#838552 (C++17) No.2211 Frequency Table of GCD

• 問題: No.2211 Frequency Table of GCD
• ユーザー: 👑 Nachia
• 提出日時: 2023-02-10 21:28:12
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 37 ms / 2,000 ms
• コード長: 4,966 bytes
• コンパイル時間: 1,230 ms
• コンパイル使用メモリ: 91,800 KB
• 実行使用メモリ: 5,468 KB
• 最終ジャッジ日時: 2023-09-22 00:57:51
• 合計ジャッジ時間: 3,499 ms
• ジャッジサーバーID （参考情報）: judge14 / judge11

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 4,380 KB
testcase_01	AC	2 ms; 4,376 KB
testcase_02	AC	1 ms; 4,376 KB
testcase_03	AC	15 ms; 4,564 KB
testcase_04	AC	20 ms; 4,376 KB
testcase_05	AC	27 ms; 4,832 KB
testcase_06	AC	21 ms; 4,608 KB
testcase_07	AC	28 ms; 5,216 KB
testcase_08	AC	6 ms; 4,380 KB
testcase_09	AC	5 ms; 4,376 KB
testcase_10	AC	11 ms; 4,380 KB
testcase_11	AC	9 ms; 4,380 KB
testcase_12	AC	12 ms; 4,376 KB
testcase_13	AC	18 ms; 4,380 KB
testcase_14	AC	21 ms; 4,876 KB
testcase_15	AC	17 ms; 4,612 KB
testcase_16	AC	21 ms; 4,560 KB
testcase_17	AC	25 ms; 4,876 KB
testcase_18	AC	36 ms; 5,364 KB
testcase_19	AC	37 ms; 5,464 KB
testcase_20	AC	36 ms; 5,360 KB
testcase_21	AC	36 ms; 5,388 KB
testcase_22	AC	36 ms; 5,400 KB
testcase_23	AC	15 ms; 4,572 KB
testcase_24	AC	33 ms; 5,404 KB
testcase_25	AC	13 ms; 4,376 KB
testcase_26	AC	1 ms; 4,376 KB
testcase_27	AC	33 ms; 5,360 KB
testcase_28	AC	33 ms; 5,468 KB

ソースコード

#line 1 "Main.cpp"
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <atcoder/modint>
#line 2 "nachia\\array\\divisor-convolution.hpp"

#line 4 "nachia\\array\\divisor-convolution.hpp"
#include <cassert>

#line 2 "nachia\\math\\prime-sieve-explicit.hpp"

#line 7 "nachia\\math\\prime-sieve-explicit.hpp"


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 7 "nachia\\array\\divisor-convolution.hpp"

namespace nachia{

template<class Elem>
void DivisorZeta(::std::vector<Elem>& a){
    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 DivisorReversedZeta(::std::vector<Elem>& a){
    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){
    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 DivisorReversedMobius(::std::vector<Elem>& a){
    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());
    DivisorReversedZeta(a);
    DivisorReversedZeta(b);
    for(int i=1; i<(int)a.size(); i++) a[i] *= b[i];
    DivisorReversedMobius(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;
}

} // namespace nachia
#line 7 "Main.cpp"
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>;


int main(){
    int N,M; cin >> N >> M;
    vector<int> A(N); rep(i,N) cin >> A[i];
    vector<int> C(M+1);
    rep(i,N) C[A[i]]++;
    nachia::DivisorReversedZeta(C);
    vector<Modint> PC(M+1);
    rep(i,M+1) PC[i] = Modint(2).pow(C[i])-1;
    nachia::DivisorReversedMobius(PC);
    for(int i=1; i<=M; i++){
        cout << PC[i].val() << '\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;