data_structure/test/range_kth_smallest.test.cpp

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• Last update: 2025-06-28 10:05:47+09:00
• Problem: https://judge.yosupo.jp/problem/range_kth_smallest

Depends on

• data_structure/bit_vector.hpp
• data_structure/wavelet_matrix.hpp
• other/coordinate_compression.hpp
• template/bitop.hpp
• template/template.hpp

Code

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

#include "../../data_structure/wavelet_matrix.hpp"
#include "../../other/coordinate_compression.hpp"
#include "../../template/template.hpp"

int main() {
    i32 n, q;
    cin >> n >> q;
    V<i32> a(n);
    REP(i, n) { cin >> a[i]; }
    CoordinateCompression<i32> cc(a);
    WaveletMatrix<i32> wm(a);
    REP(qi, q) {
        i32 l, r, k;
        cin >> l >> r >> k;
        i32 sm = wm.kth_smallest(l, r, k);
        cout << cc[sm] << '\n';
    }
}

#line 1 "data_structure/test/range_kth_smallest.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/range_kth_smallest"
#define FAST_IO

#line 2 "data_structure/wavelet_matrix.hpp"

#include <algorithm>
#include <cassert>
#include <utility>
#line 2 "data_structure/bit_vector.hpp"
#include <vector>
#line 2 "template/bitop.hpp"

template <typename T, typename U>
bool ith_bit(T n, U i) {
    return (n & ((T)1 << i)) != 0;
}

int popcount(int x) { return __builtin_popcount(x); }
unsigned popcount(unsigned x) { return __builtin_popcount(x); }
long long popcount(long long x) { return __builtin_popcountll(x); }
unsigned long long popcount(unsigned long long x) {
    return __builtin_popcountll(x);
}

// x must not be 0
int clz(int x) { return __builtin_clz(x); }
unsigned clz(unsigned x) { return __builtin_clz(x); }
long long clz(long long x) { return __builtin_clzll(x); }
unsigned long long clz(unsigned long long x) { return __builtin_clzll(x); }

// x must not be 0
int ctz(int x) { return __builtin_ctz(x); }
unsigned ctz(unsigned int x) { return __builtin_ctz(x); }
long long ctz(long long x) { return __builtin_ctzll(x); }
unsigned long long ctz(unsigned long long x) { return __builtin_ctzll(x); }

int floor_log2(int x) { return 31 - clz(x); }
unsigned floor_log2(unsigned x) { return 31 - clz(x); }
long long floor_log2(long long x) { return 63 - clz(x); }
unsigned long long floor_log2(unsigned long long x) { return 63 - clz(x); }

template <typename T>
T mask_n(T x, T n) {
    T mask = ((T)1 << n) - 1;
    return x & mask;
}
#line 4 "data_structure/bit_vector.hpp"

class BitVector {
    static constexpr int WIDTH = 64;

    int n;
    std::vector<unsigned long long> bits;
    std::vector<unsigned long long> sum;
    int zeros;

public:
    BitVector(int _n)
        : n(_n), bits(n / WIDTH + 1, 0), sum(n / WIDTH + 1, 0), zeros(0) {}

    void rev(int idx) { bits[idx / WIDTH] ^= 1ULL << (idx % WIDTH); }

    bool operator[](int idx) const {
        return (bits[idx / WIDTH] & (1ULL << (idx % WIDTH))) != 0;
    }

    void build() {
        for (int i = 1; i < (int)sum.size(); ++i) {
            sum[i] = sum[i - 1] + popcount(bits[i - 1]);
        }
        zeros = rank0(n);
    }

    int rank0(int n) const { return n - rank1(n); }
    int rank1(int n) const {
        return sum[n / WIDTH] +
               popcount(
                   mask_n(bits[n / WIDTH], (unsigned long long)(n % WIDTH)));
    }
    int all_zeros() const { return zeros; }
};
#line 7 "data_structure/wavelet_matrix.hpp"

template <typename T>
class WaveletMatrix {
    int n;
    int ht;
    std::vector<BitVector> vecs;

public:
    WaveletMatrix(std::vector<T> a) : n((int)a.size()), ht(0), vecs() {
        assert(n > 0);
        for (T ele : a) {
            assert(ele >= 0);
        }

        T mx = std::max(T(1), *std::max_element(a.begin(), a.end()));
        ht = (int)floor_log2(mx) + 1;
        vecs.reserve(ht);

        for (T d = ht; d-- > 0;) {
            BitVector vec(n);
            for (int i = 0; i < n; ++i) {
                if (ith_bit(a[i], d)) {
                    vec.rev(i);
                }
            }
            vec.build();
            std::vector<T> nxt(n);
            auto it0 = nxt.begin();
            auto it1 = nxt.begin() + vec.all_zeros();
            for (int i = 0; i < n; ++i) {
                if (vec[i]) {
                    *(it1++) = a[i];
                } else {
                    *(it0++) = a[i];
                }
            }
            std::swap(nxt, a);
            vecs.emplace_back(std::move(vec));
        }
    }

