結果

問題 No.2795 Perfect Number
ユーザー SlephySlephy
提出日時 2024-06-30 12:28:05
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 8,402 bytes
コンパイル時間 7,314 ms
コンパイル使用メモリ 432,888 KB
実行使用メモリ 6,948 KB
最終ジャッジ日時 2024-06-30 12:28:14
合計ジャッジ時間 8,754 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge2
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
6,812 KB
testcase_01 AC 2 ms
6,940 KB
testcase_02 AC 2 ms
6,944 KB
testcase_03 AC 2 ms
6,944 KB
testcase_04 AC 2 ms
6,944 KB
testcase_05 AC 2 ms
6,940 KB
testcase_06 AC 2 ms
6,940 KB
testcase_07 AC 2 ms
6,940 KB
testcase_08 AC 2 ms
6,944 KB
testcase_09 AC 2 ms
6,944 KB
testcase_10 AC 2 ms
6,940 KB
testcase_11 AC 2 ms
6,944 KB
testcase_12 AC 2 ms
6,944 KB
testcase_13 AC 2 ms
6,944 KB
testcase_14 AC 2 ms
6,940 KB
testcase_15 AC 2 ms
6,944 KB
testcase_16 AC 2 ms
6,940 KB
testcase_17 AC 2 ms
6,940 KB
testcase_18 AC 2 ms
6,944 KB
testcase_19 AC 2 ms
6,940 KB
testcase_20 AC 2 ms
6,944 KB
testcase_21 AC 2 ms
6,940 KB
testcase_22 AC 2 ms
6,940 KB
testcase_23 AC 2 ms
6,940 KB
testcase_24 AC 2 ms
6,940 KB
testcase_25 AC 2 ms
6,940 KB
testcase_26 AC 2 ms
6,944 KB
testcase_27 AC 2 ms
6,944 KB
testcase_28 AC 2 ms
6,944 KB
testcase_29 AC 2 ms
6,944 KB
testcase_30 AC 2 ms
6,944 KB
testcase_31 AC 2 ms
6,944 KB
testcase_32 AC 1 ms
6,940 KB
testcase_33 AC 2 ms
6,944 KB
testcase_34 AC 2 ms
6,940 KB
testcase_35 AC 2 ms
6,940 KB
testcase_36 AC 2 ms
6,948 KB
testcase_37 AC 2 ms
6,940 KB
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ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int INF = (int)1e9 + 1001010;
const ll llINF = (long long)4e18 + 22000020;
const string endn = "\n";
template <class T> inline auto vector2(size_t i, size_t j, const T &init = T()) {return vector(i, vector<T>(j, init));}
const string ELEM_SEPARATION = " ", VEC_SEPARATION = endn;
template<class T> istream& operator >>(istream &i, vector<T> &A) {for(auto &I : A) {i >> I;} return i;}
template<class T> ostream& operator <<(ostream &o, const vector<T> &A) {int i=A.size(); for(const auto &I : A){o << I << (--i ? ELEM_SEPARATION : "");} return o;}
template<class T> ostream& operator <<(ostream &o, const vector<vector<T>> &A) {int i=A.size(); for(const auto &I : A){o << I << (--i ? VEC_SEPARATION : "");} return o;}
template<class T> vector<T>& operator ++(vector<T> &A, int n) {for(auto &I : A) {I++;} return A;}
template<class T> vector<T>& operator --(vector<T> &A, int n) {for(auto &I : A) {I--;} return A;}
template<class T, class U> bool chmax(T &a, const U &b) {return ((a < b) ? (a = b, true) : false);}
template<class T, class U> bool chmin(T &a, const U &b) {return ((a > b) ? (a = b, true) : false);}
ll floor(ll a, ll b){if (b < 0) a = -a, b = -b; if(a >= 0) return a / b; else return (a + 1) / b - 1;}
ll ceil(ll a, ll b){if (b < 0) a = -a, b = -b; if(a > 0) return (a - 1) / b + 1; else return a / b;}
ll bit(unsigned long long val, unsigned long long digit){return (val >> digit) & 1;}
#ifdef DEBUG
#include <debug_slephy.cpp>
#else
#define debug(...)
#endif
// ================================== ここまでテンプレ ==================================


