結果

問題 No.2795 Perfect Number
ユーザー torisasami4torisasami4
提出日時 2024-07-09 17:17:50
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 9 ms / 2,000 ms
コード長 12,166 bytes
コンパイル時間 4,734 ms
コンパイル使用メモリ 244,788 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-07-09 17:17:57
合計ジャッジ時間 5,199 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge4
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
5,248 KB
testcase_01 AC 2 ms
5,376 KB
testcase_02 AC 2 ms
5,376 KB
testcase_03 AC 2 ms
5,376 KB
testcase_04 AC 2 ms
5,376 KB
testcase_05 AC 2 ms
5,376 KB
testcase_06 AC 2 ms
5,376 KB
testcase_07 AC 2 ms
5,376 KB
testcase_08 AC 2 ms
5,376 KB
testcase_09 AC 2 ms
5,376 KB
testcase_10 AC 1 ms
5,376 KB
testcase_11 AC 2 ms
5,376 KB
testcase_12 AC 1 ms
5,376 KB
testcase_13 AC 2 ms
5,376 KB
testcase_14 AC 8 ms
5,376 KB
testcase_15 AC 8 ms
5,376 KB
testcase_16 AC 8 ms
5,376 KB
testcase_17 AC 9 ms
5,376 KB
testcase_18 AC 9 ms
5,376 KB
testcase_19 AC 1 ms
5,376 KB
testcase_20 AC 1 ms
5,376 KB
testcase_21 AC 2 ms
5,376 KB
testcase_22 AC 2 ms
5,376 KB
testcase_23 AC 1 ms
5,376 KB
testcase_24 AC 1 ms
5,376 KB
testcase_25 AC 2 ms
5,376 KB
testcase_26 AC 2 ms
5,376 KB
testcase_27 AC 2 ms
5,376 KB
testcase_28 AC 2 ms
5,376 KB
testcase_29 AC 1 ms
5,376 KB
testcase_30 AC 2 ms
5,376 KB
testcase_31 AC 2 ms
5,376 KB
testcase_32 AC 2 ms
5,376 KB
testcase_33 AC 1 ms
5,376 KB
testcase_34 AC 2 ms
5,376 KB
testcase_35 AC 2 ms
5,376 KB
testcase_36 AC 2 ms
5,376 KB
testcase_37 AC 2 ms
5,376 KB
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 # 

// #define _GLIBCXX_DEBUG
#pragma GCC optimize("O2,no-stack-protector,unroll-loops,fast-math")
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < int(n); i++)
#define per(i, n) for (int i = (n)-1; 0 <= i; i--)
#define rep2(i, l, r) for (int i = (l); i < int(r); i++)
#define per2(i, l, r) for (int i = (r)-1; int(l) <= i; i--)
#define each(e, v) for (auto& e : v)
#define MM << " " <<
#define pb push_back
#define eb emplace_back
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define sz(x) (int)x.size()
template <typename T> void print(const vector<T>& v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' ');
    if (v.empty()) cout << '\n';
}
using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
template <typename T> bool chmax(T& x, const T& y) {
    return (x < y) ? (x = y, true) : false;
}
template <typename T> bool chmin(T& x, const T& y) {
    return (x > y) ? (x = y, true) : false;
}
template <class T>
using minheap = std::priority_queue<T, std::vector<T>, std::greater<T>>;
template <class T> using maxheap = std::priority_queue<T>;
template <typename T> int lb(const vector<T>& v, T x) {
    return lower_bound(begin(v), end(v), x) - begin(v);
}
template <typename T> int ub(const vector<T>& v, T x) {
    return upper_bound(begin(v), end(v), x) - begin(v);
}
template <typename T> void rearrange(vector<T>& v) {
    sort(begin(v), end(v));
    v.erase(unique(begin(v), end(v)), end(v));
}

// __int128_t gcd(__int128_t a, __int128_t b) {
//     if (a == 0)
//         return b;
//     if (b == 0)
//         return a;
//     __int128_t cnt = a % b;
//     while (cnt != 0) {
//         a = b;
//         b = cnt;
//         cnt = a % b;
//     }
//     return b;
// }

struct Union_Find_Tree {
    vector<int> data;
    const int n;
    int cnt;
 