    T access(int idx) const {
        assert(0 <= idx && idx < n);
        T ret(0);
        for (int i = 0; i < ht; ++i) {
            ret <<= 1;
            if (vecs[i][idx]) {
                ret ^= 1;
                idx = vecs[i].all_zeros() + vecs[i].rank1(idx);
            } else {
                idx = vecs[i].rank0(idx);
            }
        }
        return ret;
    }

    T kth_smallest(int l, int r, int k) const {
        assert(0 <= l && l <= r && r <= n && 0 <= k && k < r - l);
        T ret = 0;
        for (int i = 0; i < ht; ++i) {
            int l0 = vecs[i].rank0(l);
            int r0 = vecs[i].rank0(r);
            ret <<= 1;
            if (k < r0 - l0) {
                l = l0;
                r = r0;
            } else {
                ret ^= T(1);
                l += vecs[i].all_zeros() - l0;
                r += vecs[i].all_zeros() - r0;
                k -= r0 - l0;
            }
        }
        return ret;
    }
    T kth_largest(int l, int r, int k) const {
        return kth_smallest(l, r, r - l - k - 1);
    }

    // no two ranges intersect
    T kth_smallest_many_ranges(std::vector<std::pair<int, int>> ranges,
                               int k) const {
        int s = 0;
        for (auto [l, r] : ranges) {
            assert(0 <= l && l <= r && r <= n);
            s += r - l;
        }
        assert(0 <= k && k < s);
        T ret = 0;
        for (int i = 0; i < ht; ++i) {
            int zs = 0;
            for (auto [l, r] : ranges) {
                zs += vecs[i].rank0(r) - vecs[i].rank0(l);
            }
            ret <<= 1;
            if (k < zs) {
                for (auto &[l, r] : ranges) {
                    l = vecs[i].rank0(l);
                    r = vecs[i].rank0(r);
                }
            } else {
                ret ^= T(1);
                for (auto &[l, r] : ranges) {
                    l = vecs[i].all_zeros() + vecs[i].rank1(l);
                    r = vecs[i].all_zeros() + vecs[i].rank1(r);
                }
                k -= zs;
            }
        }
        return ret;
    }

    // count i s.t. i in [l, r) and a[i] = v
    int rank(int l, int r, T v) const {
        assert(0 <= l && l <= r && r <= n);
        if (v != 0 && floor_log2(v) >= ht) {
            return 0;
        }
        for (int i = 0; i < ht; ++i) {
            int l0 = vecs[i].rank0(l);
            int r0 = vecs[i].rank0(r);
            if (ith_bit(v, ht - 1 - i)) {
                l += vecs[i].all_zeros() - l0;
                r += vecs[i].all_zeros() - r0;
            } else {
                l = l0;
                r = r0;
            }
        }
        return r - l;
    }

    // count i s.t. i in [l, r) and a[i] < upper
    int range_freq(int l, int r, T upper) const {
        assert(0 <= l && l <= r && r <= n);
        if (l == r) {
            return 0;
        }
        if (upper != 0 && floor_log2(upper) >= ht) {
            return r - l;
        }
        int cnt = 0;
        for (int i = 0; i < ht; ++i) {
            int l0 = vecs[i].rank0(l);
            int r0 = vecs[i].rank0(r);
            if (ith_bit(upper, ht - 1 - i)) {
                cnt += r0 - l0;
                l += vecs[i].all_zeros() - l0;
                r += vecs[i].all_zeros() - r0;
            } else {
                l = l0;
                r = r0;
            }
        }
        return cnt;
    }
    // count i s.t. i in [l, r) and a[i] in [lower, upper)
    int range_freq(int l, int r, T lower, T upper) const {
        if (lower >= upper) {
            return 0;
        } else {
            return range_freq(l, r, upper) - range_freq(l, r, lower);
        }
    }

    // max v s.t. v in a[l, r) and v < upper
    int prev(int l, int r, T upper) const {
        int freq = range_freq(l, r, upper);
        if (freq == 0) {
            return T(-1);
        } else {
            return kth_smallest(l, r, freq - 1);
        }
    }

    // min v s.t. v in a[l, r) and v geq lower
    int next(int l, int r, T lower) const {
        int freq = range_freq(l, r, lower);
        if (freq == r - l) {
            return T(-1);
        } else {
            return kth_smallest(l, r, freq);
        }
    }
};
#line 2 "other/coordinate_compression.hpp"

