verify/data-structure/LC_range_kth_smallest.test.cpp

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• Last update: 2026-06-28 16:21:49+09:00
• Problem: https://judge.yosupo.jp/problem/range_kth_smallest

Depends on

• data-structure/bit-vector.hpp
• Wavelet Matrix (data-structure/wavelet-matrix.hpp)
• template/debug.hpp
• template/inout.hpp
• template/macro.hpp
• template/template.hpp
• template/util.hpp

Code

#define PROBLEM "https://judge.yosupo.jp/problem/range_kth_smallest"

#include "template/template.hpp"
#include "data-structure/wavelet-matrix.hpp"

int main() {
  int n, q;
  in(n, q);
  vector<int> a(n);
  in(a);
  WaveletMatrix<int, 30> wm(a);
  while (q--) {
    int l, r, k;
    in(l, r, k);
    out(wm.kth_smallest(l, r, k));
  }
}

#line 1 "verify/data-structure/LC_range_kth_smallest.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/range_kth_smallest"

#line 2 "template/template.hpp"
#include <bits/stdc++.h>
using namespace std;

#line 2 "template/macro.hpp"
#define rep(i, a, b) for (int i = (a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (int)(b) - 1; i >= (a); i--)
#define ALL(v) (v).begin(), (v).end()
#define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end())
#define SZ(v) (int)v.size()
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin())
#define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin())
#define YN(b) cout << ((b) ? "YES" : "NO") << "\n";
#define Yn(b) cout << ((b) ? "Yes" : "No") << "\n";
#define yn(b) cout << ((b) ? "yes" : "no") << "\n";
#line 6 "template/template.hpp"

#line 2 "template/util.hpp"
using uint = unsigned int;
using ll = long long int;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;

template <class T, class S = T>
S SUM(const vector<T>& a) {
  return accumulate(ALL(a), S(0));
}
template <class T>
inline bool chmin(T& a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T>
inline bool chmax(T& a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}

template <class T>
int popcnt(T x) {
  return __builtin_popcountll(x);
}
template <class T>
int topbit(T x) {
  return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
template <class T>
int lowbit(T x) {
  return (x == 0 ? -1 : __builtin_ctzll(x));
}
#line 8 "template/template.hpp"

#line 2 "template/inout.hpp"
struct Fast {
  Fast() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(15);
  }
} fast;

ostream& operator<<(ostream& os, __uint128_t x) {
  char buf[40];
  size_t k = 0;
  while (x > 0) buf[k++] = (char)(x % 10 + '0'), x /= 10;
  if (k == 0) buf[k++] = '0';
  while (k) os << buf[--k];
  return os;
}
ostream& operator<<(ostream& os, __int128_t x) {
  return x < 0 ? (os << '-' << (__uint128_t)(-x)) : (os << (__uint128_t)x);
}
template <class T1, class T2>
istream& operator>>(istream& is, pair<T1, T2>& p) {
  return is >> p.first >> p.second;
}
template <class T1, class T2>
ostream& operator<<(ostream& os, const pair<T1, T2>& p) {
  return os << p.first << " " << p.second;
}
template <class T>
istream& operator>>(istream& is, vector<T>& a) {
  for (auto& v : a) is >> v;
  return is;
}
template <class T>
ostream& operator<<(ostream& os, const vector<T>& a) {
  for (auto it = a.begin(); it != a.end();) {
    os << *it;
    if (++it != a.end()) os << " ";
  }
  return os;
}
template <class T>
ostream& operator<<(ostream& os, const set<T>& st) {
  os << "{";
  for (auto it = st.begin(); it != st.end();) {
    os << *it;
    if (++it != st.end()) os << ",";
  }
  os << "}";
  return os;
}
template <class T1, class T2>
ostream& operator<<(ostream& os, const map<T1, T2>& mp) {
  os << "{";
  for (auto it = mp.begin(); it != mp.end();) {
    os << it->first << ":" << it->second;
    if (++it != mp.end()) os << ",";
  }
  os << "}";
  return os;
}

