結果

問題 No.2977 Kth Xor Pair
ユーザー apricity
提出日時 2024-12-01 17:06:35
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 2,387 ms / 3,000 ms
コード長 17,472 bytes
コンパイル時間 1,519 ms
コンパイル使用メモリ 140,404 KB
実行使用メモリ 170,036 KB
最終ジャッジ日時 2024-12-01 17:07:50
合計ジャッジ時間 45,012 ms
ジャッジサーバーID
(参考情報)
judge2 / judge3
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 2
other AC * 34
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

#include<iostream>
#include<string>
#include<vector>
#include<algorithm>
#include<numeric>
#include<cmath>
#include<utility>
#include<tuple>
#include<array>
#include<cstdint>
#include<cstdio>
#include<iomanip>
#include<map>
#include<set>
#include<unordered_map>
#include<unordered_set>
#include<queue>
#include<stack>
#include<deque>
#include<bitset>
#include<cctype>
#include<chrono>
#include<random>
#include<cassert>
#include<cstddef>
#include<iterator>
#include<string_view>
#include<type_traits>
#include<functional>
#ifdef LOCAL
# include "debug_print.hpp"
# define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
# define debug(...) (static_cast<void>(0))
#endif
using namespace std;
namespace io {
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
is >> p.first >> p.second;
return is;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (auto &x : v) is >> x;
return is;
}
template <typename T, size_t N = 0>
istream &operator>>(istream &is, array<T, N> &v) {
for (auto &x : v) is >> x;
return is;
}
template <size_t N = 0, typename T>
istream& cin_tuple_impl(istream &is, T &t) {
if constexpr (N < std::tuple_size<T>::value) {
auto &x = std::get<N>(t);
is >> x;
cin_tuple_impl<N + 1>(is, t);
}
return is;
}
template <class... T>
istream &operator>>(istream &is, tuple<T...> &t) {
return cin_tuple_impl(is, t);
}
template<typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
os << p.first << " " << p.second;
return os;
}
template<typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
int s = (int)v.size();
for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
return os;
}
template<typename T, size_t N>
ostream &operator<<(ostream &os, const array<T, N> &v) {
size_t n = v.size();
for (size_t i = 0; i < n; i++) {
if (i) os << " ";
os << v[i];
}
return os;
}
template <size_t N = 0, typename T>
ostream& cout_tuple_impl(ostream &os, const T &t) {
if constexpr (N < std::tuple_size<T>::value) {
if constexpr (N > 0) os << " ";
const auto &x = std::get<N>(t);
os << x;
cout_tuple_impl<N + 1>(os, t);
}
return os;
}
template <class... T>
ostream &operator<<(ostream &os, const tuple<T...> &t) {
return cout_tuple_impl(os, t);
}
void in() {}
template<typename T, class... U>
void in(T &t, U &...u) {
cin >> t;
in(u...);
}
void out() { cout << "\n"; }
template<typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
cout << t;
if (sizeof...(u)) cout << sep;
out(u...);
}
void outr() {}
template<typename T, class... U, char sep = ' '>
void outr(const T &t, const U &...u) {
cout << t;
outr(u...);
}
void __attribute__((constructor)) _c() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
cout << fixed << setprecision(15);
}
} // namespace io
using io::in;
using io::out;
using io::outr;
using ll = long long;
using D = double;
using LD = long double;
using P = pair<ll, ll>;
using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using i128 = __int128;
using u128 = unsigned __int128;
using vi = vector<ll>;
template <class T> using vc = vector<T>;
template <class T> using vvc = vector<vc<T>>;
template <class T> using vvvc = vector<vvc<T>>;
template <class T> using vvvvc = vector<vvvc<T>>;
template <class T> using vvvvvc = vector<vvvvc<T>>;
#define vv(type, name, h, ...) \
vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...) \
vector<vector<vector<type>>> name( \
h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...) \
vector<vector<vector<vector<type>>>> name( \
a, vector<vector<vector<type>>>( \
b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
template<typename T> using PQ = priority_queue<T,vector<T>>;
template<typename T> using minPQ = priority_queue<T, vector<T>, greater<T>>;
