結果

問題 No.2724 Coprime Game 1
ユーザー 👑 Nachia
提出日時 2024-04-12 21:30:58
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 2,695 bytes
コンパイル時間 939 ms
コンパイル使用メモリ 95,824 KB
最終ジャッジ日時 2025-02-21 00:06:36
ジャッジサーバーID
（参考情報） 		judge4 / judge1
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 * 1
other AC * 1 WA * 1 TLE * 1 -- * 4
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

#ifdef NACHIA
#define _GLIBCXX_DEBUG
#else
#define NDEBUG
#endif
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <utility>
#include <queue>
#include <array>
#include <cmath>
#include <atcoder/modint>
namespace nachia{
long long CountingPrimes(long long maxval){
    using i64 = long long;
    i64 n = maxval;
    if(n <= 1) return 0;
    i64 sqrtn = 0; while(sqrtn * sqrtn <= n) sqrtn++; sqrtn--;
    
    std::vector<i64> prefix_sum_fairy(sqrtn+1, 0);
    for(i64 i=1; i<=sqrtn; i++) prefix_sum_fairy[i] = i-1;
    std::vector<i64> prefix_sum_devil(sqrtn+1, 0);
    for(i64 i=1; i<=sqrtn; i++) prefix_sum_devil[i] = n/i-1;
    for(i64 p=2; p<=sqrtn; p++){
        i64 prime_count_p = prefix_sum_fairy[p];
        i64 prime_count_p_minus1 = prefix_sum_fairy[p-1];
        if(prime_count_p == prime_count_p_minus1) continue;
        for(i64 devil_id = 1; devil_id <= sqrtn; devil_id++){
            if(devil_id * p <= sqrtn){
                prefix_sum_devil[devil_id] -= prefix_sum_devil[devil_id * p] - prime_count_p_minus1;
            }
            else{
                i64 tg_fairy = n / (devil_id * p);
                if(tg_fairy < p) break;
                prefix_sum_devil[devil_id] -= prefix_sum_fairy[tg_fairy] - prime_count_p_minus1;
            }
        }
        for(i64 fairy_id = sqrtn/p; fairy_id >= p; fairy_id--){
            i64 dc = prefix_sum_fairy[fairy_id] - prime_count_p_minus1;
            i64 max_tg = std::min(fairy_id * p + p - 1, sqrtn);
            for(i64 tg_fairy = fairy_id * p; tg_fairy <= max_tg; tg_fairy++) prefix_sum_fairy[tg_fairy] -= dc;
        }
    }
    return prefix_sum_devil[1];
}
} // namespace nachia
using i64 = long long;
using u64 = unsigned long long;
#define rep(i,n) for(int i=0; i<int(n); i++)
#define repr(i,n) for(int i=int(n)-1; i>=0; i--)
const i64 INF = 1001001001001001001;
const char* yn(bool x){ return x ? "Yes" : "No"; }
template<typename A> void chmin(A& l, const A& r){ if(r < l) l = r; }
template<typename A> void chmax(A& l, const A& r){ if(l < r) l = r; }
template<typename A> using nega_queue = std::priority_queue<A,std::vector<A>,std::greater<A>>;
using Modint = atcoder::static_modint<998244353>;
//#include "nachia/vec.hpp"
using namespace std;
void unit(){
    int N; cin >> N;
    int n = N/2+1;
    int c = N - 1 - nachia::CountingPrimes(N-1) + nachia::CountingPrimes(n-1);
    cout << (c%2 == 0 ? "K\n" : "P\n");
}
void testcase(){
    int T; cin >> T;
    rep(t,T) unit();
}
int main(){
    ios::sync_with_stdio(false); cin.tie(nullptr);
    #ifdef NACHIA
    int T; cin >> T; for(int t=0; t<T; T!=++t?(cout<<'\n'),0:0)
    #endif
    testcase();
    return 0;
}
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