This documentation is automatically generated by online-judge-tools/verification-helper
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/range_kth_smallest
#include "../../template/template.hpp"
#include "../../structure/wavelet/succinct-indexable-dictionary.hpp"
#include "../../structure/wavelet/wavelet-tree.hpp"
int main() {
int N, Q;
cin >> N >> Q;
vector< int > A(N);
cin >> A;
CompressedWaveletTree< int, 18 > mat(A);
for(int i = 0; i < Q; i++) {
int a, b, c;
cin >> a >> b >> c;
cout << mat.kth_smallest(a, b, c) << "\n";
}
}
#line 1 "test/verify/yosupo-range-kth-smallest-2.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/range_kth_smallest
#line 1 "template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
using int64 = long long;
const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;
struct IoSetup {
IoSetup() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(10);
cerr << fixed << setprecision(10);
}
} iosetup;
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
os << p.first << " " << p.second;
return os;
}
template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
for (int i = 0; i < (int)v.size(); i++) {
os << v[i] << (i + 1 != v.size() ? " " : "");
}
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (T &in : v) is >> in;
return is;
}
template <typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {
return a < b && (a = b, true);
}
template <typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {
return a > b && (a = b, true);
}
template <typename T = int64>
vector<T> make_v(size_t a) {
return vector<T>(a);
}
template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}
template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
t = v;
}
template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
for (auto &e : t) fill_v(e, v);
}
template <typename F>
struct FixPoint : F {
explicit FixPoint(F &&f) : F(forward<F>(f)) {}
template <typename... Args>
decltype(auto) operator()(Args &&...args) const {
return F::operator()(*this, forward<Args>(args)...);
}
};
template <typename F>
inline decltype(auto) MFP(F &&f) {
return FixPoint<F>{forward<F>(f)};
}
#line 4 "test/verify/yosupo-range-kth-smallest-2.test.cpp"
#line 1 "structure/wavelet/succinct-indexable-dictionary.hpp"
/**
* @brief Succinct Indexable Dictionary(完備辞書)
*/
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)); }
};
#line 1 "structure/wavelet/wavelet-tree.hpp"
/*
* @brief Wavelet Tree(ウェーブレット木)
*
*/
template <typename T, int MAXLOG>
struct WaveletTree {
struct Node {
SuccinctIndexableDictionary sid;
Node *ch[2];
Node() = default;
Node(size_t length) : sid(length + 1), ch{nullptr} {}
};
Node *root;
Node *build(vector<T> &v, vector<T> &rbuff, int bit, int l, int r) {
if (l >= r || bit == -1) return nullptr;
Node *node = new Node(r - l);
int left = 0, right = 0;
for (int k = l; k < r; k++) {
if (((v[k] >> bit) & 1)) {
rbuff[right++] = v[k];
node->sid.set(k - l);
} else {
v[l + left++] = v[k];
}
}
for (int k = 0; k < right; k++) {
v[l + left + k] = rbuff[k];
}
node->sid.build();
node->ch[0] = build(v, rbuff, bit - 1, l, l + left);
node->ch[1] = build(v, rbuff, bit - 1, l + left, r);
return node;
}
WaveletTree() = default;
WaveletTree(vector<T> v) {
vector<T> rbuff(v.size());
root = build(v, rbuff, MAXLOG - 1, 0, v.size());
}
int rank(Node *t, int l, int r, const T &x, int level) {
if (l >= r || t == nullptr) return 0;
if (level == -1) return r - l;
bool f = (x >> level) & 1;
l = t->sid.rank(f, l), r = t->sid.rank(f, r);
return rank(t->ch[f], l, r, x, level - 1);
}
int rank(const T &x, int r) { return rank(root, 0, r, x, MAXLOG - 1); }
T kth_smallest(Node *t, int l, int r, int k, int level) {
if (l >= r || t == nullptr) return 0;
int cnt = t->sid.rank(false, r) - t->sid.rank(false, l);
bool f = cnt <= k;
l = t->sid.rank(f, l), r = t->sid.rank(f, r);
if (f)
return kth_smallest(t->ch[f], l, r, k - cnt, level - 1) |
((T(1) << level));
return kth_smallest(t->ch[f], l, r, k, level - 1);
}
// 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);
return kth_smallest(root, l, r, k, MAXLOG - 1);