//------------------------------//
// Prime Functions
//------------------------------//

// montgomery modint (MOD < 2^62, MOD is odd)
struct MontgomeryModInt64 {
    using mint = MontgomeryModInt64;
    using u64 = uint64_t;
    using u128 = __uint128_t;

    // static menber
    static u64 MOD;
    static u64 INV_MOD;  // INV_MOD * MOD ≡ 1 (mod 2^64)
    static u64 T128;  // 2^128 (mod MOD)

    // inner value
    u64 val;

    // constructor
    MontgomeryModInt64() : val(0) { }
    MontgomeryModInt64(long long v) : val(reduce((u128(v) + MOD) * T128)) { }
    u64 get() const {
        u64 res = reduce(val);
        return res >= MOD ? res - MOD : res;
    }

    // mod getter and setter
    static u64 get_mod() { return MOD; }
    static void set_mod(u64 mod) {
        assert(mod < (1LL << 62));
        assert((mod & 1));
        MOD = mod;
        T128 = -u128(mod) % mod;
        INV_MOD = get_inv_mod();
    }
    static u64 get_inv_mod() {
        u64 res = MOD;
        for (int i = 0; i < 5; ++i) res *= 2 - MOD * res;
        return res;
    }
    static u64 reduce(const u128 &v) {
        return (v + u128(u64(v) * u64(-INV_MOD)) * MOD) >> 64;
    }

    // arithmetic operators
    mint operator + () const { return mint(*this); }
    mint operator - () const { return mint() - mint(*this); }
    mint operator + (const mint &r) const { return mint(*this) += r; }
    mint operator - (const mint &r) const { return mint(*this) -= r; }
    mint operator * (const mint &r) const { return mint(*this) *= r; }
    mint operator / (const mint &r) const { return mint(*this) /= r; }
    mint& operator += (const mint &r) {
        if ((val += r.val) >= 2 * MOD) val -= 2 * MOD;
        return *this;
    }
    mint& operator -= (const mint &r) {
        if ((val += 2 * MOD - r.val) >= 2 * MOD) val -= 2 * MOD;
        return *this;
    }
    mint& operator *= (const mint &r) {
        val = reduce(u128(val) * r.val);
        return *this;
    }
    mint& operator /= (const mint &r) {
        *this *= r.inv();
        return *this;
    }
    mint inv() const { return pow(MOD - 2); }
    mint pow(u128 n) const {
        mint res(1), mul(*this);
        while (n > 0) {
            if (n & 1) res *= mul;
            mul *= mul;
            n >>= 1;
        }
        return res;
    }

    // other operators
    bool operator == (const mint &r) const {
        return (val >= MOD ? val - MOD : val) == (r.val >= MOD ? r.val - MOD : r.val);
    }
    bool operator != (const mint &r) const {
        return (val >= MOD ? val - MOD : val) != (r.val >= MOD ? r.val - MOD : r.val);
    }
    mint& operator ++ () {
        ++val;
        if (val >= MOD) val -= MOD;
        return *this;
    }
    mint& operator -- () {
        if (val == 0) val += MOD;
        --val;
        return *this;
    }
    mint operator ++ (int) {
        mint res = *this;
        ++*this;
        return res;
    }
    mint operator -- (int) {
        mint res = *this;
        --*this;
        return res;
    }
    friend istream& operator >> (istream &is, mint &x) {
        long long t;
        is >> t;
        x = mint(t);
        return is;
    }
    friend ostream& operator << (ostream &os, const mint &x) {
        return os << x.get();
    }
    friend mint pow(const mint &r, long long n) {
        return r.pow(n);
    }
    friend mint inv(const mint &r) {
        return r.inv();
    }
};

typename MontgomeryModInt64::u64
MontgomeryModInt64::MOD, MontgomeryModInt64::INV_MOD, MontgomeryModInt64::T128;