#define rep1(a) for(ll i = 0; i < a; i++)
#define rep2(i, a) for(ll i = 0; i < a; i++)
#define rep3(i, a, b) for(ll i = a; i < b; i++)
#define rep4(i, a, b, c) for(ll i = a; i < b; i += c)
#define overload4(a, b, c, d, e, ...) e
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define rrep1(a) for(ll i = (a)-1; i >= 0; i--)
#define rrep2(i, a) for(ll i = (a)-1; i >= 0; i--)
#define rrep3(i, a, b) for(ll i = (b)-1; i >= a; i--)
#define rrep4(i, a, b, c) for(ll i = (b)-1; i >= a; i -= c)
#define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__)
#define for_subset(t, s) for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define ALL(v) v.begin(), v.end()
#define RALL(v) v.rbegin(), v.rend()
#define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() )
#define SZ(v) ll(v.size())
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(c, x) distance((c).begin(), lower_bound(ALL(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(ALL(c), (x)))
template <typename T, typename U>
T SUM(const vector<U> &v) {
T res = 0;
for(auto &&a : v) res += a;
return res;
}
template <typename T>
vector<pair<T,int>> RLE(const vector<T> &v) {
if (v.empty()) return {};
T cur = v.front();
int cnt = 1;
vector<pair<T,int>> res;
for (int i = 1; i < (int)v.size(); i++) {
if (cur == v[i]) cnt++;
else {
res.emplace_back(cur, cnt);
cnt = 1; cur = v[i];
}
}
res.emplace_back(cur, cnt);
return res;
}
template<class T, class S>
inline bool chmax(T &a, const S &b) { return (a < b ? a = b, true : false); }
template<class T, class S>
inline bool chmin(T &a, const S &b) { return (a > b ? a = b, true : false); }
void YESNO(bool flag) { out(flag ? "YES" : "NO"); }
void yesno(bool flag) { out(flag ? "Yes" : "No"); }
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_sgn(int x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(ll x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(u64 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int highbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int highbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int highbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int highbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
template <typename T>
T get_bit(T x, int k) { return x >> k & 1; }
template <typename T>
T set_bit(T x, int k) { return x | T(1) << k; }
template <typename T>
T reset_bit(T x, int k) { return x & ~(T(1) << k); }
template <typename T>
T flip_bit(T x, int k) { return x ^ T(1) << k; }
template <typename T>
T popf(deque<T> &que) { T a = que.front(); que.pop_front(); return a; }
template <typename T>
T popb(deque<T> &que) { T a = que.back(); que.pop_back(); return a; }
template <typename T>
T pop(queue<T> &que) { T a = que.front(); que.pop(); return a; }
template <typename T>
T pop(stack<T> &que) { T a = que.top(); que.pop(); return a; }
template <typename T>
T pop(PQ<T> &que) { T a = que.top(); que.pop(); return a; }
template <typename T>
T pop(minPQ<T> &que) { T a = que.top(); que.pop(); return a; }
template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
if (check_ok) assert(check(ok));
while (abs(ok - ng) > 1) {
ll mid = (ok + ng) / 2;
(check(mid) ? ok : ng) = mid;
}
return ok;
}
template <typename F>
ll binary_search_real(F check, double ok, double ng, int iter = 60) {
for (int _ = 0; _ < iter; _++) {
double mid = (ok + ng) / 2;
(check(mid) ? ok : ng) = mid;
}
return (ok + ng) / 2;
}
// max x s.t. b*x <= a
ll div_floor(ll a, ll b) {
assert(b != 0);
if (b < 0) a = -a, b = -b;
return a / b - (a % b < 0);
}
// max x s.t. b*x < a
ll div_under(ll a, ll b) {
assert(b != 0);
if (b < 0) a = -a, b = -b;
return a / b - (a % b <= 0);
}
// min x s.t. b*x >= a
ll div_ceil(ll a, ll b) {
assert(b != 0);
if (b < 0) a = -a, b = -b;
return a / b + (a % b > 0);
}
// min x s.t. b*x > a
ll div_over(ll a, ll b) {
assert(b != 0);
if (b < 0) a = -a, b = -b;
return a / b + (a % b >= 0);
}
// x = a mod b (b > 0), 0 <= x < b
ll modulo(ll a, ll b) {
assert(b > 0);
ll c = a % b;
return c < 0 ? c + b : c;
}