void in() {}
template <typename T, class... U>
void in(T& t, U&... u) {
  cin >> t;
  in(u...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T& t, const U&... u) {
  cout << t;
  if (sizeof...(u)) cout << sep;
  out(u...);
}

namespace IO {
namespace Graph {
vector<vector<int>> unweighted(int n, int m, bool directed = false, int offset = 1) {
  vector<vector<int>> g(n);
  for (int i = 0; i < m; i++) {
    int u, v;
    cin >> u >> v;
    u -= offset, v -= offset;
    g[u].push_back(v);
    if (!directed) g[v].push_back(u);
  }
  return g;
}
template <class T>
vector<vector<pair<int, T>>> weighted(int n, int m, bool directed = false, int offset = 1) {
  vector<vector<pair<int, T>>> g(n);
  for (int i = 0; i < m; i++) {
    int u, v;
    T w;
    cin >> u >> v >> w;
    u -= offset, v -= offset;
    g[u].push_back({v, w});
    if (!directed) g[v].push_back({u, w});
  }
  return g;
}
}  // namespace Graph
namespace Tree {
vector<vector<int>> unweighted(int n, bool directed = false, int offset = 1) {
  return Graph::unweighted(n, n - 1, directed, offset);
}
template <class T>
vector<vector<pair<int, T>>> weighted(int n, bool directed = false, int offset = 1) {
  return Graph::weighted<T>(n, n - 1, directed, offset);
}
vector<vector<int>> rooted(int n, bool to_root = true, bool to_leaf = true, int offset = 1) {
  vector<vector<int>> g(n);
  for (int i = 1; i < n; i++) {
    int p;
    cin >> p;
    p -= offset;
    if (to_root) g[i].push_back(p);
    if (to_leaf) g[p].push_back(i);
  }
  return g;
}
}  // namespace Tree
}  // namespace IO
#line 10 "template/template.hpp"

#line 2 "template/debug.hpp"
#ifdef LOCAL
#define debug 1
#define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__)
#else
#define debug 0
#define show(...) true
#endif
template <class T>
void _show(int i, T name) {
  cerr << '\n';
}
template <class T1, class T2, class... T3>
void _show(int i, const T1& a, const T2& b, const T3&... c) {
  for (; a[i] != ',' && a[i] != '\0'; i++) cerr << a[i];
  cerr << ":" << b << " ";
  _show(i + 1, a, c...);
}
#line 2 "data-structure/wavelet-matrix.hpp"

#line 2 "data-structure/bit-vector.hpp"

struct BitVector {
  using i32 = int32_t;
  using u32 = uint32_t;
  using u64 = uint64_t;

  static constexpr u32 W = 64;
  inline u32 get(u32 i) const { return u32(block[i / W] >> (i % W)) & 1u; }
  inline void set(u32 i) { block[i / W] |= 1ull << (i % W); }

  vector<u64> block;
  vector<i32> count;
  u32 n, zeros;
  BitVector() {}
  BitVector(int _n) : n(_n) {
    block.resize(n / W + 1, 0);
    count.resize(block.size(), 0);
  }
  void build() {
    for (u32 i = 1; i < block.size(); i++)
      count[i] = count[i - 1] + __builtin_popcountll(block[i - 1]);
    zeros = rank0(n);
  }
  inline u32 rank0(u32 i) const { return i - rank1(i); }
  inline u32 rank1(u32 i) const { return count[i / W] + __builtin_popcountll(block[i / W] & ((1ull << i % W) - 1)); }
};
#line 4 "data-structure/wavelet-matrix.hpp"

template <class T, int B = 30>
struct WaveletMatrix {
  using u32 = uint32_t;
  using i64 = int64_t;
  using u64 = uint64_t;

  int n;
  vector<T> a;
  vector<BitVector> bv;

