結果

問題 No.2977 Kth Xor Pair
ユーザー hitonanode
提出日時 2024-12-03 01:38:16
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,793 ms / 3,000 ms
コード長 9,529 bytes
コンパイル時間 2,011 ms
コンパイル使用メモリ 187,224 KB
実行使用メモリ 58,504 KB
最終ジャッジ日時 2024-12-03 01:39:00
合計ジャッジ時間 39,782 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge5
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 * 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 <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <numeric>
#include <optional>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }
template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r
    .first, l.second + r.second); }
template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r
    .first, l.second - r.second); }
template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end
    ()); return vec; }
template <class T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <class T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << 
    ']'; return os; }
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v 
    << ','; os << ']'; return os; }
template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, 
    tpl); return is; }
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { 
    ((os << args << ','), ...);}, tpl); return os << ')'; }
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os 
    << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << 
    ']'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; 
    return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << 
    '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << 
    ','; os << '}'; return os; }
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa
    .second << ')'; }
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v
    .first << "=>" << v.second << ','; os << '}'; return os; }
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp) { os << '{'; for 
    (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9
    ;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET 
    << std::endl
#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << 
    __FILE__ << COLOR_RESET << std::endl : std::cerr)
#else
#define dbg(x) ((void)0)
#define dbgif(cond, x) ((void)0)
#endif
#include <vector>
// disjoint set of nonnegative integers
template <class Int, class Count>
struct BinaryTrie {
    int maxD;
    std::vector<Count> deg, subtree_sum;
    std::vector<int> ch0, ch1, par;
    int _new_node(int id_par) {
        deg.emplace_back(Count());
        subtree_sum.emplace_back(Count());
        ch0.emplace_back(-1);
        ch1.emplace_back(-1);
        par.emplace_back(id_par);
        return (int)ch0.size() - 1;
    }
    BinaryTrie(int maxD = 0) : maxD(maxD) { _new_node(-1); }
    // Return index of x.
    // Create nodes to express x if needed.
    int _goto(Int x) {
        int now = 0;
        for (int d = maxD - 1; d >= 0; --d) {
            int nxt = ((x >> d) & 1) ? ch1[now] : ch0[now];
            if (nxt == -1) {
                nxt = _new_node(now);
                (((x >> d) & 1) ? ch1[now] : ch0[now]) = nxt;
            }
            now = nxt;
        }
        return now;
    }
    // insert x
    void insert(Int x, Count c = 1) {
        int now = _goto(x);
        deg[now] += c;
        while (now >= 0) subtree_sum[now] += c, now = par[now];
    }
    // delete x if exists
    void erase(Int x) {
        int now = _goto(x);
        if (deg[now] > 0) {
            Int r = deg[now];
            deg[now] = 0;
            while (now >= 0) subtree_sum[now] -= r, now = par[now];
        }
    }
    // min(y ^ x) for y in trie
    Int xor_min(Int x) {
        Int ret = 0;
        int now = 0;
        if (!subtree_sum[now]) return -1;
        for (int d = maxD - 1; d >= 0; d--) {
            int y = ((x >> d) & 1) ? ch1[now] : ch0[now];
            if (y != -1 and subtree_sum[y]) {
                now = y;
            } else {
                ret += Int(1) << d, now = ch0[now] ^ ch1[now] ^ y;
            }
        }
        return ret;
    }
    // Count elements y such that x ^ y < thres
    Count count_less_xor(Int x, Int thres) const {
        Count ret = Count();
        int now = 0;
        for (int d = maxD - 1; d >= 0; d--) {
            if (now == -1) break;
            const bool bit_x = (x >> d) & 1;
            
            if ((thres >> d) & 1) {
                const int child = bit_x ? ch1[now] : ch0[now];
                if (child != -1) ret += subtree_sum[child];
                now = bit_x ? ch0[now] : ch1[now];
            } else {
                now = bit_x ? ch1[now] : ch0[now];
            }
        }
        return ret;
    }
};
int main() {
    int N;
    long long K;
    cin >> N >> K;
    vector<int> A(N);
    for (auto &x : A) cin >> x;
    constexpr int D = 30;
    BinaryTrie<int, int> trie(D);
    for (int a : A) trie.insert(a);
    int lo = 0, hi = 1 << D;  // [lo, hi)
    while (lo + 1 < hi) {
        const int mid = (lo + hi) / 2;
        long long cnt = 0;
        for (int a : A) cnt += trie.count_less_xor(a, mid);
        (cnt >= K * 2 + N ? hi : lo) = mid;
    }
    cout << lo << '\n';
}
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