    Union_Find_Tree(int n) : data(n, -1), n(n), cnt(n) {}
 
    int root(int x) {
        if (data[x] < 0) return x;
        return data[x] = root(data[x]);
    }
 
    int operator[](int i) { return root(i); }
 
    bool unite(int x, int y) {
        x = root(x), y = root(y);
        if (x == y) return false;
        if (data[x] > data[y]) swap(x, y);
        data[x] += data[y], data[y] = x;
        cnt--;
        return true;
    }
 
    int size(int x) { return -data[root(x)]; }
 
    int count() { return cnt; };
 
    bool same(int x, int y) { return root(x) == root(y); }
 
    void clear() {
        cnt = n;
        fill(begin(data), end(data), -1);
    }
};

template <int mod> struct Mod_Int {
    int x;

    Mod_Int() : x(0) {}

    Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

    static int get_mod() { return mod; }

    Mod_Int& operator+=(const Mod_Int& p) {
        if ((x += p.x) >= mod) x -= mod;
        return *this;
    }

    Mod_Int& operator-=(const Mod_Int& p) {
        if ((x += mod - p.x) >= mod) x -= mod;
        return *this;
    }

    Mod_Int& operator*=(const Mod_Int& p) {
        x = (int)(1LL * x * p.x % mod);
        return *this;
    }

    Mod_Int& operator/=(const Mod_Int& p) {
        *this *= p.inverse();
        return *this;
    }

    Mod_Int& operator++() { return *this += Mod_Int(1); }

    Mod_Int operator++(int) {
        Mod_Int tmp = *this;
        ++*this;
        return tmp;
    }

    Mod_Int& operator--() { return *this -= Mod_Int(1); }

    Mod_Int operator--(int) {
        Mod_Int tmp = *this;
        --*this;
        return tmp;
    }

    Mod_Int operator-() const { return Mod_Int(-x); }

    Mod_Int operator+(const Mod_Int& p) const { return Mod_Int(*this) += p; }

    Mod_Int operator-(const Mod_Int& p) const { return Mod_Int(*this) -= p; }

    Mod_Int operator*(const Mod_Int& p) const { return Mod_Int(*this) *= p; }

    Mod_Int operator/(const Mod_Int& p) const { return Mod_Int(*this) /= p; }

    bool operator==(const Mod_Int& p) const { return x == p.x; }

    bool operator!=(const Mod_Int& p) const { return x != p.x; }

    Mod_Int inverse() const {
        assert(*this != Mod_Int(0));
        return pow(mod - 2);
    }

    Mod_Int pow(long long k) const {
        Mod_Int now = *this, ret = 1;
        for (; k > 0; k >>= 1, now *= now) {
            if (k & 1) ret *= now;
        }
        return ret;
    }

    friend ostream& operator<<(ostream& os, const Mod_Int& p) {
        return os << p.x;
    }

    friend istream& operator>>(istream& is, Mod_Int& p) {
        long long a;
        is >> a;
        p = Mod_Int<mod>(a);
        return is;
    }
};

ll mpow2(ll x, ll n, ll mod) {
    ll ans = 1;
    x %= mod;
    while (n != 0) {
        if (n & 1) ans = ans * x % mod;
        x = x * x % mod;
        n = n >> 1;
    }
    ans %= mod;
    return ans;
}

template <typename T> T modinv(T a, const T& m) {
    T b = m, u = 1, v = 0;
    while (b > 0) {
        T t = a / b;
        swap(a -= t * b, b);
        swap(u -= t * v, v);
    }
    return u >= 0 ? u % m : (m - (-u) % m) % m;
}

ll divide_int(ll a, ll b) {
    if (b < 0) a = -a, b = -b;
    return (a >= 0 ? a / b : (a - b + 1) / b);
}

// const int MOD = 1000000007;
const int MOD = 998244353;
using mint = Mod_Int<MOD>;

// ----- library -------
struct Montgomery_Mod_Int_64 {
    using u64 = uint64_t;
    using u128 = __uint128_t;

    static u64 mod;
    static u64 r;  // m*r ≡ 1 (mod 2^64)
    static u64 n2; // 2^128 (mod mod)

    u64 x;

