結果

問題 No.2977 Kth Xor Pair
ユーザー ecottea
提出日時 2024-12-01 02:02:20
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
TLE  
実行時間 -
コード長 15,773 bytes
コンパイル時間 7,131 ms
コンパイル使用メモリ 308,588 KB
実行使用メモリ 88,064 KB
最終ジャッジ日時 2024-12-01 02:03:47
合計ジャッジ時間 87,457 ms
ジャッジサーバーID
(参考情報)
judge1 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 2
other AC * 18 TLE * 16
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

// QCFium
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#ifndef HIDDEN_IN_VS //
//
#define _CRT_SECURE_NO_WARNINGS
//
#include <bits/stdc++.h>
using namespace std;
//
using ll = long long; using ull = unsigned long long; // -2^63 2^63 = 9e18int -2^31 2^31 = 2e9
using pii = pair<int, int>; using pll = pair<ll, ll>; using pil = pair<int, ll>; using pli = pair<ll, int>;
using vi = vector<int>; using vvi = vector<vi>; using vvvi = vector<vvi>; using vvvvi = vector<vvvi>;
using vl = vector<ll>; using vvl = vector<vl>; using vvvl = vector<vvl>; using vvvvl = vector<vvvl>;
using vb = vector<bool>; using vvb = vector<vb>; using vvvb = vector<vvb>;
using vc = vector<char>; using vvc = vector<vc>; using vvvc = vector<vvc>;
using vd = vector<double>; using vvd = vector<vd>; using vvvd = vector<vvd>;
template <class T> using priority_queue_rev = priority_queue<T, vector<T>, greater<T>>;
using Graph = vvi;
//
const double PI = acos(-1);
int DX[4] = { 1, 0, -1, 0 }; // 4
int DY[4] = { 0, 1, 0, -1 };
int INF = 1001001001; ll INFL = 4004004003094073385LL; // (int)INFL = INF, (int)(-INFL) = -INF;
//
struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp;
//
#define all(a) (a).begin(), (a).end()
#define sz(x) ((int)(x).size())
#define lbpos(a, x) (int)distance((a).begin(), std::lower_bound(all(a), (x)))
#define ubpos(a, x) (int)distance((a).begin(), std::upper_bound(all(a), (x)))
#define Yes(b) {cout << ((b) ? "Yes\n" : "No\n");}
#define rep(i, n) for(int i = 0, i##_len = int(n); i < i##_len; ++i) // 0 n-1
#define repi(i, s, t) for(int i = int(s), i##_end = int(t); i <= i##_end; ++i) // s t
#define repir(i, s, t) for(int i = int(s), i##_end = int(t); i >= i##_end; --i) // s t
#define repe(v, a) for(const auto& v : (a)) // a
#define repea(v, a) for(auto& v : (a)) // a
#define repb(set, d) for(int set = 0, set##_ub = 1 << int(d); set < set##_ub; ++set) // d
#define repis(i, set) for(int i = lsb(set), bset##i = set; i < 32; bset##i -= 1 << i, i = lsb(bset##i)) // set
#define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a
#define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} //
#define EXIT(a) {cout << (a) << endl; exit(0);} //
#define inQ(x, y, u, l, d, r) ((u) <= (x) && (l) <= (y) && (x) < (d) && (y) < (r)) //
//
template <class T> inline ll powi(T n, int k) { ll v = 1; rep(i, k) v *= n; return v; }
template <class T> inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // true
    
template <class T> inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // true
    
template <class T> inline T getb(T set, int i) { return (set >> i) & T(1); }
template <class T> inline T smod(T n, T m) { n %= m; if (n < 0) n += m; return n; } // mod
//
template <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p) { is >> p.first >> p.second; return is; }
template <class T> inline istream& operator>>(istream& is, vector<T>& v) { repea(x, v) is >> x; return is; }
template <class T> inline vector<T>& operator--(vector<T>& v) { repea(x, v) --x; return v; }
template <class T> inline vector<T>& operator++(vector<T>& v) { repea(x, v) ++x; return v; }
#endif //
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#ifdef _MSC_VER
#include "localACL.hpp"
#endif
using mint = modint998244353;
//using mint = static_modint<1000000007>;
//using mint = modint; // mint::set_mod(m);
namespace atcoder {
inline istream& operator>>(istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; }
inline ostream& operator<<(ostream& os, const mint& x) { os << x.val(); return os; }
}
using vm = vector<mint>; using vvm = vector<vm>; using vvvm = vector<vvm>; using vvvvm = vector<vvvm>; using pim = pair<int, mint>;
#endif
#ifdef _MSC_VER // Visual Studio
#include "local.hpp"
#else // gcc
inline int popcount(int n) { return __builtin_popcount(n); }
inline int popcount(ll n) { return __builtin_popcountll(n); }
inline int lsb(int n) { return n != 0 ? __builtin_ctz(n) : 32; }
inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : 64; }
inline int msb(int n) { return n != 0 ? (31 - __builtin_clz(n)) : -1; }
inline int msb(ll n) { return n != 0 ? (63 - __builtin_clzll(n)) : -1; }
#define dump(...)
