#991342 (C++23) No.2795 Perfect Number

提出ソース
結果

問題	No.2795 Perfect Number
ユーザー	KumaTachiRen
提出日時	2024-06-28 21:44:02
言語	C++23 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	11 ms / 2,000 ms
コード長	19,474 bytes
コンパイル時間	6,694 ms
コンパイル使用メモリ	335,372 KB
実行使用メモリ	5,376 KB
最終ジャッジ日時	2024-06-28 21:44:11
合計ジャッジ時間	7,879 ms
ジャッジサーバーID （参考情報）	judge2 / judge1
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	2 ms 5,376 KB
testcase_11	AC	2 ms 5,376 KB
testcase_12	AC	2 ms 5,376 KB
testcase_13	AC	2 ms 5,376 KB
testcase_14	AC	10 ms 5,376 KB
testcase_15	AC	11 ms 5,376 KB
testcase_16	AC	11 ms 5,376 KB
testcase_17	AC	11 ms 5,376 KB
testcase_18	AC	11 ms 5,376 KB
testcase_19	AC	2 ms 5,376 KB
testcase_20	AC	2 ms 5,376 KB
testcase_21	AC	2 ms 5,376 KB
testcase_22	AC	2 ms 5,376 KB
testcase_23	AC	2 ms 5,376 KB
testcase_24	AC	2 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	2 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	2 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

raw source code
#include <bits/stdc++.h>
using namespace std;

#if __has_include(<atcoder/all>)

#include <atcoder/all>
/*
using namespace atcoder;

using mint = modint998244353;
using vm = vector<mint>;
using vvm = vector<vm>;
inline ostream &operator<<(ostream &os, const mint x)
{
    return os << x.val();
};
inline istream &operator>>(istream &is, mint &x)
{
    long long v;
    is >> v;
    x = v;
    return is;
};
*/

#endif

struct Fast
{
    Fast()
    {
        std::cin.tie(nullptr);
        ios::sync_with_stdio(false);
        cout << setprecision(10);
    }
} fast;

#define all(a) (a).begin(), (a).end()
#define contains(a, x) ((a).find(x) != (a).end())
#define rep(i, a, b) for (int i = (a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (int)(b) - 1; i >= (a); i--)
#define YN(b) cout << ((b) ? "YES" : "NO") << "\n";
#define Yn(b) cout << ((b) ? "Yes" : "No") << "\n";
#define yn(b) cout << ((b) ? "yes" : "no") << "\n";

template <class T>
inline bool chmin(T &a, T b)
{
    if (a > b)
    {
        a = b;
        return true;
    }
    return false;
}
template <class T>
inline bool chmax(T &a, T b)
{
    if (a < b)
    {
        a = b;
        return true;
    }
    return false;
}

using ll = long long;
using vb = vector<bool>;
using vvb = vector<vb>;
using vi = vector<int>;
using vvi = vector<vi>;
using vl = vector<ll>;
using vvl = vector<vl>;

template <typename T1, typename T2>
ostream &operator<<(ostream &os, pair<T1, T2> &p)
{
    os << "(" << p.first << "," << p.second << ")";
    return os;
}

template <typename T>
ostream &operator<<(ostream &os, vector<T> &vec)
{
    for (int i = 0; i < (int)vec.size(); i++)
    {
        os << vec[i] << (i + 1 == (int)vec.size() ? "" : " ");
    }
    return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &vec)
{
    for (int i = 0; i < (int)vec.size(); i++)
        is >> vec[i];
    return is;
}

ll floor(ll a, ll b) { return a >= 0 ? a / b : (a + 1) / b - 1; }
ll ceil(ll a, ll b) { return a > 0 ? (a - 1) / b + 1 : a / b; }

// https://nyaannyaan.github.io/library/prime/fast-factorize.hpp.html

#line 2 "prime/fast-factorize.hpp"

#include <cstdint>
#include <numeric>
#include <vector>
using namespace std;

#line 2 "internal/internal-math.hpp"

#line 2 "internal/internal-type-traits.hpp"

