結果

問題 No.2798 Multiple Chain
コンテスト
ユーザー noya2
提出日時 2024-06-23 01:35:59
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 5,724 bytes
コンパイル時間 3,536 ms
コンパイル使用メモリ 259,792 KB
実行使用メモリ 6,948 KB
最終ジャッジ日時 2024-06-23 01:36:04
合計ジャッジ時間 5,088 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge3
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 * 3
other AC * 51
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<bits/stdc++.h>
using namespace std;
using ll = long long;


namespace fast_factorize {

/*
    See : https://judge.yosupo.jp/submission/189742
*/

// ---- gcd ----

uint64_t gcd_stein_impl( uint64_t x, uint64_t y ) {
    if( x == y ) { return x; }
    const uint64_t a = y - x;
    const uint64_t b = x - y;
    const int n = __builtin_ctzll( b );
    const uint64_t s = x < y ? a : b;
    const uint64_t t = x < y ? x : y;
    return gcd_stein_impl( s >> n, t );
}

uint64_t gcd_stein( uint64_t x, uint64_t y ) {
    if( x == 0 ) { return y; }
    if( y == 0 ) { return x; }
    const int n = __builtin_ctzll( x );
    const int m = __builtin_ctzll( y );
    return gcd_stein_impl( x >> n, y >> m ) << ( n < m ? n : m );
}

// ---- is_prime ----

uint64_t mod_pow( uint64_t x, uint64_t y, uint64_t mod ) {
    uint64_t ret = 1;
    uint64_t acc = x;
    for( ; y; y >>= 1 ) {
        if( y & 1 ) {
            ret = __uint128_t(ret) * acc % mod;
        }
        acc = __uint128_t(acc) * acc % mod;
    }
    return ret;
}

bool miller_rabin( uint64_t n, const std::initializer_list<uint64_t>& as ) {
    return std::all_of( as.begin(), as.end(), [n]( uint64_t a ) {
        if( n <= a ) { return true; }

        int e = __builtin_ctzll( n - 1 );
        uint64_t z = mod_pow( a, ( n - 1 ) >> e, n );
        if( z == 1 || z == n - 1 ) { return true; }

        while( --e ) {
            z = __uint128_t(z) * z % n;
            if( z == 1 ) { return false; }
            if( z == n - 1 ) { return true; }
        }

        return false;
    });
}

bool is_prime( uint64_t n ) {
    if( n == 2 ) { return true; }
    if( n % 2 == 0 ) { return false; }
    if( n < 4759123141 ) { return miller_rabin( n, { 2, 7, 61 } ); }
    return miller_rabin( n, { 2, 325, 9375, 28178, 450775, 9780504, 1795265022 } );
}

// ---- Montgomery ----

class Montgomery {
    uint64_t mod;
    uint64_t R;
public:
    Montgomery( uint64_t n ) : mod(n), R(n) {
       for( size_t i = 0; i < 5; ++i ) {
          R *= 2 - mod * R;
       }
    }

    uint64_t fma( uint64_t a, uint64_t b, uint64_t c ) const {
        const __uint128_t d = __uint128_t(a) * b;
        const uint64_t    e = c + mod + ( d >> 64 );
        const uint64_t    f = uint64_t(d) * R;
        const uint64_t    g = ( __uint128_t(f) * mod ) >> 64;
        return e - g;
    }

    uint64_t mul( uint64_t a, uint64_t b ) const {
        return fma( a, b, 0 );
    }
};

// ---- Pollard's rho algorithm ----

uint64_t pollard_rho( uint64_t n ) {
    if( n % 2 == 0 ) { return 2; }
    const Montgomery m( n );

    constexpr uint64_t C1 = 1;
    constexpr uint64_t C2 = 2;
    constexpr uint64_t M = 512;

    uint64_t Z1 = 1;
    uint64_t Z2 = 2;
retry:
    uint64_t z1 = Z1;
    uint64_t z2 = Z2;
    for( size_t k = M; ; k *= 2 ) {
        const uint64_t x1 = z1 + n;
        const uint64_t x2 = z2 + n;
        for( size_t j = 0; j < k; j += M ) {
            const uint64_t y1 = z1;
            const uint64_t y2 = z2;

            uint64_t q1 = 1;
            uint64_t q2 = 2;
            z1 = m.fma( z1, z1, C1 );
            z2 = m.fma( z2, z2, C2 );
            for( size_t i = 0; i < M; ++i ) {
                const uint64_t t1 = x1 - z1;
                const uint64_t t2 = x2 - z2;
                z1 = m.fma( z1, z1, C1 );
                z2 = m.fma( z2, z2, C2 );
                q1 = m.mul( q1, t1 );
                q2 = m.mul( q2, t2 );
            }
            q1 = m.mul( q1, x1 - z1 );
            q2 = m.mul( q2, x2 - z2 );

            const uint64_t q3 = m.mul( q1, q2 );
            const uint64_t g3 = gcd_stein( n, q3 );
            if( g3 == 1 ) { continue; }
            if( g3 != n ) { return g3; }

            const uint64_t g1 = gcd_stein( n, q1 );
            const uint64_t g2 = gcd_stein( n, q2 );

            const uint64_t C = g1 != 1 ? C1 : C2;
            const uint64_t x = g1 != 1 ? x1 : x2;
            uint64_t       z = g1 != 1 ? y1 : y2;
            uint64_t       g = g1 != 1 ? g1 : g2;

            if( g == n ) {
                do {
                    z = m.fma( z, z, C );
                    g = gcd_stein( n, x - z );
                } while( g == 1 );
            }
            if( g != n ) {
                return g;
            }

            Z1 += 2;
            Z2 += 2;
            goto retry;
        }
    }
}

void factorize_impl( uint64_t n, std::vector<uint64_t>& ret ) {
    if( n <= 1 ) { return; }
    if( is_prime( n ) ) { ret.push_back( n ); return; }

    const uint64_t p = pollard_rho( n );

    factorize_impl( p, ret );
    factorize_impl( n / p, ret );
}

std::vector<uint64_t> factorize( uint64_t n ) {
    std::vector<uint64_t> ret;
    factorize_impl( n, ret );
    std::sort( ret.begin(), ret.end() );
    return ret;
}

} // namespace fast_factorize

std::vector<std::pair<long long, int>> factorize(long long n){
    std::vector<std::pair<long long, int>> ans;
    auto ps = fast_factorize::factorize(n);
    int sz = ps.size();
    for (int l = 0, r = 0; l < sz; l = r){
        while (r < sz && ps[l] == ps[r]) r++;
        ans.emplace_back(ps[l], r-l);
    }
    return ans;
}


int main(){
    const int mx = 61;
    vector<ll> partition_numbers(mx,0);
    partition_numbers[0] = 1;
    for (int n = 1; n < mx; n++){
        for (int k = 1; k*(3*k-1)/2 <= n; k++){
            partition_numbers[n] += partition_numbers[n-k*(3*k-1)/2] * (k % 2 == 0 ? -1 : 1);
        }
        for (int k = -1; k*(3*k-1)/2 <= n; k--){
            partition_numbers[n] += partition_numbers[n-k*(3*k-1)/2] * (k % 2 == 0 ? -1 : 1);
        }
    }
    ll n; cin >> n;
    ll ans = 1;
    for (auto [p, e] : factorize(n)){
        ans *= partition_numbers[e];
    }
    cout << ans << endl;
}
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