  WaveletMatrix(u32 _n) : n(max<u32>(_n, 1)), a(n) {}
  WaveletMatrix(const vector<T>& _a) : n(_a.size()), a(_a) { build(); }

  void set(u32 i, const T& x) {
    assert(x >= 0);
    a[i] = x;
  }

  void build() {
    bv.assign(B, n);
    vector<T> cur = a, nxt(n);
    for (int h = B - 1; h >= 0; --h) {
      for (int i = 0; i < n; ++i)
        if ((cur[i] >> h) & 1) bv[h].set(i);
      bv[h].build();
      array<decltype(begin(nxt)), 2> it{begin(nxt), begin(nxt) + bv[h].zeros};
      for (int i = 0; i < n; ++i) *it[bv[h].get(i)]++ = cur[i];
      swap(cur, nxt);
    }
  }

  inline pair<u32, u32> succ0(int l, int r, int h) const {
    return make_pair(bv[h].rank0(l), bv[h].rank0(r));
  }
  inline pair<u32, u32> succ1(int l, int r, int h) const {
    u32 l0 = bv[h].rank0(l);
    u32 r0 = bv[h].rank0(r);
    u32 zeros = bv[h].zeros;
    return make_pair(l + zeros - l0, r + zeros - r0);
  }

  // return a[k]
  T access(u32 k) const {
    T ret = 0;
    for (int h = B - 1; h >= 0; --h) {
      u32 f = bv[h].get(k);
      ret |= f ? T(1) << h : 0;
      k = f ? bv[h].rank1(k) + bv[h].zeros : bv[h].rank0(k);
    }
    return ret;
  }

  // k-th (0-indexed) smallest number in { a[i] ^ value_xor : i in [l, r) }
  T kth_smallest(u32 l, u32 r, u32 k, T value_xor = 0) const {
    T res = value_xor;
    for (int h = B - 1; h >= 0; --h) {
      u32 l0 = bv[h].rank0(l), r0 = bv[h].rank0(r);
      u32 c0 = r0 - l0;
      if ((k < c0) ^ ((value_xor >> h) & 1))
        l = l0, r = r0;
      else {
        k -= c0;
        res ^= (T)1 << h;
        l += bv[h].zeros - l0;
        r += bv[h].zeros - r0;
      }
    }
    return res;
  }
  // k-th (0-indexed) largest number in { a[i] ^ value_xor : i in [l, r) }
  T kth_largest(u32 l, u32 r, u32 k, T value_xor = 0) {
    return kth_smallest(l, r, r - l - k - 1);
  }

  // count i s.t. (l <= i < r) && (v[i] ^ value_xor < upper)
  int range_freq(int l, int r, T upper, T value_xor = 0) {
    if (upper >= (T(1) << B)) return r - l;
    int ret = 0;
    for (int h = B - 1; h >= 0; --h) {
      bool f = (upper >> h) & 1;
      u32 l0 = bv[h].rank0(l), r0 = bv[h].rank0(r);
      u32 zeros = bv[h].zeros;
      u32 l1 = l + zeros - l0, r1 = r + zeros - r0;
      if ((value_xor >> h) & 1) {
        swap(l0, l1);
        swap(r0, r1);
      }
      if (f) {
        ret += r0 - l0;
        l += zeros - l0;
        r += zeros - r0;
      } else {
        l = l0;
        r = r0;
      }
    }
    return ret;
  }
  int range_freq(int l, int r, T lower, T upper, T value_xor) {
    return range_freq(l, r, upper, value_xor) - range_freq(l, r, lower, value_xor);
  }

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

  // min v[i] s.t. (l <= i < r) && (lower ^ value_xor <= v[i])
  T next_value(int l, int r, T lower, T value_xor = 0) {
    int cnt = range_freq(l, r, lower, value_xor);
    return cnt == r - l ? T(-1) : kth_smallest(l, r, cnt, value_xor);
  }
};

/**
 * @brief Wavelet Matrix
 * @docs docs/data-structure/wavelet-matrix.md
 */
#line 5 "verify/data-structure/LC_range_kth_smallest.test.cpp"

int main() {
  int n, q;
  in(n, q);
  vector<int> a(n);
  in(a);
  WaveletMatrix<int, 30> wm(a);
  while (q--) {
    int l, r, k;
    in(l, r, k);
    out(wm.kth_smallest(l, r, k));
  }
}

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