#define dumpel(...)
#define dump_list(v)
#define dump_mat(v)
#define input_from_file(f)
#define output_to_file(f)
#define Assert(b) { if (!(b)) { vc MLE(1<<30); EXIT(MLE.back()); } } // RE MLE
#endif
//O(log|ok - ng|)
/*
* okQ() ok ng
* ok
* debug_mode = true 調
*/
template <class T, class FUNC>
T meguru_search(T ok, T ng, const FUNC& okQ, bool debug_mode = false) {
// : https://twitter.com/meguru_comp/status/697008509376835584
// verify : https://atcoder.jp/contests/typical90/tasks/typical90_a
Assert(ok != ng);
#ifdef _MSC_VER
// 調
if (debug_mode) {
T step = ok < ng ? 1 : -1; T res = ok; bool is_ok = true;
for (T i = ok; i != ng + step; i += step) {
auto b = okQ(i);
if (b) {
if (!is_ok) {
cout << "not monotony!" << endl;
for (T i = ok; i != ng + step; i += step) {
cout << i << " : " << okQ(i) << endl;
}
exit(1);
}
}
else {
if (is_ok) res = i - step;
is_ok = false;
}
}
return res;
}
#endif
//
while (abs(ok - ng) > 1) {
//
T mid = (ok + ng) / 2;
// OK
if (okQ(mid)) ok = mid;
else ng = mid;
}
return ok;
/* okQ
auto okQ = [&](ll x) {
return true || false;
};
*/
}
//binary trie
/*
* Binary_trie<T = ll>(int B = 62) : O(1)
* T B
*
* ll size() : O(1)
*
*
* bool empty() : O(1)
* 0
*
* insert(T val, ll cnt = 1) : O(B)
* val cnt
*
* erase(T val, ll cnt = 1) : O(B)
* val cnt
*
* T max_element(T mask = 0) : O(B)
* mask XOR
* mask XOR
*
* T min_element(T mask = 0) : O(B)
* mask XOR
*
* T get(ll i, T mask = 0) : O(B)
* mask XOR i 0-indexed -1
*
* ll lower_bound(T val, T mask = 0) : O(B)
* mask XOR
* val 0-indexed
*
* ll upper_bound(T val, T mask = 0) : O(B)
* mask XOR
* val 0-indexed
*
* ll count(T val) : O(B)
* val
*
* ll count(T l, T r, T mask = 0) : O(B)
* mask XOR [l..r)
*/
template <class T = ll>
class Binary_trie {
// : https://kazuma8128.hatenablog.com/entry/2018/05/06/022654
struct Node {
ll cnt; //
Node* ch[2]; //
Node() : cnt(0), ch{ nullptr, nullptr } {}
};
Node* root; //
int B; //
Node* insert_sub(Node* t, T val, ll cnt, int b) {
//
if (t == nullptr) t = new Node;
//
t->cnt += cnt;
//
if (b < 0) return t;
//
T f = (val >> b) & T(1);
t->ch[f] = insert_sub(t->ch[f], val, cnt, b - 1);
//
return t;
}
Node* erase_sub(Node* t, T val, ll cnt, int b) {
//
Assert(t != nullptr && t->cnt >= cnt);
//
t->cnt -= cnt;
// 0
if (t->cnt == 0) {
delete t;
return nullptr;
}
//
if (b < 0) return t;
//
T f = (val >> b) & T(1);
t->ch[f] = erase_sub(t->ch[f], val, cnt, b - 1);
//
return t;
}
T min_element_sub(Node* t, T mask, int b) const {
Assert(t != nullptr);
// 0
if (b < 0) return 0;
//
int g = (int)((mask >> b) & T(1));
if (t->ch[g] == nullptr) g ^= 1;
T val = min_element_sub(t->ch[g], mask, b - 1);
//
val |= g << b;
return val;
}
T get_sub(Node* t, T mask, ll k, int b) const {
// 0
if (b < 0) return 0;
//
T g = (mask >> b) & T(1);
ll lk = (t->ch[g] != nullptr ? t->ch[g]->cnt : 0);
T val;
if (k < lk) val = get_sub(t->ch[g], mask, k, b - 1) | (g << b);
else val = get_sub(t->ch[g ^ T(1)], mask, k - lk, b - 1) | ((g ^ T(1)) << b);
return val;
}
ll lower_bound_sub(Node* t, T mask, T val, int b) const {
// 0
if (t == nullptr || b < 0) return 0;
// val b
T f = (val >> b) & T(1);
T g = (mask >> b) & T(1);
ll res = 0;
if (f == T(1) && t->ch[g] != nullptr) res += t->ch[g]->cnt;
res += lower_bound_sub(t->ch[f ^ g], mask, val, b - 1);
return res;
}
void free_sub(Node* t) {
if (t == nullptr) return;
free_sub(t->ch[0]);
