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Verify/LC_range_kth_smallest-2.test.cpp

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• Last update: 2025-05-25 16:11:40+09:00
• Problem: https://judge.yosupo.jp/problem/range_kth_smallest

Depends on

• Persistent Randomized Binary Search Tree (set) (DataStructure/persistentrbstset.hpp)
• Template/template.hpp
• Fast IO (Utility/fastio.hpp)
• Random (Utility/random.hpp)

Code

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

#include "Template/template.hpp"

#include "Utility/fastio.hpp"

#include "DataStructure/persistentrbstset.hpp"


const int LIM=201010*20*5;
using np=PRBSTset<int,LIM>::np;

int main(){
    int n,q;
    read(n,q);
    vector<int> a(n);
    read(a);

    vector<int> zip;
    rep(i,0,n)zip.push_back(a[i]);
    sort(ALL(zip));
    zip.erase(unique(ALL(zip)),zip.end());
    rep(i,0,n)a[i]=lower_bound(ALL(zip),a[i])-zip.begin();

    PRBSTset<int,LIM> manager;
    vector<np> buf(1,nullptr);
    rep(i,0,n)buf.push_back(manager.insert(buf.back(),a[i]));
    int L,R,k;
    
    while(q--){
        read(L,R,k);
        int lb=0,rb=zip.size();
        while(rb-lb>1){
            int mid=(lb+rb)>>1;
            int cnt=manager.upper_bound(buf[R],mid)-manager.upper_bound(buf[L],mid);
            if(cnt<=k)lb=mid;
            else rb=mid;
        }
        print(zip[lb]);
    }
    return 0;
}

#line 1 "Verify/LC_range_kth_smallest-2.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/range_kth_smallest"

#line 1 "Template/template.hpp"
#include <bits/stdc++.h>

using namespace std;

#define rep(i, a, b) for (int i = (int)(a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (int)(b)-1; i >= (int)(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())

using uint = unsigned int;
using ll = long long int;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
const int inf = 0x3fffffff;
const ll INF = 0x1fffffffffffffff;

template <typename T, typename S = T> S SUM(const vector<T> &a) {
    return accumulate(ALL(a), S(0));
}
template <typename S, typename T = S> S POW(S a, T b) {
    S ret = 1, base = a;
    for (;;) {
        if (b & 1)
            ret *= base;
        b >>= 1;
        if (b == 0)
            break;
        base *= base;
    }
    return ret;
}
template <typename T> inline bool chmax(T &a, T b) {
    if (a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <typename T> inline bool chmin(T &a, T b) {
    if (a > b) {
        a = b;
        return 1;
    }
    return 0;
}
template <typename T, typename U> T ceil(T x, U y) {
    assert(y != 0);
    if (y < 0)
        x = -x, y = -y;
    return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U> T floor(T x, U y) {
    assert(y != 0);
    if (y < 0)
        x = -x, y = -y;
    return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T> int popcnt(T x) {
    return __builtin_popcountll(x);
}
template <typename T> int topbit(T x) {
    return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
template <typename T> int lowbit(T x) {
    return (x == 0 ? -1 : __builtin_ctzll(x));
}

template <class T, class U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
    os << "P(" << p.first << ", " << p.second << ")";
    return os;
}
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) {
    os << "{";
    for (int i = 0; i < vec.size(); i++) {
        os << vec[i] << (i + 1 == vec.size() ? "" : ", ");
    }
    os << "}";
    return os;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, const map<T, U> &map_var) {
    os << "{";
    for (auto itr = map_var.begin(); itr != map_var.end(); itr++) {
        os << "(" << itr->first << ", " << itr->second << ")";
        itr++;
        if (itr != map_var.end())
            os << ", ";
        itr--;
    }
    os << "}";
    return os;
}
template <typename T> ostream &operator<<(ostream &os, const set<T> &set_var) {
    os << "{";
    for (auto itr = set_var.begin(); itr != set_var.end(); itr++) {
        os << *itr;
        ++itr;
        if (itr != set_var.end())
            os << ", ";
        itr--;
    }
    os << "}";
    return os;
}
#ifdef LOCAL
#define debug 1
#define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__)
#else
#define debug 0
#define show(...) true
#endif
template <typename T> void _show(int i, T name) {
    cerr << '\n';
}
template <typename T1, typename T2, typename... 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 "Utility/fastio.hpp"
#include <unistd.h>

namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf


uint32_t pil = 0, pir = 0, por = 0;

struct Pre {
    char num[10000][4];
    constexpr Pre() : num() {
        for (int i = 0; i < 10000; i++) {
            int n = i;
            for (int j = 3; j >= 0; j--) {
                num[i][j] = n % 10 | '0';
                n /= 10;
            }
        }
    }
} constexpr pre;