#include <type_traits>
using namespace std;

namespace internal
{
    template <typename T>
    using is_broadly_integral =
        typename conditional_t<is_integral_v<T> || is_same_v<T, __int128_t> ||
                                   is_same_v<T, __uint128_t>,
                               true_type, false_type>::type;

    template <typename T>
    using is_broadly_signed =
        typename conditional_t<is_signed_v<T> || is_same_v<T, __int128_t>,
                               true_type, false_type>::type;

    template <typename T>
    using is_broadly_unsigned =
        typename conditional_t<is_unsigned_v<T> || is_same_v<T, __uint128_t>,
                               true_type, false_type>::type;

#define ENABLE_VALUE(x)   \
    template <typename T> \
    constexpr bool x##_v = x<T>::value;

    ENABLE_VALUE(is_broadly_integral);
    ENABLE_VALUE(is_broadly_signed);
    ENABLE_VALUE(is_broadly_unsigned);
#undef ENABLE_VALUE

#define ENABLE_HAS_TYPE(var)                                 \
    template <class, class = void>                           \
    struct has_##var : false_type                            \
    {                                                        \
    };                                                       \
    template <class T>                                       \
    struct has_##var<T, void_t<typename T::var>> : true_type \
    {                                                        \
    };                                                       \
    template <class T>                                       \
    constexpr auto has_##var##_v = has_##var<T>::value;

#define ENABLE_HAS_VAR(var)                                   \
    template <class, class = void>                            \
    struct has_##var : false_type                             \
    {                                                         \
    };                                                        \
    template <class T>                                        \
    struct has_##var<T, void_t<decltype(T::var)>> : true_type \
    {                                                         \
    };                                                        \
    template <class T>                                        \
    constexpr auto has_##var##_v = has_##var<T>::value;

} // namespace internal
#line 4 "internal/internal-math.hpp"

namespace internal
{

#include <cassert>
#include <utility>
#line 10 "internal/internal-math.hpp"
    using namespace std;

    // a mod p
    template <typename T>
    T safe_mod(T a, T p)
    {
        a %= p;
        if constexpr (is_broadly_signed_v<T>)
        {
            if (a < 0)
                a += p;
        }
        return a;
    }

    // 返り値：pair(g, x)
    // s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
    template <typename T>
    pair<T, T> inv_gcd(T a, T p)
    {
        static_assert(is_broadly_signed_v<T>);
        a = safe_mod(a, p);
        if (a == 0)
            return {p, 0};
        T b = p, x = 1, y = 0;
        while (a != 0)
        {
            T q = b / a;
            swap(a, b %= a);
            swap(x, y -= q * x);
        }
        if (y < 0)
            y += p / b;
        return {b, y};
    }

    // 返り値 : a^{-1} mod p
    // gcd(a, p) != 1 が必要
    template <typename T>
    T inv(T a, T p)
    {
        static_assert(is_broadly_signed_v<T>);
        a = safe_mod(a, p);
        T b = p, x = 1, y = 0;
        while (a != 0)
        {
            T q = b / a;
            swap(a, b %= a);
            swap(x, y -= q * x);
        }
        assert(b == 1);
        return y < 0 ? y + p : y;
    }

    // T : 底の型
    // U : T*T がオーバーフローしない かつ 指数の型
    template <typename T, typename U>
    T modpow(T a, U n, T p)
    {
        a = safe_mod(a, p);
        T ret = 1 % p;
        while (n != 0)
        {
            if (n % 2 == 1)
                ret = U(ret) * a % p;
            a = U(a) * a % p;
            n /= 2;
        }
        return ret;
    }

