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:heavy_check_mark: verify/yosupo-range_kth_smallest.test.cpp

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Code

#define PROBLEM "https://judge.yosupo.jp/problem/range_kth_smallest"
#include "library/template/template.cpp"
// library
#include "library/structure/wavelet/WaveletMatrix.cpp"
int main() {
    int n, q;
    cin >> n >> q;
    vl a(n);
    scan(a);
    WaveletMatrix<ll, 32> wm(a);
    rep(_, q) {
        int l, r, k;
        cin >> l >> r >> k;
        print(wm.kth_smallest(l, r, k));
    }
}
#line 1 "verify/yosupo-range_kth_smallest.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/range_kth_smallest"
#line 2 "library/template/template.cpp"
/* #region header */
#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
using namespace std;
// types
using ll = long long;
using ull = unsigned long long;
using ld = long double;
typedef pair<ll, ll> Pl;
typedef pair<int, int> Pi;
typedef vector<ll> vl;
typedef vector<int> vi;
typedef vector<char> vc;
template <typename T>
using mat = vector<vector<T>>;
typedef vector<vector<int>> vvi;
typedef vector<vector<long long>> vvl;
typedef vector<vector<char>> vvc;
// abreviations
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define rep_(i, a_, b_, a, b, ...) for (ll i = (a), max_i = (b); i < max_i; i++)
#define rep(i, ...) rep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define rrep_(i, a_, b_, a, b, ...) \
    for (ll i = (b - 1), min_i = (a); i >= min_i; i--)
#define rrep(i, ...) rrep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define srep(i, a, b, c) for (ll i = (a), max_i = (b); i < max_i; i += c)
#define SZ(x) ((int)(x).size())
#define pb(x) push_back(x)
#define eb(x) emplace_back(x)
#define mp make_pair
//ε…₯ε‡ΊεŠ›
#define print(x) cout << x << endl
template <class T>
ostream &operator<<(ostream &os, const vector<T> &v)
{
    for (auto &e : v)
        cout << e << " ";
    cout << endl;
    return os;
}
void scan(int &a) { cin >> a; }
void scan(long long &a) { cin >> a; }
void scan(char &a) { cin >> a; }
void scan(double &a) { cin >> a; }
void scan(string &a) { cin >> a; }
template <class T>
void scan(vector<T> &a)
{
    for (auto &i : a)
        scan(i);
}
#define vsum(x) accumulate(all(x), 0LL)
#define vmax(a) *max_element(all(a))
#define vmin(a) *min_element(all(a))
#define lb(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define ub(c, x) distance((c).begin(), upper_bound(all(c), (x)))
// functions
// gcd(0, x) fails.
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }
template <class T>
bool chmax(T &a, const T &b)
{
    if (a < b)
    {
        a = b;
        return 1;
    }
    return 0;
}
template <class T>
bool chmin(T &a, const T &b)
{
    if (b < a)
    {
        a = b;
        return 1;
    }
    return 0;
}
template <typename T>
T mypow(T x, ll n)
{
    T ret = 1;
    while (n > 0)
    {
        if (n & 1)
            (ret *= x);
        (x *= x);
        n >>= 1;
    }
    return ret;
}
ll modpow(ll x, ll n, const ll mod)
{
    ll ret = 1;
    while (n > 0)
    {
        if (n & 1)
            (ret *= x);
        (x *= x);
        n >>= 1;
        x %= mod;
        ret %= mod;
    }
    return ret;
}
ll safemod(ll x, ll mod) { return (x % mod + mod) % mod; }
int popcnt(ull x) { return __builtin_popcountll(x); }
template <typename T>
vector<int> IOTA(vector<T> a)
{
    int n = a.size();
    vector<int> id(n);
    iota(all(id), 0);
    sort(all(id), [&](int i, int j)
         { return a[i] < a[j]; });
    return id;
}
long long xor64(long long range) {
    static uint64_t x = 88172645463325252ULL;
    x ^= x << 13;
    x ^= x >> 7;
    return (x ^= x << 17) % range;
}
struct Timer
{
    clock_t start_time;
    void start() { start_time = clock(); }
    int lap()
    {
        // return x ms.
        return (clock() - start_time) * 1000 / CLOCKS_PER_SEC;
    }
};
template <typename T = int>
struct Edge
{
    int from, to;
    T cost;
    int idx;

    Edge() = default;

    Edge(int from, int to, T cost = 1, int idx = -1)
        : from(from), to(to), cost(cost), idx(idx) {}

    operator int() const { return to; }
};

template <typename T = int>
struct Graph
{
    vector<vector<Edge<T>>> g;
    int es;

    Graph() = default;

    explicit Graph(int n) : g(n), es(0) {}

    size_t size() const { return g.size(); }

    void add_directed_edge(int from, int to, T cost = 1)
    {
        g[from].emplace_back(from, to, cost, es++);
    }

    void add_edge(int from, int to, T cost = 1)
    {
        g[from].emplace_back(from, to, cost, es);
        g[to].emplace_back(to, from, cost, es++);
    }

    void read(int M, int padding = -1, bool weighted = false,
              bool directed = false)
    {
        for (int i = 0; i < M; i++)
        {
            int a, b;
            cin >> a >> b;
            a += padding;
            b += padding;
            T c = T(1);
            if (weighted)
                cin >> c;
            if (directed)
                add_directed_edge(a, b, c);
            else
                add_edge(a, b, c);
        }
    }
};

/* #endregion*/
// constant
#define inf 1000000000ll
#define INF 4000000004000000000LL
#define endl '\n'
const long double eps = 0.000000000000001;
const long double PI = 3.141592653589793;
#line 3 "verify/yosupo-range_kth_smallest.test.cpp"
// library
#line 1 "library/structure/wavelet/WaveletMatrix.cpp"
struct SuccinctIndexableDictionary {
    size_t length;
    size_t blocks;
    vector<unsigned> bit, sum;

    SuccinctIndexableDictionary() = default;

    SuccinctIndexableDictionary(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)); }
};
template <typename T, int MAXLOG>
struct WaveletMatrix {
    size_t length;
    SuccinctIndexableDictionary matrix[MAXLOG];
    int mid[MAXLOG];

    WaveletMatrix() = default;

    WaveletMatrix(vector<T> v) : length(v.size()) {
        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];
            }
        }
    }

    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--) {
            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;
            }
            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);
            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);
    }

    // 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);
    }

    // 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);
    }
};
#line 5 "verify/yosupo-range_kth_smallest.test.cpp"
int main() {
    int n, q;
    cin >> n >> q;
    vl a(n);
    scan(a);
    WaveletMatrix<ll, 32> wm(a);
    rep(_, q) {
        int l, r, k;
        cin >> l >> r >> k;
        print(wm.kth_smallest(l, r, k));
    }
}
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