test/ds/wavelet_matrix/quantile.test.cpp

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• Last update: 2024-11-09 00:49:07+00:00
• Problem: https://judge.yosupo.jp/problem/range_kth_smallest

Depends on

• bit/popcnt.hpp
• ds/bit_vector.hpp
• ds/wavelet_matrix.hpp
• prelude.hpp

Code

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

#include "ds/wavelet_matrix.hpp"

int n, q, a[200000];

int main() {
  scanf("%d%d", &n, &q);
  rep(i, n) scanf("%d", a+i);

  wavelet_matrix<int, 1000000001> wm(a, a+n);
  while (q--) {
    int l, r, k; scanf("%d%d%d", &l, &r, &k);
    printf("%d\n", wm.rquantile(l, r, k));
  }
}

#line 1 "test/ds/wavelet_matrix/quantile.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/range_kth_smallest

#line 2 "prelude.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using vi = vector<int>;
using vvi = vector<vector<int>>;
using vll = vector<ll>;
using vvll = vector<vector<ll>>;
using vc = vector<char>;
#define rep2(i, m, n) for (auto i = (m); i < (n); i++)
#define rep(i, n) rep2(i, 0, n)
#define repr2(i, m, n) for (auto i = (n); i-- > (m);)
#define repr(i, n) repr2(i, 0, n)
#define all(x) begin(x), end(x)
auto ndvec(int n, auto e) { return vector(n, e); }
auto ndvec(int n, auto ...e) { return vector(n, ndvec(e...)); }
auto comp_key(auto&& f) { return [&](auto&& a, auto&& b) { return f(a) < f(b); }; }
auto& max(const auto& a, const auto& b) { return a < b ? b : a; }
auto& min(const auto& a, const auto& b) { return b < a ? b : a; }
#if __cpp_lib_ranges
namespace R = std::ranges;
namespace V = std::views;
#endif
#line 3 "bit/popcnt.hpp"

#pragma GCC target("popcnt")

template <class T>
int popcnt(T a) {
  if constexpr (sizeof(T) <= sizeof(unsigned)) {
    return __builtin_popcount((unsigned)a);
  } else if constexpr (sizeof(T) <= sizeof(unsigned long long)) {
    return __builtin_popcountll((unsigned long long)a);
  } else if constexpr (sizeof(T) <= sizeof(unsigned long long) * 2) {
    return popcnt((unsigned long long)a) +
           popcnt((unsigned long long)(a >> sizeof(unsigned long long) * 8));
  }
}
#line 4 "ds/bit_vector.hpp"

class bit_vector {
 public:
  bit_vector(int n = 0) : bit(n / 8 + 1), sum(n / 8 + 2) {}
  template <class It>
  bit_vector(It a, It last) : bit_vector(last - a) {
    int n = last - a;
    rep(i, n) bit[i / 64] |= uint64_t(a[i] != 0) << (i % 64);
    rep(i, bit.size()) sum[i + 1] = sum[i] + popcnt(bit[i]);
  }
  int size() const { return bit.size() * 64; }
  bool operator[](int i) const { return bit[i / 64] >> (i % 64) & 1; }
  int rank0(int r) const { return r - rank1(r); }
  int rank0(int l, int r) const { return rank0(r) - rank0(l); }
  int rank1(int r) const {
    return sum[r / 64] + popcnt(bit[r / 64] & ~(~uint64_t(0) << (r % 64)));
  }
  int rank1(int l, int r) const { return rank1(r) - rank1(l); }
  int rank(bool b, int r) const { return b ? rank1(r) : rank0(r); }
  int rank(bool b, int l, int r) const { return b ? rank1(l, r) : rank0(l, r); }
  int select0(int l, int k) const {
    int r = bit.size() * 8;
    while (l + 1 < r) {
      int m = (l + r) / 2;
      (rank0(m) <= k ? l : r) = m;
    }
    return l;
  }
  int select0(int k) const { return select0(0, k); }
  int select1(int l, int k) const {
    int r = bit.size() * 8;
    while (l + 1 < r) {
      int m = (l + r) / 2;
      (rank1(m) <= k ? l : r) = m;
    }
    return l;
  }
  int select1(int k) const { return select1(0, k); }
  int select(bool v, int k) const { return v ? select1(k) : select0(k); }
  int select(bool v, int l, int k) const {
    return v ? select1(l, k) : select0(l, k);
  }

 private:
  vector<uint64_t> bit;
  vector<int> sum;
};
#line 3 "ds/wavelet_matrix.hpp"

template <class T, T U>
class wavelet_matrix {
 public:
  template <class It>
  wavelet_matrix(It first, It last) : wavelet_matrix(vector<T>(first, last)) { }
  wavelet_matrix(vector<T> a) : size_(a.size()) {
    vector<bool> bit(size_);
    vector<T> nxt(size_);
    repr(t, B) {
      int l = 0, r = size_;
      rep(i, size_) {
        bit[i] = a[i] >> t & 1;
        (bit[i] ? nxt[--r] : nxt[l++]) = a[i];
      }
      mat[t] = bit_vector(all(bit));
      zeros[t] = l;
      reverse(nxt.begin() + r, nxt.end());
      swap(a, nxt);
    }
  }