    // 返り値 : pair(rem, mod)
    // 解なしのときは {0, 0} を返す
    template <typename T>
    pair<T, T> crt(const vector<T> &r, const vector<T> &m)
    {
        static_assert(is_broadly_signed_v<T>);
        assert(r.size() == m.size());
        int n = int(r.size());
        T r0 = 0, m0 = 1;
        for (int i = 0; i < n; i++)
        {
            assert(1 <= m[i]);
            T r1 = safe_mod(r[i], m[i]), m1 = m[i];
            if (m0 < m1)
                swap(r0, r1), swap(m0, m1);
            if (m0 % m1 == 0)
            {
                if (r0 % m1 != r1)
                    return {0, 0};
                continue;
            }
            auto [g, im] = inv_gcd(m0, m1);
            T u1 = m1 / g;
            if ((r1 - r0) % g)
                return {0, 0};
            T x = (r1 - r0) / g % u1 * im % u1;
            r0 += x * m0;
            m0 *= u1;
            if (r0 < 0)
                r0 += m0;
        }
        return {r0, m0};
    }

} // namespace internal
#line 2 "misc/rng.hpp"

#line 2 "internal/internal-seed.hpp"

#include <chrono>
using namespace std;

namespace internal
{
    unsigned long long non_deterministic_seed()
    {
        unsigned long long m =
            chrono::duration_cast<chrono::nanoseconds>(
                chrono::high_resolution_clock::now().time_since_epoch())
                .count();
        m ^= 9845834732710364265uLL;
        m ^= m << 24, m ^= m >> 31, m ^= m << 35;
        return m;
    }
    unsigned long long deterministic_seed() { return 88172645463325252UL; }

    // 64 bit の seed 値を生成 (手元では seed 固定)
    // 連続で呼び出すと同じ値が何度も返ってくるので注意
    // #define RANDOMIZED_SEED するとシードがランダムになる
    unsigned long long seed()
    {
#if defined(NyaanLocal) && !defined(RANDOMIZED_SEED)
        return deterministic_seed();
#else
        return non_deterministic_seed();
#endif
    }

} // namespace internal
#line 4 "misc/rng.hpp"

namespace my_rand
{
    using i64 = long long;
    using u64 = unsigned long long;

    // [0, 2^64 - 1)
    u64 rng()
    {
        static u64 _x = internal::seed();
        return _x ^= _x << 7, _x ^= _x >> 9;
    }

    // [l, r]
    i64 rng(i64 l, i64 r)
    {
        assert(l <= r);
        return l + rng() % u64(r - l + 1);
    }

    // [l, r)
    i64 randint(i64 l, i64 r)
    {
        assert(l < r);
        return l + rng() % u64(r - l);
    }

    // choose n numbers from [l, r) without overlapping
    vector<i64> randset(i64 l, i64 r, i64 n)
    {
        assert(l <= r && n <= r - l);
        unordered_set<i64> s;
        for (i64 i = n; i; --i)
        {
            i64 m = randint(l, r + 1 - i);
            if (s.find(m) != s.end())
                m = r - i;
            s.insert(m);
        }
        vector<i64> ret;
        for (auto &x : s)
            ret.push_back(x);
        sort(begin(ret), end(ret));
        return ret;
    }

    // [0.0, 1.0)
    double rnd() { return rng() * 5.42101086242752217004e-20; }
    // [l, r)
    double rnd(double l, double r)
    {
        assert(l < r);
        return l + rnd() * (r - l);
    }

    template <typename T>
    void randshf(vector<T> &v)
    {
        int n = v.size();
        for (int i = 1; i < n; i++)
            swap(v[i], v[randint(0, i + 1)]);
    }

} // namespace my_rand

using my_rand::randint;
using my_rand::randset;
using my_rand::randshf;
using my_rand::rnd;
using my_rand::rng;
#line 2 "modint/arbitrary-montgomery-modint.hpp"

#include <iostream>
using namespace std;

template <typename Int, typename UInt, typename Long, typename ULong, int id>
struct ArbitraryLazyMontgomeryModIntBase
{
    using mint = ArbitraryLazyMontgomeryModIntBase;

    inline static UInt mod;
    inline static UInt r;
    inline static UInt n2;
    static constexpr int bit_length = sizeof(UInt) * 8;

    static UInt get_r()
    {
        UInt ret = mod;
        while (mod * ret != 1)
            ret *= UInt(2) - mod * ret;
        return ret;
    }
    static void set_mod(UInt m)
    {
        assert(m < (UInt(1u) << (bit_length - 2)));
        assert((m & 1) == 1);
        mod = m, n2 = -ULong(m) % m, r = get_r();
    }
    UInt a;