    Montgomery_Mod_Int_64() : x(0) {}

    Montgomery_Mod_Int_64(long long b) : x(reduce((u128(b) + mod) * n2)) {}

    // mod 2^64 での逆元
    static u64 get_r() {
        u64 ret = mod;
        for (int i = 0; i < 5; i++) ret *= 2 - mod * ret;
        return ret;
    }

    static u64 get_mod() { return mod; }

    static void set_mod(u64 m) {
        assert(m < (1LL << 62));
        assert((m & 1) == 1);
        mod = m;
        n2 = -u128(m) % m;
        r = get_r();
        assert(r * mod == 1);
    }

    static u64 reduce(const u128 &b) { return (b + u128(u64(b) * u64(-r)) * mod) >> 64; }

    Montgomery_Mod_Int_64 &operator+=(const Montgomery_Mod_Int_64 &p) {
        if ((x += p.x) >= 2 * mod) x -= 2 * mod;
        return *this;
    }

    Montgomery_Mod_Int_64 &operator-=(const Montgomery_Mod_Int_64 &p) {
        if ((x += 2 * mod - p.x) >= 2 * mod) x -= 2 * mod;
        return *this;
    }

    Montgomery_Mod_Int_64 &operator*=(const Montgomery_Mod_Int_64 &p) {
        x = reduce(u128(x) * p.x);
        return *this;
    }

    Montgomery_Mod_Int_64 &operator/=(const Montgomery_Mod_Int_64 &p) {
        *this *= p.inverse();
        return *this;
    }

    Montgomery_Mod_Int_64 &operator++() { return *this += Montgomery_Mod_Int_64(1); }

    Montgomery_Mod_Int_64 operator++(int) {
        Montgomery_Mod_Int_64 tmp = *this;
        ++*this;
        return tmp;
    }

    Montgomery_Mod_Int_64 &operator--() { return *this -= Montgomery_Mod_Int_64(1); }

    Montgomery_Mod_Int_64 operator--(int) {
        Montgomery_Mod_Int_64 tmp = *this;
        --*this;
        return tmp;
    }

    Montgomery_Mod_Int_64 operator+(const Montgomery_Mod_Int_64 &p) const { return Montgomery_Mod_Int_64(*this) += p; };

    Montgomery_Mod_Int_64 operator-(const Montgomery_Mod_Int_64 &p) const { return Montgomery_Mod_Int_64(*this) -= p; };

    Montgomery_Mod_Int_64 operator*(const Montgomery_Mod_Int_64 &p) const { return Montgomery_Mod_Int_64(*this) *= p; };

    Montgomery_Mod_Int_64 operator/(const Montgomery_Mod_Int_64 &p) const { return Montgomery_Mod_Int_64(*this) /= p; };

    bool operator==(const Montgomery_Mod_Int_64 &p) const { return (x >= mod ? x - mod : x) == (p.x >= mod ? p.x - mod : p.x); };

    bool operator!=(const Montgomery_Mod_Int_64 &p) const { return (x >= mod ? x - mod : x) != (p.x >= mod ? p.x - mod : p.x); };

    Montgomery_Mod_Int_64 inverse() const {
        assert(*this != Montgomery_Mod_Int_64(0));
        return pow(mod - 2);
    }

    Montgomery_Mod_Int_64 pow(long long k) const {
        Montgomery_Mod_Int_64 now = *this, ret = 1;
        for (; k > 0; k >>= 1, now *= now) {
            if (k & 1) ret *= now;
        }
        return ret;
    }

    u64 get() const {
        u64 ret = reduce(x);
        return ret >= mod ? ret - mod : ret;
    }

    friend ostream &operator<<(ostream &os, const Montgomery_Mod_Int_64 &p) { return os << p.get(); }

    friend istream &operator>>(istream &is, Montgomery_Mod_Int_64 &p) {
        long long a;
        is >> a;
        p = Montgomery_Mod_Int_64(a);
        return is;
    }
};

typename Montgomery_Mod_Int_64::u64 Montgomery_Mod_Int_64::mod, Montgomery_Mod_Int_64::r, Montgomery_Mod_Int_64::n2;

struct Random_Number_Generator {
    mt19937_64 mt;