// (q,r) s.t. a = b*q + r, 0 <= r < b (b > 0)
// div_floor(a,b), modulo(a,b)
pair<ll,ll> divmod(ll a, ll b) {
ll q = div_floor(a,b);
return {q, a - b*q};
}
template <typename T, int MAX_LOG>
struct BinaryTrie {
public:
struct Node {
Node *nxt[2];
int exist;
vector<int> accept;
Node(): nxt{nullptr, nullptr}, exist(0) {}
};
Node *root;
T lazy;
explicit BinaryTrie(): root(new Node()), lazy(T(0)) {}
void insert(const T &x, int idx = -1) {
insert(root, x, MAX_LOG, 1, idx);
}
void erase(const T &x) {
insert(root, x, MAX_LOG, -1, -1);
}
Node *find(const T &x) {
return find(root, x, MAX_LOG);
}
int count(const T &x) {
Node *nx = find(x);
return nx == nullptr ? 0 : nx->exist;
}
pair<T, Node *> min_element() {
assert(root->exist > 0);
return kth_element(0);
}
pair<T, Node *> max_element() {
assert(root->exist > 0);
return kth_element(root->exist - 1);
}
pair<T, Node *> kth_element(int k) {
assert(0 <= k and k < root->exist);
return kth_element(root, k, MAX_LOG);
}
int count_less(const T &x) {
return count_less(root, x, MAX_LOG);
}
int count_leq(const T &x) {
return count_less(root, x+1, MAX_LOG);
}
int count_greater(const T &x) {
return root->exist - count_less(root, x+1, MAX_LOG);
}
int count_geq(const T &x) {
return root->exist - count_less(root, x, MAX_LOG);
}
void operate_xor(const T &x) {
lazy ^= x;
}
private:
void insert(Node *n_cur, const T &x, int depth, int delta, int idx) {
if (depth == -1) {
n_cur->exist += delta;
if (idx != -1) n_cur->accept.emplace_back(idx);
}
else {
bool nxt_01 = (lazy >> depth & 1) ^ (x >> depth & 1);
if(!n_cur->nxt[nxt_01]) n_cur->nxt[nxt_01] = new Node();
insert(n_cur->nxt[nxt_01], x, depth - 1, delta, idx);
n_cur->exist += delta;
}
}
Node *find(Node *n_cur, const T &x, int depth) {
if (depth == -1) {
return n_cur;
}
else {
bool nxt_01 = (lazy >> depth & 1) ^ (x >> depth & 1);
Node *n_nxt = n_cur->nxt[nxt_01];
return n_nxt == nullptr ? n_nxt : find(n_nxt, x, depth - 1);
}
}
pair<T, Node *> kth_element(Node *n_cur, int k, int depth) {
if (depth == -1) {
return make_pair(0, n_cur);
}
else {
bool nxt_01 = lazy >> depth & 1;
int comp = n_cur->nxt[nxt_01] == nullptr ?
0 : n_cur->nxt[nxt_01]->exist;
if (comp <= k) {
pair<T, Node*> ret = kth_element(
n_cur->nxt[nxt_01 ^ 1], k - comp, depth - 1);
ret.first |= T(1) << depth;
return ret;
}
else{
return kth_element(n_cur->nxt[nxt_01], k, depth - 1);
}
}
}
int count_less(Node *n_cur, const T &x, int depth) {
if (depth == -1) return 0;
int ret = 0;
bool nxt_01 = lazy >> depth & 1;
bool xi = x >> depth & 1;
if (xi and n_cur->nxt[nxt_01] != nullptr)
ret += n_cur->nxt[nxt_01]->exist;
if (n_cur->nxt[nxt_01 ^ xi] != nullptr)
ret += count_less(n_cur->nxt[nxt_01 ^ xi], x, depth - 1);
return ret;
}
};
template<typename T, int MAX_LOG>
struct BinaryTrie_Pool {
struct Node {
int nxt[2];
int exist;
vector<int> accept;
Node(): nxt{-1, -1}, exist(0) {}
};
vector<Node> nodes;
int root;
T lazy;
explicit BinaryTrie_Pool(): root(0), lazy(T(0)) {
nodes.emplace_back(Node());
}
void insert(const T &x, int delta, int idx = -1) {
int n_cur = root;
for (int depth = MAX_LOG - 1; depth >= 0; depth--) {
bool nxt_01 = (x >> depth & 1) ^ (lazy >> depth & 1);
if (nodes[n_cur].nxt[nxt_01] == -1) {
nodes[n_cur].nxt[nxt_01] = (int)nodes.size();
nodes.emplace_back(Node());
}
nodes[n_cur].exist += delta;
n_cur = nodes[n_cur].nxt[nxt_01];
}
nodes[n_cur].exist += delta;
if(idx != -1) nodes[n_cur].accept.emplace_back(idx);
}
void insert(const T &x, int idx = -1) {
insert(x, 1, idx);
}
void erase(const T &x) {
insert(x, -1, -1);
}
int find(const T &x) const {
int n_cur = root;
for (int depth = MAX_LOG - 1; depth >= 0; depth--) {
bool nxt_01 = (x >> depth & 1) ^ (lazy >> depth & 1);
int n_nxt = nodes[n_cur].nxt[nxt_01];
if (n_nxt == -1) return -1;
n_cur = n_nxt;
}
return n_cur;
}
int count(const T &x) const {
int nx = find(x);
return nx == -1 ? 0 : nodes[nx].exist;
}
pair<int, int> kth_element(int n_cur, int k, int depth) const {
if (depth == -1) return make_pair(0, n_cur);
bool nxt_01 = (lazy >> depth) & 1;
int comp = nodes[n_cur].nxt[nxt_01] == -1 ?