free_sub(t->ch[1]);
delete t;
}
void print_sub(Node* t, T val, int b, ostream& os) const {
if (t == nullptr) return;
if (b < 0) {
os << "(" << val << "," << t->cnt << ") ";
return;
}
print_sub(t->ch[0], val << 1, b - 1, os);
print_sub(t->ch[1], (val << 1) | T(1), b - 1, os);
}
public:
// : O(1)
Binary_trie(int B_ = 62) : root(nullptr), B(B_) {
// verify : https://judge.yosupo.jp/problem/ordered_set
}
// O(n B)
~Binary_trie() {
free_sub(root);
}
// : O(1)
ll size() const {
return root != nullptr ? root->cnt : 0;
}
// 0 : O(1)
bool empty() const {
return root == nullptr;
}
// val cnt[=1] : O(B)
void insert(T val, ll cnt = 1) {
// verify : https://judge.yosupo.jp/problem/set_xor_min
root = insert_sub(root, val, cnt, B - 1);
}
// val cnt[=1] : O(B)
void erase(T val, ll cnt = 1) {
// verify : https://judge.yosupo.jp/problem/set_xor_min
root = erase_sub(root, val, cnt, B - 1);
}
// mask[=0] XOR : O(B)
T max_element(T mask = 0) const {
// verify : https://judge.yosupo.jp/problem/double_ended_priority_queue
return min_element_sub(root, ~mask, B - 1);
}
// mask[=0] XOR : O(B)
T min_element(T mask = 0) const {
// verify : https://judge.yosupo.jp/problem/set_xor_min
return min_element_sub(root, mask, B - 1);
}
// mask[=0] XOR i 0-indexed -1
T get(ll i, T mask = 0) const {
// verify : https://judge.yosupo.jp/problem/ordered_set
if (i < 0 || size() <= i) return T(-1);
return get_sub(root, mask, i, B - 1);
}
// mask[=0] XOR val 0-indexed : O(B)
ll lower_bound(T val, T mask = 0) const {
// verify : https://judge.yosupo.jp/problem/ordered_set
// if (val <= 0) return 0LL;
// if (val >= (T(1) << B)) return size();
return lower_bound_sub(root, mask, val, B - 1);
}
// mask[=0] XOR val 0-indexed : O(B)
ll upper_bound(T val, T mask = 0) const {
// verify : https://judge.yosupo.jp/problem/ordered_set
return lower_bound_sub(root, mask, val + 1, B - 1);
}
// val : O(B)
ll count(T val) const {
// verify : https://judge.yosupo.jp/problem/associative_array
return upper_bound(val) - lower_bound(val);
}
// mask[=0] XOR [l..r) : O(B)
ll count(T l, T r, T mask = 0) const {
// verify : https://judge.yosupo.jp/problem/ordered_set
return lower_bound(r, mask);// -lower_bound(l, mask);
}
#ifdef _MSC_VER
friend ostream& operator<<(ostream& os, const Binary_trie& bt) {
bt.print_sub(bt.root, T(0), bt.B - 1, os);
return os;
}
#endif
};
void make_testcase() {
int n = (int)2e5;
ll k = (ll)n * (n - 1) / 2;
vl a(n);
// iota(all(a), 0);
cout << n << " " << k << endl;
rep(i, n) cout << a[i] << " \n"[i == n - 1];
exit(0);
}
int main() {
// input_from_file("input.txt");
// output_to_file("output.txt");
int n; ll k;
cin >> n >> k;
vi a(n);
cin >> a;
// sort(all(a)); //
//
mt19937_64 mt((int)time(NULL));
shuffle(all(a), mt);
dump(n, k); dump(a); dump("-----------");
//vl aa;
//rep(i, n) repi(j, i + 1, n - 1) aa.push_back(a[i] ^ a[j]);
//sort(all(aa));
//dump(aa);
int b = 29;
// x k
auto okQ = [&](int x) {
dump("-------", bitset<30>(x), x, "-------");
// bit
Binary_trie<int> B(30 - b);
ll cnt = 0; ll rem = (ll)n * (n - 1) / 2;
rep(i, n) {
cnt += B.count(0, (x >> b), a[i] >> b);
rem -= i;
// a
// a
// Binary_trie
if (cnt >= k) break;
if (cnt + rem < k) break;
B.insert(a[i] >> b);
}
b--;
dump(cnt);
return cnt >= k;
};
cout << meguru_search((1 << 30), 0, okQ) - 1 << "\n";
}
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