    ArbitraryLazyMontgomeryModIntBase() : a(0) {}
    ArbitraryLazyMontgomeryModIntBase(const Long &b)
        : a(reduce(ULong(b % mod + mod) * n2)){};

    static UInt reduce(const ULong &b)
    {
        return (b + ULong(UInt(b) * UInt(-r)) * mod) >> bit_length;
    }

    mint &operator+=(const mint &b)
    {
        if (Int(a += b.a - 2 * mod) < 0)
            a += 2 * mod;
        return *this;
    }
    mint &operator-=(const mint &b)
    {
        if (Int(a -= b.a) < 0)
            a += 2 * mod;
        return *this;
    }
    mint &operator*=(const mint &b)
    {
        a = reduce(ULong(a) * b.a);
        return *this;
    }
    mint &operator/=(const mint &b)
    {
        *this *= b.inverse();
        return *this;
    }

    mint operator+(const mint &b) const { return mint(*this) += b; }
    mint operator-(const mint &b) const { return mint(*this) -= b; }
    mint operator*(const mint &b) const { return mint(*this) *= b; }
    mint operator/(const mint &b) const { return mint(*this) /= b; }

    bool operator==(const mint &b) const
    {
        return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
    }
    bool operator!=(const mint &b) const
    {
        return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
    }
    mint operator-() const { return mint(0) - mint(*this); }
    mint operator+() const { return mint(*this); }

    mint pow(ULong n) const
    {
        mint ret(1), mul(*this);
        while (n > 0)
        {
            if (n & 1)
                ret *= mul;
            mul *= mul, n >>= 1;
        }
        return ret;
    }

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

    friend istream &operator>>(istream &is, mint &b)
    {
        Long t;
        is >> t;
        b = ArbitraryLazyMontgomeryModIntBase(t);
        return (is);
    }

    mint inverse() const
    {
        Int x = get(), y = get_mod(), u = 1, v = 0;
        while (y > 0)
        {
            Int t = x / y;
            swap(x -= t * y, y);
            swap(u -= t * v, v);
        }
        return mint{u};
    }

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

    static UInt get_mod() { return mod; }
};

// id に適当な乱数を割り当てて使う
template <int id>
using ArbitraryLazyMontgomeryModInt =
    ArbitraryLazyMontgomeryModIntBase<int, unsigned int, long long,
                                      unsigned long long, id>;
template <int id>
using ArbitraryLazyMontgomeryModInt64bit =
    ArbitraryLazyMontgomeryModIntBase<long long, unsigned long long, __int128_t,
                                      __uint128_t, id>;
#line 2 "prime/miller-rabin.hpp"

#line 4 "prime/miller-rabin.hpp"
using namespace std;

#line 8 "prime/miller-rabin.hpp"

namespace fast_factorize
{

    template <typename T, typename U>
    bool miller_rabin(const T &n, vector<T> ws)
    {
        if (n <= 2)
            return n == 2;
        if (n % 2 == 0)
            return false;

        T d = n - 1;
        while (d % 2 == 0)
            d /= 2;
        U e = 1, rev = n - 1;
        for (T w : ws)
        {
            if (w % n == 0)
                continue;
            T t = d;
            U y = internal::modpow<T, U>(w, t, n);
            while (t != n - 1 && y != e && y != rev)
                y = y * y % n, t *= 2;
            if (y != rev && t % 2 == 0)
                return false;
        }
        return true;
    }

    bool miller_rabin_u64(unsigned long long n)
    {
        return miller_rabin<unsigned long long, __uint128_t>(
            n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022});
    }

    template <typename mint>
    bool miller_rabin(unsigned long long n, vector<unsigned long long> ws)
    {
        if (n <= 2)
            return n == 2;
        if (n % 2 == 0)
            return false;

