結果

問題 No.2672 Subset Xor Sum
コンテスト
ユーザー Xelmeph
提出日時 2024-02-28 19:23:52
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 88 ms / 2,000 ms
コード長 5,501 bytes
コンパイル時間 1,347 ms
コンパイル使用メモリ 136,148 KB
最終ジャッジ日時 2025-02-19 21:55:21
ジャッジサーバーID
（参考情報） 		judge1 / judge4
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 * 66
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 # 

#include <iostream>
#include <iomanip>
#include <fstream>
#include <string>
#include <array>
#include <vector>
#include <deque>
#include <list>
#include <set>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <stack>
#include <queue>
#include <bitset>
#include <tuple>
#include <cmath>
#include <complex>
#include <algorithm>
#include <utility>
#include <regex>
#include <cstdint>
#include <numeric>
#include <functional>
#include <cassert>

using namespace std;

namespace utils{
#define ALL(x) begin(x), end(x)
#define RALL(x) rbegin(x), rend(x)
    ///----- aliases
    using ll = long long int;
    using ull = unsigned long long;

    template<class T, class Compare> using p_queue = priority_queue<T, vector<T>, Compare>;
    template<class T> using min_queue = p_queue<T, greater<T>>;
    template<class T> using max_queue = p_queue<T, less<T>>;

    template<class T> inline bool CHMIN(T& X, const T& A){ if(X > A) {X = A; return true;} return false; }
    template<class T> inline bool CHMAX(T& X, const T& A){ if(X < A) {X = A; return true;} return false; }

    ///----- vector I/O
    template<class T>
    vector<T> VEC(size_t n, T t){
        return vector<T>(n, t);
    }

    template<class ...Ts>
    auto VEC(size_t n, Ts ... ts){
        return vector<decltype(VEC(ts...))>(n, VEC(ts...));
    }


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

    template<class T>
    ostream& operator<<(ostream& os, const vector<T>& v){
        auto p = v.begin();
        assert(p != v.end());
        os << *p++;
        while(p != v.end()){
            os << ' ' << *p++;
        }
        return os ;
    }

    template<class T>
    ostream& operator<<(ostream& os, const vector<vector<T>>& v){
        auto p = v.begin();
        assert(p != v.end());
        os << *p++;
        while(p != v.end()){
            os << '\n' << *p++;
        }
        return os;
    }

    ///----- tuple I/O
    template <class S, class T>
    istream& operator>>(istream& is, tuple<S, T>& t){
        return is >> get<0>(t) >> get<1>(t);
    }

    template <class S, class T>
    istream& operator>>(istream& is, pair<S, T>& t){
        return is >> get<0>(t) >> get<1>(t);
    }

    template <class S, class T, class U>
    istream& operator>>(istream& is, tuple<S, T, U>& t){
        return is >> get<0>(t) >> get<1>(t) >> get<2>(t);
    }

    template <class S, class T>
    ostream& operator<<(ostream& os, const tuple<S, T>& t){
        return os << get<0>(t) << ' ' <<  get<1>(t);
    }

    template <class S, class T>
    ostream& operator<<(ostream& os, const pair<S, T>& t){
        return os << get<0>(t) << ' ' <<  get<1>(t);
    }

    template <class S, class T, class U>
    ostream& operator<<(ostream& os, const tuple<S, T, U>& t){
        return os << get<0>(t) << ' ' <<  get<1>(t) << ' ' <<  get<2>(t);
    }

    ///----- constants
    constexpr ll INFLL   = 1'000'000'000'000'000'020ll;
    constexpr ll INF     = 1'000'000'009;
    constexpr double PI      = 3.14'159'265'358'979'323'846;
    constexpr double EPS     = 1e-12;
}
using namespace utils;


class solver{
    istream& is;
    ostream& os;

public:
    solver(istream& I, ostream& O) :is(I), os(O) {}
    int N;
    vector<int> A;
    const int amax = 1<<13;

    bool input() {
        N = 0;
        is >> N;
        A.resize(N);
        is >> A;
        return !!is;
    }

    bool reduce(){
        // XOR A =/= 0
        if(accumulate(ALL(A), 0, [](int a, int b) { return a ^ b;})){
            os << "No\n";
            return true;
        }
        if(N==2){
            if(A[0] != 0){
                os << "No\n";
                return true;
            }
            else {
                os << "Yes\n";
                return true;
            }
        }

        return false;
    }

    bool check(const vector<int>& v) const {
        for (auto &&x: v) {
            assert(x <= 1);
        } // end x
        // S[i][j]:: i以下でjを作れるか? 0: NG, 1: OK (ALL), 2: OK (PARTIAL)
        auto S = VEC(amax, 0);
        int f = 0;

        for (int i = 0; i < amax; ++i) {
            if(v[i] == 0) continue;
            auto nx = VEC(amax, 0);
            for (int j = 0; j < amax; ++j) {
                nx[j] = S[j] > 0 ? 2 : 0;
            } // end j
            for (int j = 0; j < amax; ++j) {
                CHMAX(nx[i^j], S[j]);
            } // end j;
            nx[i] = (f > 0) + 1;
            f++;
            S = std::move(nx);
        } // end i
        return S[0] == 2;
    }

    void run();
};

void solver::run(){
    if(!input()) return;

    if(reduce()) return;
    // XOR A == 0

    vector<int> bn(amax);
    for (auto &&a: A) {
        bn[a]++;
        if(bn[a] >= 2 ){
            os << "Yes\n";
            return;
        }
    } // end a

    os << (check(bn) ? "Yes\n" : "No\n");
}

int main(int argc, char *argv[]) {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << setprecision(16) << scientific;
#ifdef XELMH
    string test_cases = "test_b.txt";
    cerr << test_cases << " -->" << endl;
    auto fs = fstream(test_cases, fstream::in);
    int loop = 0;
    while(fs) {
        loop++;
        cout << '#' << loop << "#------\n";
        solver(fs, cout).run();
    }
    if(loop <= 1) {
        cout << "===" << endl;
        while(cin) solver(cin, cout).run();
    }
#else
    solver(cin, cout).run();
#endif
    return 0;
}
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