結果

問題 No.2 素因数ゲーム
ユーザー SnowBeenDidingSnowBeenDiding
提出日時 2024-08-30 00:06:23
言語 C++23
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 2 ms / 5,000 ms
コード長 4,833 bytes
コンパイル時間 3,557 ms
コンパイル使用メモリ 258,132 KB
実行使用メモリ 6,948 KB
最終ジャッジ日時 2024-08-30 00:06:28
合計ジャッジ時間 5,149 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge1
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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
6,816 KB
testcase_01 AC 2 ms
6,944 KB
testcase_02 AC 2 ms
6,944 KB
testcase_03 AC 2 ms
6,944 KB
testcase_04 AC 2 ms
6,948 KB
testcase_05 AC 2 ms
6,944 KB
testcase_06 AC 2 ms
6,940 KB
testcase_07 AC 2 ms
6,944 KB
testcase_08 AC 2 ms
6,944 KB
testcase_09 AC 2 ms
6,944 KB
testcase_10 AC 2 ms
6,944 KB
testcase_11 AC 2 ms
6,944 KB
testcase_12 AC 2 ms
6,944 KB
testcase_13 AC 2 ms
6,940 KB
testcase_14 AC 2 ms
6,940 KB
testcase_15 AC 2 ms
6,940 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
6,944 KB
testcase_20 AC 2 ms
6,940 KB
testcase_21 AC 2 ms
6,944 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
6,944 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
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ソースコード

diff # 

#include <bits/stdc++.h>
#define rep(i, a, b) for (ll i = (ll)(a); i < (ll)(b); i++)
using namespace std;

typedef long long ll;

namespace FastPrimeFactorization {

template <typename word, typename dword, typename sword> struct UnsafeMod {
    UnsafeMod() : x(0) {}

    UnsafeMod(word _x) : x(init(_x)) {}

    bool operator==(const UnsafeMod &rhs) const { return x == rhs.x; }

    bool operator!=(const UnsafeMod &rhs) const { return x != rhs.x; }

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

    UnsafeMod &operator-=(const UnsafeMod &rhs) {
        if (sword(x -= rhs.x) < 0)
            x += mod;
        return *this;
    }

    UnsafeMod &operator*=(const UnsafeMod &rhs) {
        x = reduce(dword(x) * rhs.x);
        return *this;
    }

    UnsafeMod operator+(const UnsafeMod &rhs) const {
        return UnsafeMod(*this) += rhs;
    }

    UnsafeMod operator-(const UnsafeMod &rhs) const {
        return UnsafeMod(*this) -= rhs;
    }

    UnsafeMod operator*(const UnsafeMod &rhs) const {
        return UnsafeMod(*this) *= rhs;
    }

    UnsafeMod pow(uint64_t e) const {
        UnsafeMod ret(1);
        for (UnsafeMod base = *this; e; e >>= 1, base *= base) {
            if (e & 1)
                ret *= base;
        }
        return ret;
    }

    word get() const { return reduce(x); }

    static constexpr int word_bits = sizeof(word) * 8;

    static word modulus() { return mod; }

    static word init(word w) { return reduce(dword(w) * r2); }

    static void set_mod(word m) {
        mod = m;
        inv = mul_inv(mod);
        r2 = -dword(mod) % mod;
    }

    static word reduce(dword x) {
        word y = word(x >> word_bits) -
                 word((dword(word(x) * inv) * mod) >> word_bits);
        return sword(y) < 0 ? y + mod : y;
    }

    static word mul_inv(word n, int e = 6, word x = 1) {
        return !e ? x : mul_inv(n, e - 1, x * (2 - x * n));
    }

    static word mod, inv, r2;

    word x;
};

using uint128_t = __uint128_t;

using Mod64 = UnsafeMod<uint64_t, uint128_t, int64_t>;
template <> uint64_t Mod64::mod = 0;
template <> uint64_t Mod64::inv = 0;
template <> uint64_t Mod64::r2 = 0;

using Mod32 = UnsafeMod<uint32_t, uint64_t, int32_t>;
template <> uint32_t Mod32::mod = 0;
template <> uint32_t Mod32::inv = 0;
template <> uint32_t Mod32::r2 = 0;

bool miller_rabin_primality_test_uint64(uint64_t n) {
    Mod64::set_mod(n);
    uint64_t d = n - 1;
    while (d % 2 == 0)
        d /= 2;
    Mod64 e{1}, rev{n - 1};
    // http://miller-rabin.appspot.com/  < 2^64
    for (uint64_t a : {2, 325, 9375, 28178, 450775, 9780504, 1795265022}) {
        if (n <= a)
            break;
        uint64_t t = d;
        Mod64 y = Mod64(a).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 miller_rabin_primality_test_uint32(uint32_t n) {
    Mod32::set_mod(n);
    uint32_t d = n - 1;
    while (d % 2 == 0)
        d /= 2;
    Mod32 e{1}, rev{n - 1};
    for (uint32_t a : {2, 7, 61}) {
        if (n <= a)
            break;
        uint32_t t = d;
        Mod32 y = Mod32(a).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(uint64_t n) {
    if (n == 2)
        return true;
    if (n == 1 || n % 2 == 0)
        return false;
    if (n < uint64_t(1) << 31)
        return miller_rabin_primality_test_uint32(n);
    return miller_rabin_primality_test_uint64(n);
}

uint64_t pollard_rho(uint64_t n) {
    if (is_prime(n))
        return n;
    if (n % 2 == 0)
        return 2;
    Mod64::set_mod(n);
    uint64_t d;
    Mod64 one{1};
    for (Mod64 c{one};; c += one) {
        Mod64 x{2}, y{2};
        do {
            x = x * x + c;
            y = y * y + c;
            y = y * y + c;
            d = __gcd((x - y).get(), n);
        } while (d == 1);
        if (d < n)
            return d;
    }
    assert(0);
}

vector<uint64_t> prime_factor(uint64_t n) {
    if (n <= 1)
        return {};
    uint64_t p = pollard_rho(n);
    if (p == n)
        return {p};
    auto l = prime_factor(p);
    auto r = prime_factor(n / p);
    copy(begin(r), end(r), back_inserter(l));
    return l;
}
}; // namespace FastPrimeFactorization
// auto p = FastPrimeFactorization::prime_factor(n);

int main() {
    ll n;
    cin >> n;
    auto p = FastPrimeFactorization::prime_factor(n);
    map<ll, ll> ma;
    for (auto x : p) {
        ma[x]++;
    }
    int gr = 0;
    for (auto x : ma) {
        gr ^= x.second;
    }
    cout << (gr ? "Alice" : "Bob") << endl;
}
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