#line 5 "other/coordinate_compression.hpp"

template <typename T>
class CoordinateCompression {
    std::vector<T> data;

    int size_sum() { return 0; }

    template <typename... Tail>
    int size_sum(const std::vector<T> &head, const Tail &...tail) {
        return (int)head.size() + size_sum(tail...);
    }

    void push() {}

    template <typename... Tail>
    void push(const std::vector<T> &head, const Tail &...tail) {
        for (const T &ele : head) {
            data.emplace_back(ele);
        }
        push(tail...);
    }

    void compress() {}

    template <typename... Tail>
    void compress(std::vector<T> &head, Tail &...tail) {
        for (T &ele : head) {
            ele = (T)(std::lower_bound(data.begin(), data.end(), ele) -
                      data.begin());
        }
        compress(tail...);
    }

public:
    template <typename... V>
    CoordinateCompression(V &...v) {
        data.reserve(size_sum(v...));
        push(v...);
        std::sort(data.begin(), data.end());
        data.erase(std::unique(data.begin(), data.end()), data.end());
        compress(v...);
    }

    const T &operator[](const T &ele) const { return data[ele]; }

    int size() const { return data.size(); }

    bool contains(const T &ele) const {
        auto it = std::lower_bound(data.begin(), data.end(), ele);
        return it != data.end() && *it == ele;
    }

    T cc(const T &ele) const {
        return (T)(std::lower_bound(data.begin(), data.end(), ele) -
                   data.begin());
    }
};
#line 2 "template/template.hpp"
#include <bits/stdc++.h>
#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i)
#define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER2(i, n) for (i32 i = (i32)(n)-1; i >= 0; --i)
#define PER3(i, m, n) for (i32 i = (i32)(n)-1; i >= (i32)(m); --i)
#define PER(...) OVERRIDE(__VA_ARGS__, PER3, PER2)(__VA_ARGS__)
#define ALL(x) begin(x), end(x)
#define LEN(x) (i32)(x.size())
using namespace std;
using u32 = unsigned int;
using u64 = unsigned long long;
using i32 = signed int;
using i64 = signed long long;
using f64 = double;
using f80 = long double;
using pi = pair<i32, i32>;
using pl = pair<i64, i64>;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = V<V<T>>;
template <typename T>
using VVV = V<V<V<T>>>;
template <typename T>
using VVVV = V<V<V<V<T>>>>;
template <typename T>
using PQR = priority_queue<T, V<T>, greater<T>>;
template <typename T>
bool chmin(T &x, const T &y) {
    if (x > y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
    if (x < y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T>
i32 lob(const V<T> &arr, const T &v) {
    return (i32)(lower_bound(ALL(arr), v) - arr.begin());
}
template <typename T>
i32 upb(const V<T> &arr, const T &v) {
    return (i32)(upper_bound(ALL(arr), v) - arr.begin());
}
template <typename T>
V<i32> argsort(const V<T> &arr) {
    V<i32> ret(arr.size());
    iota(ALL(ret), 0);
    sort(ALL(ret), [&](i32 i, i32 j) -> bool {
        if (arr[i] == arr[j]) {
            return i < j;
        } else {
            return arr[i] < arr[j];
        }
    });
    return ret;
}
#ifdef INT128
using u128 = __uint128_t;
using i128 = __int128_t;
#endif
[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;
struct SetUpIO {
    SetUpIO() {
#ifdef FAST_IO
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
#endif
        cout << fixed << setprecision(15);
    }
} set_up_io;
void scan(char &x) { cin >> x; }
void scan(u32 &x) { cin >> x; }
void scan(u64 &x) { cin >> x; }
void scan(i32 &x) { cin >> x; }
void scan(i64 &x) { cin >> x; }
void scan(f64 &x) { cin >> x; }
void scan(string &x) { cin >> x; }
template <typename T>
void scan(V<T> &x) {
    for (T &ele : x) {
        scan(ele);
    }
}
void read() {}
template <typename Head, typename... Tail>
void read(Head &head, Tail &...tail) {
    scan(head);
    read(tail...);
}
#define CHAR(...)     \
    char __VA_ARGS__; \
    read(__VA_ARGS__);
#define U32(...)     \
    u32 __VA_ARGS__; \
    read(__VA_ARGS__);
#define U64(...)     \
    u64 __VA_ARGS__; \
    read(__VA_ARGS__);
#define I32(...)     \
    i32 __VA_ARGS__; \
    read(__VA_ARGS__);
#define I64(...)     \
    i64 __VA_ARGS__; \
    read(__VA_ARGS__);
#define F64(...)     \
    f64 __VA_ARGS__; \
    read(__VA_ARGS__);
#define STR(...)        \
    string __VA_ARGS__; \
    read(__VA_ARGS__);
#define VEC(type, name, size) \
    V<type> name(size);       \
    read(name);
#define VVEC(type, name, size1, size2)    \
    VV<type> name(size1, V<type>(size2)); \
    read(name);
#line 7 "data_structure/test/range_kth_smallest.test.cpp"

int main() {
    i32 n, q;
    cin >> n >> q;
    V<i32> a(n);
    REP(i, n) { cin >> a[i]; }
    CoordinateCompression<i32> cc(a);
    WaveletMatrix<i32> wm(a);
    REP(qi, q) {
        i32 l, r, k;
        cin >> l >> r >> k;
        i32 sm = wm.kth_smallest(l, r, k);
        cout << cc[sm] << '\n';
    }
}

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