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

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• 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 Matrix (ウェーブレット行列) (structure/wavelet/wavelet-matrix.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-matrix.hpp"

using namespace std;

int main() {
  int N, Q;
  cin >> N >> Q;
  vector<int> A(N);
  for (int& a : A) cin >> a;
  CompressedWaveletMatrix<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.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-matrix.hpp"

#include <algorithm>
#include <cassert>
#include <cstddef>
#include <iterator>
#include <set>
#include <tuple>
#include <utility>
#line 11 "structure/wavelet/wavelet-matrix.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 13 "structure/wavelet/wavelet-matrix.hpp"

/*
 * @brief Wavelet Matrix(ウェーブレット行列)
 *
 */
template <typename T, int MAXLOG>
struct WaveletMatrix {
  std::size_t length;
  SuccinctIndexableDictionary matrix[MAXLOG];
  int mid[MAXLOG];

  WaveletMatrix() = default;

  WaveletMatrix(std::vector<T> v) : length(v.size()) {
    std::vector<T> l(length), r(length);
    for (int level = MAXLOG - 1; level >= 0; level--) {
      matrix[level] = SuccinctIndexableDictionary(length + 1);
      int left = 0, right = 0;
      for (int i = 0; i < length; i++) {
        if (((v[i] >> level) & 1)) {
          matrix[level].set(i);
          r[right++] = v[i];
        } else {
          l[left++] = v[i];
        }
      }
      mid[level] = left;
      matrix[level].build();
      v.swap(l);
      for (int i = 0; i < right; i++) {
        v[left + i] = r[i];
      }
    }
  }

  std::pair<int, int> succ(bool f, int l, int r, int level) {
    return {matrix[level].rank(f, l) + mid[level] * f,
            matrix[level].rank(f, r) + mid[level] * f};
  }

  // v[k]
  T access(int k) {
    T ret = 0;
    for (int level = MAXLOG - 1; level >= 0; level--) {
      bool f = matrix[level][k];
      if (f) ret |= T(1) << level;
      k = matrix[level].rank(f, k) + mid[level] * f;
    }
    return ret;
  }

  T operator[](const int& k) { return access(k); }

  // count i s.t. (0 <= i < r) && v[i] == x
  int rank(const T& x, int r) {
    int l = 0;
    for (int level = MAXLOG - 1; level >= 0; level--) {
      std::tie(l, r) = succ((x >> level) & 1, l, r, level);
    }
    return r - l;
  }

  // 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);
    T ret = 0;
    for (int level = MAXLOG - 1; level >= 0; level--) {
      int cnt = matrix[level].rank(false, r) - matrix[level].rank(false, l);
      bool f = cnt <= k;
      if (f) {
        ret |= T(1) << level;
        k -= cnt;
      }
      std::tie(l, r) = succ(f, l, r, level);
    }
    return ret;
  }

  // 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);
  }

  // count i s.t. (l <= i < r) && (v[i] < upper)
  int range_freq(int l, int r, T upper) {
    int ret = 0;
    for (int level = MAXLOG - 1; level >= 0; level--) {
      bool f = ((upper >> level) & 1);
      if (f) ret += matrix[level].rank(false, r) - matrix[level].rank(false, l);
      std::tie(l, r) = succ(f, l, r, level);
    }
    return ret;
  }

  // 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 CompressedWaveletMatrix {
  WaveletMatrix<int, MAXLOG> mat;
  std::vector<T> ys;

  CompressedWaveletMatrix(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 = WaveletMatrix<int, MAXLOG>(t);
  }

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

  T access(int k) { return ys[mat.access(k)]; }

  T operator[](const int& k) { return access(k); }

  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.test.cpp"

using namespace std;

int main() {
  int N, Q;
  cin >> N >> Q;
  vector<int> A(N);
  for (int& a : A) cin >> a;
  CompressedWaveletMatrix<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	295 ms	4 MB
g++	dense_small_a_00	AC	332 ms	4 MB
g++	example_00	AC	2 ms	4 MB
g++	max_random_00	AC	484 ms	9 MB
g++	max_random_01	AC	623 ms	9 MB
g++	max_random_02	AC	490 ms	9 MB
g++	max_random_03	AC	481 ms	9 MB
g++	max_random_04	AC	481 ms	9 MB
g++	random_00	AC	356 ms	7 MB
g++	random_01	AC	365 ms	8 MB
g++	random_02	AC	263 ms	5 MB
g++	random_03	AC	124 ms	8 MB
g++	random_04	AC	175 ms	4 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	2 ms	4 MB
g++	small_06	AC	3 ms	4 MB
g++	small_07	AC	2 ms	4 MB
g++	small_08	AC	2 ms	4 MB
g++	small_09	AC	3 ms	4 MB
clang++	all_zero_00	AC	5 ms	4 MB
clang++	dense_large_a_00	AC	293 ms	4 MB
clang++	dense_small_a_00	AC	302 ms	4 MB
clang++	example_00	AC	2 ms	4 MB
clang++	max_random_00	AC	479 ms	9 MB
clang++	max_random_01	AC	480 ms	9 MB
clang++	max_random_02	AC	496 ms	9 MB
clang++	max_random_03	AC	521 ms	9 MB
clang++	max_random_04	AC	504 ms	9 MB
clang++	random_00	AC	347 ms	7 MB
clang++	random_01	AC	348 ms	8 MB
clang++	random_02	AC	300 ms	5 MB
clang++	random_03	AC	117 ms	8 MB
clang++	random_04	AC	185 ms	4 MB
clang++	small_00	AC	3 ms	4 MB
clang++	small_01	AC	2 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	2 ms	4 MB
clang++	small_09	AC	3 ms	4 MB

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