結果

問題 No.2262 Fractions
ユーザー 👑 Nachia
提出日時 2023-04-07 23:36:01
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 404 ms / 2,000 ms
コード長 6,283 bytes
コンパイル時間 1,213 ms
コンパイル使用メモリ 89,104 KB
最終ジャッジ日時 2025-02-12 03:03:56
ジャッジサーバーID
（参考情報） 		judge4 / 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 * 1
other AC * 45
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ソースコード

diff # 

#line 2 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\math\\divisor-convolution.hpp"

#line 2 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\math\\prime-sieve-explicit.hpp"

#include <vector>
#include <algorithm>
#include <cassert>
#include <iostream>


namespace nachia{

namespace prime_sieve_explicit_internal{
    std::vector<bool> isprime = { false }; // a[x] := isprime(2x+1)

    void CalcIsPrime(int z){
        if((int)isprime.size() *2+1 < z+1){
            int new_z = isprime.size();
            while(new_z*2+1 < z+1) new_z *= 2;
            z = new_z-1;
            isprime.resize(z+1, true);
            for(int i=1; i*(i+1)*2<=z; i++) if(isprime[i]){
                for(int j=i*(i+1)*2; j<=z; j+=i*2+1) isprime[j] = false;
            }
        }
    }
    
    std::vector<int> prime_list = {2};
    int prime_list_max = 0;

    void CalcPrimeList(int z){
        while((int)prime_list.size() < z){
            if((int)isprime.size() <= prime_list_max + 1) CalcIsPrime(prime_list_max + 1);
            for(int p=prime_list_max+1; p<(int)isprime.size(); p++){
                if(isprime[p]) prime_list.push_back(p*2+1);
            }
            prime_list_max = isprime.size() - 1;
        }
    }

    void CalcPrimeListUntil(int z){
        if(prime_list_max < z){
            CalcIsPrime(z);
            for(int p=prime_list_max+1; p<(int)isprime.size(); p++){
                if(isprime[p]) prime_list.push_back(p*2+1);
            }
            prime_list_max = isprime.size() - 1;
        }
    }

}


bool IsprimeExplicit(int n){
    using namespace prime_sieve_explicit_internal;
    if(n == 2) return true;
    if(n % 2 == 0) return false;
    CalcIsPrime(n);
    return isprime[(n-1)/2];
}

int NthPrimeExplicit(int n){
    using namespace prime_sieve_explicit_internal;
    CalcPrimeList(n);
    return prime_list[n];
}

int PrimeCountingExplicit(int n){
    using namespace prime_sieve_explicit_internal;
    if(n < 2) return 0;
    CalcPrimeListUntil(n);
    auto res = std::upper_bound(prime_list.begin(), prime_list.end(), n) - prime_list.begin();
    return (int)res;
}

// [l, r)
std::vector<bool> SegmentedSieveExplicit(long long l, long long r){
    assert(0 <= l); assert(l <= r);
    long long d = r - l;
    if(d == 0) return {};
    std::vector<bool> res(d, true);
    for(long long p=2; p*p<=r; p++) if(IsprimeExplicit(p)){
        long long il = (l+p-1)/p, ir = (r+p-1)/p;
        if(il <= p) il = p;
        for(long long i=il; i<ir; i++) res[i*p-l] = false;
    }
    if(l < 2) for(long long p=l; p<2 && p<r; p++) res[l-p] = false;
    return res;
}


} // namespace nachia
#line 4 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\math\\divisor-convolution.hpp"

