結果

問題 No.2977 Kth Xor Pair
ユーザー noya2
提出日時 2024-12-02 23:10:48
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,685 ms / 3,000 ms
コード長 10,445 bytes
コンパイル時間 3,274 ms
コンパイル使用メモリ 255,276 KB
実行使用メモリ 56,320 KB
最終ジャッジ日時 2024-12-02 23:11:26
合計ジャッジ時間 35,397 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
（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 # 

#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
using namespace std;

#include<bits/stdc++.h>
#line 1 "/Users/noya2/Desktop/Noya2_library/template/inout_old.hpp"
namespace noya2 {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p){
    os << p.first << " " << p.second;
    return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p){
    is >> p.first >> p.second;
    return is;
}

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>
istream &operator>>(istream &is, vector<T> &v){
    for (auto &x : v) is >> x;
    return is;
}

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...);
}

template<typename T>
void out(const vector<vector<T>> &vv){
    int s = (int)vv.size();
    for (int i = 0; i < s; i++) out(vv[i]);
}

struct IoSetup {
    IoSetup(){
        cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << fixed << setprecision(15);
        cerr << fixed << setprecision(7);
    }
} iosetup_noya2;

} // namespace noya2
#line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp"
namespace noya2{

const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 =  998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";

void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }

} // namespace noya2
#line 2 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"

#line 6 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"

namespace noya2{

unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
    if (a == 0 || b == 0) return a + b;
    int n = __builtin_ctzll(a); a >>= n;
    int m = __builtin_ctzll(b); b >>= m;
    while (a != b) {
        int mm = __builtin_ctzll(a - b);
        bool f = a > b;
        unsigned long long c = f ? a : b;
        b = f ? b : a;
        a = (c - b) >> mm;
    }
    return a << std::min(n, m);
}

template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(std::abs(a),std::abs(b))); }

long long sqrt_fast(long long n) {
    if (n <= 0) return 0;
    long long x = sqrt(n);
    while ((x + 1) * (x + 1) <= n) x++;
    while (x * x > n) x--;
    return x;
}

template<typename T> T floor_div(const T n, const T d) {
    assert(d != 0);
    return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}

template<typename T> T ceil_div(const T n, const T d) {
    assert(d != 0);
    return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}

template<typename T> void uniq(std::vector<T> &v){
    std::sort(v.begin(),v.end());
    v.erase(unique(v.begin(),v.end()),v.end());
}

template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }

template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }

template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }

} // namespace noya2
#line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"

#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)
#define all(v) (v).begin(),(v).end()

using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;

namespace noya2{

/*　~ (. _________ . /)　*/

}

using namespace noya2;


#line 2 "c.cpp"

template<typename Int, int LOG>
struct binary_trie {
    struct node {
        int par;
        std::array<int,2> ch;
        int size;
        bool exists;
        node (int _par, std::array<int,2> _ch, int _size = 0, bool _exists = false) : par(_par), ch(_ch), size(_size), exists(_exists) {}
    };
    std::vector<node> nodes;
    int new_node(int par){
        int id = nodes.size();
        nodes.emplace_back(node(par, {-1, -1}));
        return id;
    }
    void update(int v){
        nodes[v].size = int(nodes[v].exists) + size(nodes[v].ch[0]) + size(nodes[v].ch[1]);
    }
    Int lazy = 0;

    binary_trie () : lazy(0) {
        new_node(-1);
    }

    int size(int id = 0){
        if (id == -1) return 0;
        return nodes[id].size;
    }
    void xor_all(Int x){
        lazy ^= x;
    }
    int insert(Int x){
        x ^= lazy;
        int v = 0;
        for (int i = LOG-1; i >= 0; i--){
            if (nodes[v].ch[x >> i & 1] == -1){
                nodes[v].ch[x >> i & 1] = new_node(v);
            }
            v = nodes[v].ch[x >> i & 1];
        }
        int ret = v;
        nodes[v].exists = true;
        update(v);
        while (v != 0){
            v = nodes[v].par;
            update(v);
        }
        return ret;
    }
    int erase(Int x){
        x ^= lazy;
        int v = 0;
        for (int i = LOG-1; i >= 0; i--){
            if (nodes[v].ch[x >> i & 1] == -1){
                return -1; // no erase
            }
            v = nodes[v].ch[x >> i & 1];
        }
        int ret = v;
        nodes[v].exists = false;
        update(v);
        while (v != 0){
            v = nodes[v].par;
            update(v);
        }
        return ret;
    }
    Int kth_element(int k){
        if (k < 0 || k >= size()) return -1;
        Int ret{};
        int v = 0;
        for (int i = LOG-1; i >= 0; i--){
            if (k < size(nodes[v].ch[lazy >> i & 1])){
                v = nodes[v].ch[lazy >> i & 1];
            }
            else {
                k -= size(nodes[v].ch[lazy >> i & 1]);
                v = nodes[v].ch[~lazy >> i & 1];
                ret |= Int{1} << i;
            }
        }
        return ret;
    }
};