inline void load() {
    memmove(ibuf, ibuf + pil, pir - pil);
    pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
    pil = 0;
    if (pir < SZ)
        ibuf[pir++] = '\n';
}

inline void flush() {
    fwrite(obuf, 1, por, stdout);
    por = 0;
}

void rd(char &c) {
    do {
        if (pil + 1 > pir)
            load();
        c = ibuf[pil++];
    } while (isspace(c));
}

void rd(string &x) {
    x.clear();
    char c;
    do {
        if (pil + 1 > pir)
            load();
        c = ibuf[pil++];
    } while (isspace(c));
    do {
        x += c;
        if (pil == pir)
            load();
        c = ibuf[pil++];
    } while (!isspace(c));
}

template <typename T> void rd_real(T &x) {
    string s;
    rd(s);
    x = stod(s);
}

template <typename T> void rd_integer(T &x) {
    if (pil + 100 > pir)
        load();
    char c;
    do
        c = ibuf[pil++];
    while (c < '-');
    bool minus = 0;
    if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
        if (c == '-') {
            minus = 1, c = ibuf[pil++];
        }
    }
    x = 0;
    while ('0' <= c) {
        x = x * 10 + (c & 15), c = ibuf[pil++];
    }
    if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
        if (minus)
            x = -x;
    }
}

void rd(int &x) {
    rd_integer(x);
}
void rd(ll &x) {
    rd_integer(x);
}
void rd(i128 &x) {
    rd_integer(x);
}
void rd(uint &x) {
    rd_integer(x);
}
void rd(ull &x) {
    rd_integer(x);
}
void rd(u128 &x) {
    rd_integer(x);
}
void rd(double &x) {
    rd_real(x);
}
void rd(long double &x) {
    rd_real(x);
}

template <class T, class U> void rd(pair<T, U> &p) {
    return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T> void rd_tuple(T &t) {
    if constexpr (N < std::tuple_size<T>::value) {
        auto &x = std::get<N>(t);
        rd(x);
        rd_tuple<N + 1>(t);
    }
}
template <class... T> void rd(tuple<T...> &tpl) {
    rd_tuple(tpl);
}

template <size_t N = 0, typename T> void rd(array<T, N> &x) {
    for (auto &d : x)
        rd(d);
}
template <class T> void rd(vector<T> &x) {
    for (auto &d : x)
        rd(d);
}

void read() {}
template <class H, class... T> void read(H &h, T &...t) {
    rd(h), read(t...);
}

void wt(const char c) {
    if (por == SZ)
        flush();
    obuf[por++] = c;
}
void wt(const string s) {
    for (char c : s)
        wt(c);
}
void wt(const char *s) {
    size_t len = strlen(s);
    for (size_t i = 0; i < len; i++)
        wt(s[i]);
}

template <typename T> void wt_integer(T x) {
    if (por > SZ - 100)
        flush();
    if (x < 0) {
        obuf[por++] = '-', x = -x;
    }
    int outi;
    for (outi = 96; x >= 10000; outi -= 4) {
        memcpy(out + outi, pre.num[x % 10000], 4);
        x /= 10000;
    }
    if (x >= 1000) {
        memcpy(obuf + por, pre.num[x], 4);
        por += 4;
    } else if (x >= 100) {
        memcpy(obuf + por, pre.num[x] + 1, 3);
        por += 3;
    } else if (x >= 10) {
        int q = (x * 103) >> 10;
        obuf[por] = q | '0';
        obuf[por + 1] = (x - q * 10) | '0';
        por += 2;
    } else
        obuf[por++] = x | '0';
    memcpy(obuf + por, out + outi + 4, 96 - outi);
    por += 96 - outi;
}

template <typename T> void wt_real(T x) {
    ostringstream oss;
    oss << fixed << setprecision(15) << double(x);
    string s = oss.str();
    wt(s);
}

void wt(int x) {
    wt_integer(x);
}
void wt(ll x) {
    wt_integer(x);
}
void wt(i128 x) {
    wt_integer(x);
}
void wt(uint x) {
    wt_integer(x);
}
void wt(ull x) {
    wt_integer(x);
}
void wt(u128 x) {
    wt_integer(x);
}
void wt(double x) {
    wt_real(x);
}
void wt(long double x) {
    wt_real(x);
}