    Random_Number_Generator() : mt(chrono::steady_clock::now().time_since_epoch().count()) {}

    int64_t operator()(int64_t l, int64_t r) { // 区間 [l,r) の整数で乱数発生
        uniform_int_distribution<int64_t> dist(l, r - 1);
        return dist(mt);
    }

    int64_t operator()(int64_t r) { // 区間 [0,r) の整数で乱数発生
        return (*this)(0, r);
    }
} rng;

bool Miller_Rabin(long long n, vector<long long> as) {
    using Mint = Montgomery_Mod_Int_64;
    if (Mint::get_mod() != uint64_t(n)) Mint::set_mod(n);
    long long d = n - 1;
    while (!(d & 1)) d >>= 1;
    Mint e = 1, rev = n - 1;
    for (long long a : as) {
        if (n <= a) break;
        long long t = d;
        Mint y = Mint(a).pow(t);
        while (t != n - 1 && y != e && y != rev) {
            y *= y;
            t <<= 1;
        }
        if (y != rev && (!(t & 1))) return false;
    }
    return true;
}

bool is_prime(long long n) {
    if (!(n & 1)) return n == 2;
    if (n <= 1) return false;
    if (n < (1LL << 30)) return Miller_Rabin(n, {2, 7, 61});
    return Miller_Rabin(n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022});
}

long long Pollard_rho(long long n) {
    using Mint = Montgomery_Mod_Int_64;
    if (!(n & 1)) return 2;
    if (is_prime(n)) return n;
    if (Mint::get_mod() != uint64_t(n)) Mint::set_mod(n);
    Mint R, one = 1;
    auto f = [&](Mint x) { return x * x + R; };
    auto rnd = [&]() { return rng(n - 2) + 2; };
    while (true) {
        Mint x, y, ys, q = one;
        R = rnd(), y = rnd();
        long long g = 1;
        int m = 128;
        for (int r = 1; g == 1; r <<= 1) {
            x = y;
            for (int i = 0; i < r; i++) y = f(y);
            for (int k = 0; g == 1 && k < r; k += m) {
                ys = y;
                for (int i = 0; i < m && i < r - k; i++) q *= x - (y = f(y));
                g = gcd(q.get(), n);
            }
        }
        if (g == n) {
            do { g = gcd((x - (ys = f(ys))).get(), n); } while (g == 1);
        }
        if (g != n) return g;
    }
    return 0;
}

vector<long long> factorize(long long n) {
    if (n <= 1) return {};
    long long p = Pollard_rho(n);
    if (p == n) return {n};
    auto l = factorize(p);
    auto r = factorize(n / p);
    copy(begin(r), end(r), back_inserter(l));
    return l;
}

vector<pair<long long, int>> prime_factor(long long n) {
    auto ps = factorize(n);
    sort(begin(ps), end(ps));
    vector<pair<long long, int>> ret;
    for (auto &e : ps) {
        if (!ret.empty() && ret.back().first == e) {
            ret.back().second++;
        } else {
            ret.emplace_back(e, 1);
        }
    }
    return ret;
}

vector<long long> divisors(long long n) {
    auto ps = prime_factor(n);
    int cnt = 1;
    for (auto &[p, t] : ps) cnt *= t + 1;
    vector<long long> ret(cnt, 1);
    cnt = 1;
    for (auto &[p, t] : ps) {
        long long pw = 1;
        for (int i = 1; i <= t; i++) {
            pw *= p;
            for (int j = 0; j < cnt; j++) ret[cnt * i + j] = ret[j] * pw;
        }
        cnt *= t + 1;
    }
    sort(begin(ret), end(ret));
    return ret;
}
// ----- library -------

int main() {
    ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    cout << fixed << setprecision(15);

    ll n;
    cin >> n;
    auto div = divisors(n);
    __int128_t s = 0;
    each(d, div) s += d;
    cout << (s == n * 2 ? "Yes" : "No") << endl;
}
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