0 : nodes[n_cur].nxt[nxt_01].exist;
if (comp <= k) {
pair<int, int> ret = kth_element(
nodes[n_cur].nxt[nxt_01 ^ 1], k - comp, depth - 1);
ret.first |= T(1) << depth;
return ret;
}
else{
return kth_element(nodes[n_cur].nxt[nxt_01], k, depth-1);
}
}
pair<int, int> kth_element(int k) const {
assert(0 <= k and k < nodes[root].exist);
int n_cur = root;
T ret = 0;
for (int depth = MAX_LOG - 1; depth >= 0; depth--) {
bool nxt_01 = (lazy >> depth) & 1;
int comp = nodes[n_cur].nxt[nxt_01] == -1 ?
0 : nodes[n_cur].nxt[nxt_01].exist;
if (comp <= k) {
k -= comp;
n_cur = nodes[n_cur].nxt[nxt_01 ^ 1];
ret |= T(1) << depth;
}
else{
n_cur = nodes[n_cur].nxt[nxt_01];
}
}
// return make_pair(ret, n_cur);
return kth_element(root, k, MAX_LOG - 1);
}
pair<int, int> min_element() const {
assert(nodes[root].exist > 0);
return kth_element(0);
}
pair<int, int> max_element() const {
assert(nodes[root].exist > 0);
return kth_element(nodes[root].exist - 1);
}
int count_less(int n_cur, const T &x, int depth) const {
if (depth == -1) return 0;
int ret = 0;
bool nxt_01 = (lazy >> depth) & 1;
bool xi = (x >> depth) & 1;
if (xi and nodes[n_cur].nxt[nxt_01] != -1)
ret += nodes[nodes[n_cur].nxt[nxt_01]].exist;
if (nodes[n_cur].nxt[nxt_01 ^ xi] != -1)
ret += count_less(nodes[n_cur].nxt[nxt_01 ^ xi], x, depth - 1);
return ret;
}
int count_less(const T &x) const {
/*
int ret = 0;
int n_cur = root;
for (int depth = MAX_LOG - 1; depth >= 0; depth--) {
bool nxt_01 = (lazy >> depth) & 1;
bool xi = (x >> depth) & 1;
if (xi and nodes[n_cur].nxt[nxt_01] != -1) {
ret += nodes[nodes[n_cur].nxt[nxt_01]].exist;
}
if (nodes[n_cur].nxt[nxt_01 ^ xi] != -1) {
n_cur = nodes[n_cur].nxt[nxt_01 ^ xi];
}
else break;
}
return ret;
*/
return count_less(root, x, MAX_LOG - 1);
}
int count_leq(const T &x) const {
return count_less(root, x+1, MAX_LOG - 1);
}
int count_greater(const T &x) const {
return nodes[root].exist - count_less(x+1);
}
int count_geq(const T &x) const {
return nodes[root].exist - count_less(x);
}
void operate_xor(const T &x) {
lazy ^= x;
}
};
int main() {
ll n,k; in(n,k);
k = k*2 + n;
vector<int> a(n); in(a);
BinaryTrie_Pool<int, 30> bt;
rep(i,n) bt.insert(a[i]);
int ans = binary_search([&](int m){
ll cleq = 0;
rep(i,n) {
bt.operate_xor(a[i]);
cleq += bt.count_leq(m);
bt.operate_xor(a[i]);
}
return cleq >= k;
}, (1<<30)-1, -1, false);
out(ans);
}
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