nullptr) return 0;
    if (level == -1) return r - l;
    bool f = (x >> level) & 1;
    l = t->sid.rank(f, l), r = t->sid.rank(f, r);
    return rank(t->ch[f], l, r, x, level - 1);
  }

  int rank(const T& x, int r) { return rank(root, 0, r, x, MAXLOG - 1); }

  T kth_smallest(Node* t, int l, int r, int k, int level) {
    if (l >= r || t == nullptr) return 0;
    int cnt = t->sid.rank(false, r) - t->sid.rank(false, l);
    bool f = cnt <= k;
    l = t->sid.rank(f, l), r = t->sid.rank(f, r);
    if (f)
      return kth_smallest(t->ch[f], l, r, k - cnt, level - 1) |
             ((T(1) << level));
    return kth_smallest(t->ch[f], l, r, k, level - 1);
  }

  // k-th(0-indexed) smallest number in v[l,r)
  T kth_smallest(int l, int r, int k) {
    assert(0 <= k && k < r - l);
    return kth_smallest(root, l, r, k, MAXLOG - 1);
  }

  // k-th(0-indexed) largest number in v[l,r)
  T kth_largest(int l, int r, int k) {
    return kth_smallest(l, r, r - l - k - 1);
  }

  int range_freq(Node* t, int l, int r, T upper, int level) {
    if (t == nullptr || l >= r) return 0;
    bool f = ((upper >> level) & 1);
    int ret = 0;
    if (f) ret += t->sid.rank(false, r) - t->sid.rank(false, l);
    l = t->sid.rank(f, l), r = t->sid.rank(f, r);
    return range_freq(t->ch[f], l, r, upper, level - 1) + ret;
  }

  // count i s.t. (l <= i < r) && (v[i] < upper)
  int range_freq(int l, int r, T upper) {
    return range_freq(root, l, r, upper, MAXLOG - 1);
  }

  // count i s.t. (l <= i < r) && (lower <= v[i] < upper)
  int range_freq(int l, int r, T lower, T upper) {
    return range_freq(l, r, upper) - range_freq(l, r, lower);
  }

  // std::max v[i] s.t. (l <= i < r) && (v[i] < upper)
  T prev_value(int l, int r, T upper) {
    int cnt = range_freq(l, r, upper);
    return cnt == 0 ? T(-1) : kth_smallest(l, r, cnt - 1);
  }

  // std::min v[i] s.t. (l <= i < r) && (lower <= v[i])
  T next_value(int l, int r, T lower) {
    int cnt = range_freq(l, r, lower);
    return cnt == r - l ? T(-1) : kth_smallest(l, r, cnt);
  }
};

template <typename T, int MAXLOG>
struct CompressedWaveletTree {
  WaveletTree<int, MAXLOG> mat;
  std::vector<T> ys;

  CompressedWaveletTree(const std::vector<T>& v) : ys(v) {
    std::sort(std::begin(ys), std::end(ys));
    ys.erase(std::unique(std::begin(ys), std::end(ys)), std::end(ys));
    std::vector<int> t(v.size());
    for (int i = 0; i < v.size(); i++) t[i] = get(v[i]);
    mat = WaveletTree<int, MAXLOG>(t);
  }

  inline int get(const T& x) {
    return std::lower_bound(std::begin(ys), std::end(ys), x) - std::begin(ys);
  }

  int rank(const T& x, int r) {
    auto pos = get(x);
    if (pos == ys.size() || ys[pos] != x) return 0;
    return mat.rank(pos, r);
  }

  T kth_smallest(int l, int r, int k) { return ys[mat.kth_smallest(l, r, k)]; }

  T kth_largest(int l, int r, int k) { return ys[mat.kth_largest(l, r, k)]; }

  int range_freq(int l, int r, T upper) {
    return mat.range_freq(l, r, get(upper));
  }

  int range_freq(int l, int r, T lower, T upper) {
    return mat.range_freq(l, r, get(lower), get(upper));
  }

  T prev_value(int l, int r, T upper) {
    auto ret = mat.prev_value(l, r, get(upper));
    return ret == -1 ? T(-1) : ys[ret];
  }

  T next_value(int l, int r, T lower) {
    auto ret = mat.next_value(l, r, get(lower));
    return ret == -1 ? T(-1) : ys[ret];
  }
};
#line 9 "test/verify/yosupo-range-kth-smallest-2.test.cpp"

using namespace std;

int main() {
  int N, Q;
  cin >> N >> Q;
  vector<int> A(N);
  for (int& a : A) cin >> a;
  CompressedWaveletTree<int, 18> mat(A);
  for (int i = 0; i < Q; i++) {
    int a, b, c;
    cin >> a >> b >> c;
    cout << mat.kth_smallest(a, b, c) << "\n";
  }
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	all_zero_00	AC	5 ms	4 MB
g++	dense_large_a_00	AC	260 ms	4 MB
g++	dense_small_a_00	AC	259 ms	4 MB
g++	example_00	AC	2 ms	4 MB
g++	max_random_00	AC	641 ms	39 MB
g++	max_random_01	AC	585 ms	39 MB
g++	max_random_02	AC	569 ms	39 MB
g++	max_random_03	AC	579 ms	39 MB
g++	max_random_04	AC	571 ms	39 MB
g++	random_00	AC	400 ms	26 MB
g++	random_01	AC	468 ms	30 MB
g++	random_02	AC	309 ms	13 MB
g++	random_03	AC	178 ms	33 MB
g++	random_04	AC	177 ms	6 MB
g++	small_00	AC	3 ms	4 MB
g++	small_01	AC	2 ms	4 MB
g++	small_02	AC	2 ms	4 MB
g++	small_03	AC	2 ms	4 MB
g++	small_04	AC	3 ms	4 MB
g++	small_05	AC	3 ms	4 MB
g++	small_06	AC	2 ms	4 MB
g++	small_07	AC	2 ms	4 MB
g++	small_08	AC	3 ms	4 MB
g++	small_09	AC	3 ms	4 MB
clang++	all_zero_00	AC	4 ms	4 MB
clang++	dense_large_a_00	AC	252 ms	4 MB
clang++	dense_small_a_00	AC	317 ms	4 MB
clang++	example_00	AC	2 ms	4 MB
clang++	max_random_00	AC	586 ms	39 MB
clang++	max_random_01	AC	551 ms	39 MB
clang++	max_random_02	AC	544 ms	39 MB
clang++	max_random_03	AC	606 ms	39 MB
clang++	max_random_04	AC	610 ms	39 MB
clang++	random_00	AC	379 ms	26 MB
clang++	random_01	AC	445 ms	30 MB
clang++	random_02	AC	271 ms	13 MB
clang++	random_03	AC	163 ms	33 MB
clang++	random_04	AC	169 ms	6 MB
clang++	small_00	AC	3 ms	4 MB
clang++	small_01	AC	3 ms	4 MB
clang++	small_02	AC	2 ms	4 MB
clang++	small_03	AC	2 ms	4 MB
clang++	small_04	AC	3 ms	4 MB
clang++	small_05	AC	2 ms	4 MB
clang++	small_06	AC	2 ms	4 MB
clang++	small_07	AC	2 ms	4 MB
clang++	small_08	AC	3 ms	4 MB
clang++	small_09	AC	3 ms	4 MB

Back to top page