        if (mint::get_mod() != n)
            mint::set_mod(n);
        unsigned long long d = n - 1;
        while (~d & 1)
            d >>= 1;
        mint e = 1, rev = n - 1;
        for (unsigned long long w : ws)
        {
            if (w % n == 0)
                continue;
            unsigned long long t = d;
            mint y = mint(w).pow(t);
            while (t != n - 1 && y != e && y != rev)
                y *= y, t *= 2;
            if (y != rev && t % 2 == 0)
                return false;
        }
        return true;
    }

    bool is_prime(unsigned long long n)
    {
        using mint32 = ArbitraryLazyMontgomeryModInt<96229631>;
        using mint64 = ArbitraryLazyMontgomeryModInt64bit<622196072>;

        if (n <= 2)
            return n == 2;
        if (n % 2 == 0)
            return false;
        if (n < (1uLL << 30))
        {
            return miller_rabin<mint32>(n, {2, 7, 61});
        }
        else if (n < (1uLL << 62))
        {
            return miller_rabin<mint64>(
                n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022});
        }
        else
        {
            return miller_rabin_u64(n);
        }
    }

} // namespace fast_factorize

using fast_factorize::is_prime;

/**
 * @brief Miller-Rabin primality test
 */
#line 12 "prime/fast-factorize.hpp"

namespace fast_factorize
{
    using u64 = uint64_t;

    template <typename mint, typename T>
    T pollard_rho(T n)
    {
        if (~n & 1)
            return 2;
        if (is_prime(n))
            return n;
        if (mint::get_mod() != 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 (1)
        {
            mint x, y, ys, q = one;
            R = rnd_(), y = rnd_();
            T g = 1;
            constexpr 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;
        }
        exit(1);
    }

    using i64 = long long;

    vector<i64> inner_factorize(u64 n)
    {
        using mint32 = ArbitraryLazyMontgomeryModInt<452288976>;
        using mint64 = ArbitraryLazyMontgomeryModInt64bit<401243123>;

        if (n <= 1)
            return {};
        u64 p;
        if (n <= (1LL << 30))
        {
            p = pollard_rho<mint32, uint32_t>(n);
        }
        else if (n <= (1LL << 62))
        {
            p = pollard_rho<mint64, uint64_t>(n);
        }
        else
        {
            exit(1);
        }
        if (p == n)
            return {i64(p)};
        auto l = inner_factorize(p);
        auto r = inner_factorize(n / p);
        copy(begin(r), end(r), back_inserter(l));
        return l;
    }

    vector<i64> factorize(u64 n)
    {
        auto ret = inner_factorize(n);
        sort(begin(ret), end(ret));
        return ret;
    }

    map<i64, i64> factor_count(u64 n)
    {
        map<i64, i64> mp;
        for (auto &x : factorize(n))
            mp[x]++;
        return mp;
    }

    vector<i64> divisors(u64 n)
    {
        if (n == 0)
            return {};
        vector<pair<i64, i64>> v;
        for (auto &p : factorize(n))
        {
            if (v.empty() || v.back().first != p)
            {
                v.emplace_back(p, 1);
            }
            else
            {
                v.back().second++;
            }
        }
        vector<i64> ret;
        auto f = [&](auto rc, int i, i64 x) -> void
        {
            if (i == (int)v.size())
            {
                ret.push_back(x);
                return;
            }
            rc(rc, i + 1, x);
            for (int j = 0; j < v[i].second; j++)
                rc(rc, i + 1, x *= v[i].first);
        };
        f(f, 0, 1);
        sort(begin(ret), end(ret));
        return ret;
    }

} // namespace fast_factorize

using fast_factorize::divisors;
using fast_factorize::factor_count;
using fast_factorize::factorize;

/**
 * @brief 高速素因数分解(Miller Rabin/Pollard's Rho)
 * @docs docs/prime/fast-factorize.md
 */

void solve()
{
    ll n;
    cin >> n;

    auto ds = divisors(n);
    ll rem = 2 * n;
    for (auto d : ds)
    {
        rem -= d;
        if (rem < 0)
        {
            Yn(false);
            return;
        }
    }
    Yn(rem == 0);
}

int main()
{
    int t = 1;
    // cin >> t;
    while (t--)
        solve();
}
yukicoder

結果

テストケース

ソースコード