#line 8 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\math\\divisor-convolution.hpp"

namespace nachia{

template<class Elem>
void DivisorZeta(std::vector<Elem>& a){
    using namespace prime_sieve_explicit_internal;
    int n = a.size() - 1;
    for(int d=2; d<=n; d++) if(IsprimeExplicit(d)) for(int i=1; i*d<=n; i++) a[i*d] += a[i];
}

template<class Elem>
void DivisorInvZeta(std::vector<Elem>& a){
    using namespace prime_sieve_explicit_internal;
    int n = a.size() - 1;
    for(int d=2; d<=n; d++) if(IsprimeExplicit(d)) for(int i=n/d; i>=1; i--) a[i] += a[i*d];
}

template<class Elem>
void DivisorMobius(std::vector<Elem>& a){
    using namespace prime_sieve_explicit_internal;
    int n = a.size() - 1;
    for(int d=2; d<=n; d++) if(IsprimeExplicit(d)) for(int i=n/d; i>=1; i--) a[i*d] -= a[i];
}

template<class Elem>
void DivisorInvMobius(std::vector<Elem>& a){
    using namespace prime_sieve_explicit_internal;
    int n = a.size() - 1;
    for(int d=2; d<=n; d++) if(IsprimeExplicit(d)) for(int i=1; i*d<=n; i++) a[i] -= a[i*d];
}

template<class Elem>
std::vector<Elem> GcdConvolution(std::vector<Elem> a, std::vector<Elem> b){
    assert(a.size() == b.size());
    assert(1 <= a.size());
    DivisorInvZeta(a);
    DivisorInvZeta(b);
    for(int i=1; i<(int)a.size(); i++) a[i] *= b[i];
    DivisorInvMobius(a);
    return a;
}

template<class Elem>
std::vector<Elem> LcmConvolution(std::vector<Elem> a, std::vector<Elem> b){
    assert(a.size() == b.size());
    assert(1 <= a.size());
    DivisorZeta(a);
    DivisorZeta(b);
    for(int i=1; i<(int)a.size(); i++) a[i] *= b[i];
    DivisorMobius(a);
    return a;
}

}
#line 2 "..\\Main.cpp"

#line 4 "..\\Main.cpp"
#include <string>
#line 7 "..\\Main.cpp"
#include <atcoder/modint>
using namespace std;
using i32 = int;
using u32 = unsigned int;
using i64 = long long;
using u64 = unsigned long long;
#define rep(i,n) for(int i=0; i<(int)(n); i++)
const i64 INF = 1001001001001001001;

using Modint = atcoder::static_modint<998244353>;

pair<i64,i64> testcase(){
    i64 N, K; cin >> N >> K;
    __int128_t l = 0, r = ((__int128_t)1ll << 96) + 1;
    while(l+1 < r){
        __int128_t m = (l+r)/2;
        vector<i64> cnt(N+2);
        for(i64 c=1; c<=N; c++){
            i64 r = (m * c) >> 64;
            r = min(r, N);
            if(r > c){
                cnt[c] += c;
                cnt[c+1] -= c-1;
                cnt[r+1] -= 1;
            }
            else{
                cnt[c] += r;
                cnt[c+1] -= r;
            }
        }
        cnt[0] = 0;
        for(int i=1; i<=N; i++) cnt[i] += cnt[i-1];
        nachia::DivisorMobius(cnt);
        i64 sumcnt = 0;
        for(int i=1; i<=N; i++) sumcnt += cnt[i];
        //cout << "q = " << ((double)((i64)(m >> 34)) * 0x1.p-30) << endl;
        if(sumcnt < K) l = m; else r = m;
    }
    // l < x <= r
    if(l == ((__int128_t)1ll << 96)) return {-1,-1};
    i64 a = N+1, b = 1;
    //cout << ((double)((i64)l) * 0x1.p-64) << endl;
    for(int i=1; i<=N; i++){
        i64 q = ((__int128_t)(l * i) >> 64) + 1;
        if(q > N) continue;
        //cout << "i = " << i << " , q = " << q << endl;
        if(q * b < a * i){ a = q; b = i; }
    }
    return {a,b};
}

int main(){
    int T; cin >> T;
    rep(t,T){
        auto ans = testcase();
        if(ans.first < 0) cout << "-1\n"; else cout << ans.first << '/' << ans.second << '\n';
    }
    return 0;
}



struct ios_do_not_sync{
    ios_do_not_sync(){
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
    }
} ios_do_not_sync_instance;
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