}
// 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);
}
int range_freq(Node *t, int l, int r, T upper, int level) {
if (t == nullptr || l >= r) return 0;
bool f = ((upper >> level) & 1);
int ret = 0;
if (f) ret += t->sid.rank(false, r) - t->sid.rank(false, l);
l = t->sid.rank(f, l), r = t->sid.rank(f, r);
return range_freq(t->ch[f], l, r, upper, level - 1) + ret;
}
// count i s.t. (l <= i < r) && (v[i] < upper)
int range_freq(int l, int r, T upper) {
return range_freq(root, l, r, upper, MAXLOG - 1);
}
// 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);
}
};
template <typename T, int MAXLOG>
struct CompressedWaveletTree {
WaveletTree<int, MAXLOG> mat;
vector<T> ys;
CompressedWaveletTree(const vector<T> &v) : ys(v) {
sort(begin(ys), end(ys));
ys.erase(unique(begin(ys), end(ys)), end(ys));
vector<int> t(v.size());
for (int i = 0; i < v.size(); i++) t[i] = get(v[i]);
mat = WaveletTree<int, MAXLOG>(t);
}
inline int get(const T &x) {
return lower_bound(begin(ys), end(ys), x) - begin(ys);
}
int rank(const T &x, int r) {
auto pos = get(x);
if (pos == ys.size() || ys[pos] != x) return 0;
return mat.rank(pos, r);
}
T kth_smallest(int l, int r, int k) { return ys[mat.kth_smallest(l, r, k)]; }
T kth_largest(int l, int r, int k) { return ys[mat.kth_largest(l, r, k)]; }
int range_freq(int l, int r, T upper) {
return mat.range_freq(l, r, get(upper));
}
int range_freq(int l, int r, T lower, T upper) {
return mat.range_freq(l, r, get(lower), get(upper));
}
T prev_value(int l, int r, T upper) {
auto ret = mat.prev_value(l, r, get(upper));
return ret == -1 ? T(-1) : ys[ret];
}
T next_value(int l, int r, T lower) {
auto ret = mat.next_value(l, r, get(lower));
return ret == -1 ? T(-1) : ys[ret];
}
};
#line 7 "test/verify/yosupo-range-kth-smallest-2.test.cpp"
int main() {
int N, Q;
cin >> N >> Q;
vector< int > A(N);
cin >> A;
CompressedWaveletTree< int, 18 > mat(A);
for(int i = 0; i < Q; i++) {
int a, b, c;
cin >> a >> b >> c;
cout << mat.kth_smallest(a, b, c) << "\n";
}
}
Env | Name | Status | Elapsed | Memory |
---|---|---|---|---|
g++ | all_zero_00 | AC | 8 ms | 4 MB |
g++ | dense_large_a_00 | AC | 70 ms | 4 MB |
g++ | dense_small_a_00 | AC | 68 ms | 4 MB |
g++ | example_00 | AC | 7 ms | 4 MB |
g++ | max_random_00 | AC | 330 ms | 39 MB |
g++ | max_random_01 | AC | 322 ms | 39 MB |
g++ | max_random_02 | AC | 330 ms | 39 MB |
g++ | max_random_03 | AC | 334 ms | 39 MB |
g++ | max_random_04 | AC | 313 ms | 39 MB |
g++ | random_00 | AC | 215 ms | 26 MB |
g++ | random_01 | AC | 234 ms | 30 MB |
g++ | random_02 | AC | 119 ms | 13 MB |
g++ | random_03 | AC | 110 ms | 33 MB |
g++ | random_04 | AC | 65 ms | 6 MB |
g++ | small_00 | AC | 8 ms | 4 MB |
g++ | small_01 | AC | 7 ms | 4 MB |
g++ | small_02 | AC | 7 ms | 4 MB |
g++ | small_03 | AC | 7 ms | 4 MB |
g++ | small_04 | AC | 8 ms | 4 MB |
g++ | small_05 | AC | 7 ms | 4 MB |
g++ | small_06 | AC | 7 ms | 4 MB |
g++ | small_07 | AC | 7 ms | 4 MB |
g++ | small_08 | AC | 7 ms | 4 MB |
g++ | small_09 | AC | 7 ms | 4 MB |
clang++ | all_zero_00 | AC | 8 ms | 4 MB |
clang++ | dense_large_a_00 | AC | 72 ms | 4 MB |
clang++ | dense_small_a_00 | AC | 68 ms | 3 MB |
clang++ | example_00 | AC | 8 ms | 4 MB |
clang++ | max_random_00 | AC | 321 ms | 39 MB |
clang++ | max_random_01 | AC | 323 ms | 39 MB |
clang++ | max_random_02 | AC | 314 ms | 39 MB |
clang++ | max_random_03 | AC | 307 ms | 39 MB |
clang++ | max_random_04 | AC | 297 ms | 39 MB |
clang++ | random_00 | AC | 204 ms | 26 MB |
clang++ | random_01 | AC | 219 ms | 30 MB |
clang++ | random_02 | AC | 115 ms | 13 MB |
clang++ | random_03 | AC | 100 ms | 33 MB |
clang++ | random_04 | AC | 62 ms | 6 MB |
clang++ | small_00 | AC | 8 ms | 4 MB |
clang++ | small_01 | AC | 7 ms | 4 MB |
clang++ | small_02 | AC | 7 ms | 4 MB |
clang++ | small_03 | AC | 7 ms | 4 MB |
clang++ | small_04 | AC | 7 ms | 4 MB |
clang++ | small_05 | AC | 7 ms | 4 MB |
clang++ | small_06 | AC | 8 ms | 4 MB |
clang++ | small_07 | AC | 7 ms | 4 MB |
clang++ | small_08 | AC | 7 ms | 4 MB |
clang++ | small_09 | AC | 8 ms | 4 MB |