// Miller-Rabin
bool MillerRabin(long long N, vector<long long> A) {
    using mint = MontgomeryModInt64;
    mint::set_mod(N);

    long long s = 0, d = N - 1;
    while (d % 2 == 0) {
        ++s;
        d >>= 1;
    }
    for (auto a : A) {
        if (N <= a) return true;
        mint x = mint(a).pow(d);
        if (x != 1) {
            long long t;
            for (t = 0; t < s; ++t) {
                if (x == N - 1) break;
                x *= x;
            }
            if (t == s) return false;
        }
    }
    return true;
}

bool is_prime(long long N) {
    if (N <= 1) return false;
    else if (N == 2) return true;
    else if (N % 2 == 0) return false;
    else if (N < 4759123141LL)
        return MillerRabin(N, {2, 7, 61});
    else
        return MillerRabin(N, {2, 325, 9375, 28178, 450775, 9780504, 1795265022});
}


// Pollard's Rho
unsigned int xor_shift_rng() {
    static unsigned int tx = 123456789, ty=362436069, tz=521288629, tw=88675123;
    unsigned int tt = (tx^(tx<<11));
    tx = ty, ty = tz, tz = tw;
    return ( tw=(tw^(tw>>19))^(tt^(tt>>8)) );
}

long long pollard(long long N) {
    if (N % 2 == 0) return 2;
    if (is_prime(N)) return N;

    using mint = MontgomeryModInt64;
    mint::set_mod(N);

    long long step = 0;
    while (true) {
        mint r = xor_shift_rng();  // random r
        auto f = [&](mint x) -> mint { return x * x + r; };
        mint x = ++step, y = f(x);
        while (true) {
            long long p = gcd((y - x).get(), N);
            if (p == 0 || p == N) break;
            if (p != 1) return p;
            x = f(x);
            y = f(f(y));
        }
    }
}

vector<long long> prime_factorize(long long N) {
    if (N == 1) return {};
    long long p = pollard(N);
    if (p == N) return {p};
    vector<long long> left = prime_factorize(p);
    vector<long long> right = prime_factorize(N / p);
    left.insert(left.end(), right.begin(), right.end());
    sort(left.begin(), left.end());
    return left;
}

#include <boost/multiprecision/cpp_int.hpp>
using i128 = boost::multiprecision::int128_t;
using i256 = boost::multiprecision::int256_t;
using i512 = boost::multiprecision::int512_t;
using i1024 = boost::multiprecision::int1024_t;
using iINF = boost::multiprecision::cpp_int;

#include <boost/multiprecision/cpp_dec_float.hpp>
using d30 = boost::multiprecision::number<boost::multiprecision::cpp_dec_float<30>>;
using d50 = boost::multiprecision::cpp_dec_float_50;
using d100 = boost::multiprecision::cpp_dec_float_100;

i128 powll(i128 base, i128 exponent){
    i128 ret = 1;
    while(exponent > 0){
        if(exponent & 1) ret = ret * base;
        base = base * base;
        exponent >>= 1;
    }
    return ret;
}

int main(int argc, char *argv[]){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    ll n; cin >> n;
    vector<ll> factors = prime_factorize(n);
    map<i128, i128> fac_pow;
    for(int i = 0; i < factors.size(); i++){
        fac_pow[factors[i]]++;
    }

    i128 ans = 1;
    for(auto [r, n] : fac_pow){
        i128 sum = (powll(r, n+1) - 1) / (r - 1);
        debug(r, n, sum);
        ans *= sum;
    }

    if(ans == 2*n) cout << "Yes" << endl;
    else cout << "No" << endl;
    return 0;
}
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