template <class T, class U> void wt(const pair<T, U> val) {
    wt(val.first);
    wt(' ');
    wt(val.second);
}
template <size_t N = 0, typename T> void wt_tuple(const T t) {
    if constexpr (N < std::tuple_size<T>::value) {
        if constexpr (N > 0) {
            wt(' ');
        }
        const auto x = std::get<N>(t);
        wt(x);
        wt_tuple<N + 1>(t);
    }
}
template <class... T> void wt(tuple<T...> tpl) {
    wt_tuple(tpl);
}
template <class T, size_t S> void wt(const array<T, S> val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
        if (i)
            wt(' ');
        wt(val[i]);
    }
}
template <class T> void wt(const vector<T> val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
        if (i)
            wt(' ');
        wt(val[i]);
    }
}

void print() {
    wt('\n');
}
template <class Head, class... Tail> void print(Head &&head, Tail &&...tail) {
    wt(head);
    if (sizeof...(Tail))
        wt(' ');
    print(forward<Tail>(tail)...);
}
void __attribute__((destructor)) _d() {
    flush();
}
} // namespace fastio


using fastio::flush;
using fastio::print;
using fastio::read;

inline void first(bool i = true) {
    print(i ? "first" : "second");
}
inline void Alice(bool i = true) {
    print(i ? "Alice" : "Bob");
}
inline void Takahashi(bool i = true) {
    print(i ? "Takahashi" : "Aoki");
}
inline void yes(bool i = true) {
    print(i ? "yes" : "no");
}
inline void Yes(bool i = true) {
    print(i ? "Yes" : "No");
}
inline void No() {
    print("No");
}
inline void YES(bool i = true) {
    print(i ? "YES" : "NO");
}
inline void NO() {
    print("NO");
}
inline void Yay(bool i = true) {
    print(i ? "Yay!" : ":(");
}
inline void Possible(bool i = true) {
    print(i ? "Possible" : "Impossible");
}
inline void POSSIBLE(bool i = true) {
    print(i ? "POSSIBLE" : "IMPOSSIBLE");
}

/**
 * @brief Fast IO
 */
#line 2 "Utility/random.hpp"

namespace Random {
mt19937_64 randgen(chrono::steady_clock::now().time_since_epoch().count());
using u64 = unsigned long long;
u64 get() {
    return randgen();
}
template <typename T> T get(T L) { // [0,L]

    return get() % (L + 1);
}
template <typename T> T get(T L, T R) { // [L,R]

    return get(R - L) + L;
}
double uniform() {
    return double(get(1000000000)) / 1000000000;
}
string str(int n) {
    string ret;
    rep(i, 0, n) ret += get('a', 'z');
    return ret;
}
template <typename Iter> void shuffle(Iter first, Iter last) {
    if (first == last)
        return;
    int len = 1;
    for (auto it = first + 1; it != last; it++) {
        len++;
        int j = get(0, len - 1);
        if (j != len - 1)
            iter_swap(it, first + j);
    }
}
template <typename T> vector<T> select(int n, T L, T R) { // [L,R]

    if (n * 2 >= R - L + 1) {
        vector<T> ret(R - L + 1);
        iota(ALL(ret), L);
        shuffle(ALL(ret));
        ret.resize(n);
        return ret;
    } else {
        unordered_set<T> used;
        vector<T> ret;
        while (SZ(used) < n) {
            T x = get(L, R);
            if (!used.count(x)) {
                used.insert(x);
                ret.push_back(x);
            }
        }
        return ret;
    }
}

void relabel(int n, vector<pair<int, int>> &es) {
    shuffle(ALL(es));
    vector<int> ord(n);
    iota(ALL(ord), 0);
    shuffle(ALL(ord));
    for (auto &[u, v] : es)
        u = ord[u], v = ord[v];
}
template <bool directed, bool multi, bool self>
vector<pair<int, int>> genGraph(int n, int m) {
    vector<pair<int, int>> cand, es;
    rep(u, 0, n) rep(v, 0, n) {
        if (!self and u == v)
            continue;
        if (!directed and u > v)
            continue;
        cand.push_back({u, v});
    }
    if (m == -1)
        m = get(SZ(cand));
    // chmin(m, SZ(cand));

    vector<int> ord;
    if (multi)
        rep(_, 0, m) ord.push_back(get(SZ(cand) - 1));
    else {
        ord = select(m, 0, SZ(cand) - 1);
    }
    for (auto &i : ord)
        es.push_back(cand[i]);
    relabel(n, es);
    return es;
}
vector<pair<int, int>> genTree(int n) {
    vector<pair<int, int>> es;
    rep(i, 1, n) es.push_back({get(i - 1), i});
    relabel(n, es);
    return es;
}
}; // namespace Random


