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Verify/LC_range_kth_smallest-2.test.cpp
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- Last update: 2024-04-26 03:32:16+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> 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));
}
#ifdef LOCAL
#define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__)
#else
#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...);
}
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, template <class> class C>
ostream &operator<<(ostream &os, const C<T> &v) {
os << "[";
for (auto d : v)
os << d << ", ";
os << "]";
return os;
}
#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 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 simple> vector<pair<int, int>> genGraph(int n) {
vector<pair<int, int>> cand, es;
rep(u, 0, n) rep(v, 0, n) {
if (simple and u == v)
continue;
if (!directed and u > v)
continue;
cand.push_back({u, v});
}
int m = get(SZ(cand));
vector<int> ord;
if (simple)
ord = select(m, 0, SZ(cand) - 1);
else {
rep(_, 0, m) ord.push_back(get(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;
}