template<typename Int, int LOG>
struct multi_binary_trie {
    struct node {
        int par;
        std::array<int,2> ch;
        int size;
        int exists;
        node (int _par, std::array<int,2> _ch, int _size = 0, int _exists = 0) : par(_par), ch(_ch), size(_size), exists(_exists) {}
    };
    std::vector<node> nodes;
    int new_node(int par){
        int id = nodes.size();
        nodes.emplace_back(node(par, {-1, -1}));
        return id;
    }
    void update(int v){
        nodes[v].size = int(nodes[v].exists) + size(nodes[v].ch[0]) + size(nodes[v].ch[1]);
    }
    Int lazy = 0;

    multi_binary_trie () : lazy(0) {
        new_node(-1);
    }

    int size(int id = 0){
        if (id == -1) return 0;
        return nodes[id].size;
    }
    void xor_all(Int x){
        lazy ^= x;
    }
    int insert(Int x){
        x ^= lazy;
        int v = 0;
        for (int i = LOG-1; i >= 0; i--){
            if (nodes[v].ch[x >> i & 1] == -1){
                nodes[v].ch[x >> i & 1] = new_node(v);
            }
            v = nodes[v].ch[x >> i & 1];
        }
        int ret = v;
        nodes[v].exists += 1;
        update(v);
        while (v != 0){
            v = nodes[v].par;
            update(v);
        }
        return ret;
    }
    // erase all x
    int erase(Int x){
        x ^= lazy;
        int v = 0;
        for (int i = LOG-1; i >= 0; i--){
            if (nodes[v].ch[x >> i & 1] == -1){
                return -1; // no erase
            }
            v = nodes[v].ch[x >> i & 1];
        }
        int ret = v;
        nodes[v].exists = 0;
        update(v);
        while (v != 0){
            v = nodes[v].par;
            update(v);
        }
        return ret;
    }
    // erase one x (if contains)
    int erase1(Int x){
        x ^= lazy;
        int v = 0;
        for (int i = LOG-1; i >= 0; i--){
            if (nodes[v].ch[x >> i & 1] == -1){
                return -1; // no erase
            }
            v = nodes[v].ch[x >> i & 1];
        }
        int ret = v;
        if (nodes[v].exists == 0){
            return ret;
        }
        nodes[v].exists -= 1;
        update(v);
        while (v != 0){
            v = nodes[v].par;
            update(v);
        }
        return ret;
    }
    Int kth_element(int k){
        if (k < 0 || k >= size()) return -1;
        Int ret{};
        int v = 0;
        for (int i = LOG-1; i >= 0; i--){
            if (k < size(nodes[v].ch[lazy >> i & 1])){
                v = nodes[v].ch[lazy >> i & 1];
            }
            else {
                k -= size(nodes[v].ch[lazy >> i & 1]);
                v = nodes[v].ch[~lazy >> i & 1];
                ret |= Int{1} << i;
            }
        }
        return ret;
    }
    // equal to the number of elements less than x
    int order(Int x){
        int ret = 0;
        int v = 0;
        for (int i = LOG-1; i >= 0; i--){
            if (v == -1) break;
            if (x >> i & 1){
                ret += size(nodes[v].ch[lazy >> i & 1]);
                v = nodes[v].ch[~lazy >> i & 1];
            }
            else {
                v = nodes[v].ch[lazy >> i & 1];
            }
        }
        return ret;
    }
    node operator[](int v){
        return nodes[v];
    }
    void reserve(int rsize){
        nodes.reserve(rsize);
    }
};

void solve(){
    int n; in(n);
    ll k; in(k); k--;
    multi_binary_trie<uint,30> bt;
    bt.reserve(n*29);
    vector<uint> a(n); in(a);
    rep(i,n){
        bt.insert(a[i]);
    }
    k = 2*k + n;
    uint le = 0, ri = 1U<<30;
    while (ri - le > 1){
        uint md = (le + ri) / 2;
        ll sml = 0;
        rep(i,n){
            bt.xor_all(a[i]);
            sml += bt.order(md);
            bt.xor_all(a[i]);
        }
        if (sml <= k){
            le = md;
        }
        else {
            ri = md;
        }
    }
    out(le);
}

int main(){
    int t = 1; //in(t);
    while (t--) { solve(); }
}
0