/**
 * @brief Random
 */
#line 3 "DataStructure/persistentrbstset.hpp"

template <typename T, int LIM = 10101010> struct PRBSTset {
    struct Node {
        Node *lp = nullptr, *rp = nullptr;
        int sz = 1;
        T val;
        Node() {}
        void apply() {
            sz = 1;
            if (lp)
                sz += lp->sz;
            if (rp)
                sz += rp->sz;
        }
    };
    using np = Node *;
    Node buf[LIM];
    int pos = 0;
    int sz(np root) { return root ? root->sz : 0; }
    np merge(np L, np R) {
        if (!L)
            return R;
        if (!R)
            return L;
        if (Random::uniform() * (sz(L) + sz(R)) < sz(L)) {
            auto rb = merge(L->rp, R);
            np ret = make(L->val, L->lp, rb);
            return ret;
        } else {
            auto lb = merge(L, R->lp);
            np ret = make(R->val, lb, R->rp);
            return ret;
        }
    }
    array<np, 2> split(np root, int k) {
        if (k <= 0)
            return {nullptr, root};
        if (k >= sz(root))
            return {root, nullptr};
        if (k <= sz(root->lp)) {
            auto [L, lb] = split(root->lp, k);
            np R = make(root->val, lb, root->rp);
            return {L, R};
        } else {
            auto [rb, R] = split(root->rp, k - 1 - sz(root->lp));
            np L = make(root->val, root->lp, rb);
            return {L, R};
        }
    }
    bool find(np root, T v) {
        if (!root)
            return false;
        if (root->val == v)
            return true;
        else if (root->val > v)
            return find(root->lp, v);
        else
            return find(root->rp, v);
    }
    int lower_bound(np root, T v) {
        if (!root)
            return 0;
        if (root->val > v)
            return lower_bound(root->lp, v);
        else
            return sz(root->lp) + 1 + lower_bound(root->rp, v);
    }
    int upper_bound(np root, T v) {
        if (!root)
            return 0;
        if (root->val >= v)
            return upper_bound(root->lp, v);
        else
            return sz(root->lp) + 1 + upper_bound(root->rp, v);
    }
    np make(T v, np L = nullptr, np R = nullptr) {
        np ret = &buf[pos++];
        ret->val = v;
        ret->lp = L;
        ret->rp = R;
        ret->apply();
        return ret;
    }
    void dfs(np root, vector<T> &a) {
        if (!root)
            return;
        dfs(root->lp, a);
        a.push_back(root->val);
        dfs(root->rp, a);
    }
    np rebuild(np root) {
        if (pos < LIM * .95)
            return root;
        vector<T> tmp;
        dfs(root, tmp);
        return build(tmp);
    }
    np insert(np root, T v) {
        int k = lower_bound(root, v);
        auto [L, R] = split(root, k);
        return merge(merge(L, make(v)), R);
    }
    np erase(np root, T v) {
        int k = lower_bound(root, v);
        auto [L, rb] = split(root, k);
        auto [tmp, R] = split(rb, 1);
        return merge(L, R);
    }
    T kth_elem(np root, int k) {
        assert(k <= 0 and k < sz(root));
        if (sz(root->lp) == k)
            return root->val;
        else if (sz(root->lp) > k)
            return kth_elem(root->lp, k);
        else
            return kth_elem(root->rp, k - 1 - sz(root->lp));
    }
    np build(vector<T> &a) {
        np root = nullptr;
        for (auto &x : a)
            root = merge(root, make(x));
        return root;
    }
    void dump(np root) {
        if (!root)
            return;
        dump(root->lp);
        cerr << root->val << '\n';
        dump(root->rp);
    }
};

/**
 * @brief Persistent Randomized Binary Search Tree (set)
 */
#line 6 "Verify/LC_range_kth_smallest-2.test.cpp"

const int LIM=201010*20*5;
using np=PRBSTset<int,LIM>::np;

int main(){
    int n,q;
    read(n,q);
    vector<int> a(n);
    read(a);

    vector<int> zip;
    rep(i,0,n)zip.push_back(a[i]);
    sort(ALL(zip));
    zip.erase(unique(ALL(zip)),zip.end());
    rep(i,0,n)a[i]=lower_bound(ALL(zip),a[i])-zip.begin();

    PRBSTset<int,LIM> manager;
    vector<np> buf(1,nullptr);
    rep(i,0,n)buf.push_back(manager.insert(buf.back(),a[i]));
    int L,R,k;
    
    while(q--){
        read(L,R,k);
        int lb=0,rb=zip.size();
        while(rb-lb>1){
            int mid=(lb+rb)>>1;
            int cnt=manager.upper_bound(buf[R],mid)-manager.upper_bound(buf[L],mid);
            if(cnt<=k)lb=mid;
            else rb=mid;
        }
        print(zip[lb]);
    }
    return 0;
}

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