  int size() const { return size_; }
  T operator[](int i) const { return access(i); }
  T access(int i) const {
    T res = 0;
    repr(t, B) {
      if (mat[t][i]) {
        res |= T(1) << t;
        i = zeros[t] + mat[t].rank1(i);
      } else {
        i = mat[t].rank0(i);
      }
    }
    return res;
  }
  // #occurences of x on [l, r)
  int rank(T x, int l, int r) const {
    tie(l, r) = range(x, l, r);
    return r - l;
  }
  // -1 if #occurences <= k
  int select(T x, int l, int k) const {
    int r;
    tie(l, r) = range(x, l, size());
    l += k;
    if (l >= r) return -1;
    rep(t, B) {
      if (x >> t & 1) l = mat[t].select1(l - zeros[t]);
      else l = mat[t].select0(l);
    }
    return l;
  }
  // k-th greatest on [l, r)
  T quantile(int l, int r, int k) const {
    T res = 0;
    repr(t, B) {
      int r1 = mat[t].rank1(l, r);
      if (r1 > k) {
        res |= T(1) << t;
        l = zeros[t] + mat[t].rank1(l);
        r = l + r1;
      } else {
        k -= r1;
        int r0 = r - l - r1;
        l = mat[t].rank0(l);
        r = l + r0;
      }
    }
    return res;
  }
  // k-th smallest on [l, r)
  T rquantile(int l, int r, int k) const {
    return quantile(l, r, r - l - k - 1);
  }
  int rangefreq(int l, int r, T ub) const {
    int res = 0;
    repr(t, B) {
      if (ub >> t & 1) {
        int r1l = mat[t].rank1(l), r1r = mat[t].rank1(r);
        int r0lr = (r - l) - (r1r - r1l);
        res += r0lr;
        l = zeros[t] + r1l, r = zeros[t] + r1r;
      } else {
        l = mat[t].rank0(l), r = mat[t].rank0(r);
      }
    }
    return res;
  }
  // int rangefreq(int l, int r, T lb, T ub) const {
  //   return rangefreq(B - 1, l, r, lb, ub - 1);
  // }
  int rangefreq(int l, int r, T lb, T ub) const {
    return rangefreq(l, r, ub) - rangefreq(l, r, lb);
  }
  // -1 if no such elt
  T succ(int l, int r, T x) const {
    int k = rangefreq(l, r, x);
    return k == r - l ? -1 : rquantile(l, r, k);
  }
  // -1 if no such elt
  T pred(int l, int r, T x) const {
    int k = rangefreq(l, r, x);
    return k ? rquantile(l, r, k - 1) : -1;
  }

 private:
  static constexpr int calc_b(T u) {
    int res = 0;
    for (T x = u - 1; x; x /= 2) res++;
    return res;
  }
  static constexpr int B = calc_b(U);
  static_assert(B <= sizeof(T) * CHAR_BIT);
  int size_;
  array<int, B> zeros;
  array<bit_vector, B> mat;
  pair<int, int> range(T x, int l, int r) const {
    repr(t, B) {
      if (x >> t & 1) {
        l = zeros[t] + mat[t].rank1(l);
        r = zeros[t] + mat[t].rank1(r);
      } else {
        l = mat[t].rank0(l);
        r = mat[t].rank0(r);
      }
    }
    return make_pair(l, r);
  }
  // // inclusive
  // int rangefreq(int t, int l, int r, T x, T lb, T ub) const {
  //   if (t == -1 || ()) return r - l;
  //   if (lb >> t & 1) {
  //     l = zeros[t] + mat[t].rank1(l);
  //     r = zeros[t] + mat[t].rank1(r);
  //     return rangefreq(t - 1, l, r, lb, ub);
  //   } else if (~ub >> t & 1) {
  //     l = mat[t].rank0(l);
  //     r = mat[t].rank0(r);
  //     return rangefreq(t - 1, l, r, lb, ub);
  //   } else {
  //     l = mat[t].rank0(l);
  //     r = zeros[t] + mat[t].rank1(r);
  //     return rangefreq(t - 1, l, zeros[t], lb, ~0) +
  //            rangefreq(t - 1, zeros[t], r, 0, ub);
  //   }
  // }
};
#line 4 "test/ds/wavelet_matrix/quantile.test.cpp"

int n, q, a[200000];

int main() {
  scanf("%d%d", &n, &q);
  rep(i, n) scanf("%d", a+i);

  wavelet_matrix<int, 1000000001> wm(a, a+n);
  while (q--) {
    int l, r, k; scanf("%d%d%d", &l, &r, &k);
    printf("%d\n", wm.rquantile(l, r, k));
  }
}

Test cases

Env	Name	Status	Elapsed	Memory
g++-12	all_zero_00	AC	31 ms	9 MB
g++-12	dense_large_a_00	AC	190 ms	8 MB
g++-12	dense_small_a_00	AC	180 ms	8 MB
g++-12	example_00	AC	13 ms	8 MB
g++-12	max_random_00	AC	643 ms	21 MB
g++-12	max_random_01	AC	645 ms	21 MB
g++-12	max_random_02	AC	647 ms	21 MB
g++-12	max_random_03	AC	638 ms	21 MB
g++-12	max_random_04	AC	637 ms	21 MB
g++-12	random_00	AC	433 ms	17 MB
g++-12	random_01	AC	479 ms	18 MB
g++-12	random_02	AC	251 ms	12 MB
g++-12	random_03	AC	344 ms	19 MB
g++-12	random_04	AC	148 ms	9 MB
g++-12	small_00	AC	15 ms	9 MB
g++-12	small_01	AC	13 ms	8 MB
g++-12	small_02	AC	13 ms	8 MB
g++-12	small_03	AC	13 ms	8 MB
g++-12	small_04	AC	14 ms	8 MB
g++-12	small_05	AC	15 ms	9 MB
g++-12	small_06	AC	15 ms	9 MB
g++-12	small_07	AC	14 ms	8 MB
g++-12	small_08	AC	14 ms	9 MB
g++-12	small_09	AC	13 ms	8 MB

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