#685914 (C++17) No.103 素因数ゲームリターンズ

提出ソース
結果

問題	No.103 素因数ゲームリターンズ
ユーザー	snrnsidy
提出日時	2021-08-06 11:48:14
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	4 ms / 5,000 ms
コード長	19,014 bytes
コンパイル時間	2,553 ms
コンパイル使用メモリ	209,448 KB
実行使用メモリ	6,944 KB
最終ジャッジ日時	2024-09-17 00:28:05
合計ジャッジ時間	3,327 ms
ジャッジサーバーID （参考情報）	judge2 / 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	3 ms 6,816 KB
testcase_01	AC	3 ms 6,944 KB
testcase_02	AC	3 ms 6,944 KB
testcase_03	AC	3 ms 6,944 KB
testcase_04	AC	3 ms 6,940 KB
testcase_05	AC	2 ms 6,944 KB
testcase_06	AC	2 ms 6,940 KB
testcase_07	AC	3 ms 6,940 KB
testcase_08	AC	2 ms 6,944 KB
testcase_09	AC	2 ms 6,944 KB
testcase_10	AC	3 ms 6,940 KB
testcase_11	AC	3 ms 6,940 KB
testcase_12	AC	3 ms 6,944 KB
testcase_13	AC	3 ms 6,944 KB
testcase_14	AC	3 ms 6,940 KB
testcase_15	AC	4 ms 6,944 KB
testcase_16	AC	2 ms 6,940 KB
testcase_17	AC	3 ms 6,940 KB
testcase_18	AC	3 ms 6,940 KB
testcase_19	AC	3 ms 6,940 KB
testcase_20	AC	3 ms 6,944 KB
testcase_21	AC	3 ms 6,944 KB
testcase_22	AC	3 ms 6,944 KB
testcase_23	AC	3 ms 6,940 KB
testcase_24	AC	3 ms 6,940 KB
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ソースコード

raw source code
#include <bits/stdc++.h> 

using namespace std;

namespace atcoder {

    namespace internal {

        // @param m `1 <= m`
        // @return x mod m
        constexpr long long safe_mod(long long x, long long m) {
            x %= m;
            if (x < 0) x += m;
            return x;
        }

        // Fast modular multiplication by barrett reduction
        // Reference: https://en.wikipedia.org/wiki/Barrett_reduction
        // NOTE: reconsider after Ice Lake
        struct barrett {
            unsigned int _m;
            unsigned long long im;

            // @param m `1 <= m < 2^31`
            explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}

            // @return m
            unsigned int umod() const { return _m; }

            // @param a `0 <= a < m`
            // @param b `0 <= b < m`
            // @return `a * b % m`
            unsigned int mul(unsigned int a, unsigned int b) const {
                // [1] m = 1
                // a = b = im = 0, so okay

                // [2] m >= 2
                // im = ceil(2^64 / m)
                // -> im * m = 2^64 + r (0 <= r < m)
                // let z = a*b = c*m + d (0 <= c, d < m)
                // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
                // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
                // ((ab * im) >> 64) == c or c + 1
                unsigned long long z = a;
                z *= b;
#ifdef _MSC_VER
                unsigned long long x;
                _umul128(z, im, &x);
#else
                unsigned long long x =
                    (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
                unsigned int v = (unsigned int)(z - x * _m);
                if (_m <= v) v += _m;
                return v;
            }
        };

        // @param n `0 <= n`
        // @param m `1 <= m`
        // @return `(x ** n) % m`
        constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
            if (m == 1) return 0;
            unsigned int _m = (unsigned int)(m);
            unsigned long long r = 1;
            unsigned long long y = safe_mod(x, m);
            while (n) {
                if (n & 1) r = (r * y) % _m;
                y = (y * y) % _m;
                n >>= 1;
            }
            return r;
        }

        // Reference:
        // M. Forisek and J. Jancina,
        // Fast Primality Testing for Integers That Fit into a Machine Word
        // @param n `0 <= n`
        constexpr bool is_prime_constexpr(int n) {
            if (n <= 1) return false;
            if (n == 2 || n == 7 || n == 61) return true;
            if (n % 2 == 0) return false;
            long long d = n - 1;
            while (d % 2 == 0) d /= 2;
            constexpr long long bases[3] = { 2, 7, 61 };
            for (long long a : bases) {
                long long t = d;
                long long y = pow_mod_constexpr(a, t, n);
                while (t != n - 1 && y != 1 && y != n - 1) {
                    y = y * y % n;
                    t <<= 1;
                }
                if (y != n - 1 && t % 2 == 0) {
                    return false;
                }
            }
            return true;
        }
        template <int n> constexpr bool is_prime = is_prime_constexpr(n);

        // @param b `1 <= b`
        // @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
        constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
            a = safe_mod(a, b);
            if (a == 0) return { b, 0 };

            // Contracts:
            // [1] s - m0 * a = 0 (mod b)
            // [2] t - m1 * a = 0 (mod b)
            // [3] s * |m1| + t * |m0| <= b
            long long s = b, t = a;
            long long m0 = 0, m1 = 1;

            while (t) {
                long long u = s / t;
                s -= t * u;
                m0 -= m1 * u;  // |m1 * u| <= |m1| * s <= b

                // [3]:
                // (s - t * u) * |m1| + t * |m0 - m1 * u|
                // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
                // = s * |m1| + t * |m0| <= b

                auto tmp = s;
                s = t;
                t = tmp;
                tmp = m0;
                m0 = m1;
                m1 = tmp;
            }
            // by [3]: |m0| <= b/g
            // by g != b: |m0| < b/g
            if (m0 < 0) m0 += b / s;
            return { s, m0 };
        }

        // Compile time primitive root
        // @param m must be prime
        // @return primitive root (and minimum in now)
        constexpr int primitive_root_constexpr(int m) {
            if (m == 2) return 1;
            if (m == 167772161) return 3;
            if (m == 469762049) return 3;
            if (m == 754974721) return 11;
            if (m == 998244353) return 3;
            int divs[20] = {};
            divs[0] = 2;
            int cnt = 1;
            int x = (m - 1) / 2;
            while (x % 2 == 0) x /= 2;
            for (int i = 3; (long long)(i)*i <= x; i += 2) {
                if (x % i == 0) {
                    divs[cnt++] = i;
                    while (x % i == 0) {
                        x /= i;
                    }
                }
            }
            if (x > 1) {
                divs[cnt++] = x;
            }
            for (int g = 2;; g++) {
                bool ok = true;
                for (int i = 0; i < cnt; i++) {
                    if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                        ok = false;
                        break;
                    }
                }
                if (ok) return g;
            }
        }
        template <int m> constexpr int primitive_root = primitive_root_constexpr(m);

        // @param n `n < 2^32`
        // @param m `1 <= m < 2^32`
        // @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
        unsigned long long floor_sum_unsigned(unsigned long long n,
            unsigned long long m,
            unsigned long long a,
            unsigned long long b) {
            unsigned long long ans = 0;
            while (true) {
                if (a >= m) {
                    ans += n * (n - 1) / 2 * (a / m);
                    a %= m;
                }
                if (b >= m) {
                    ans += n * (b / m);
                    b %= m;
                }

                unsigned long long y_max = a * n + b;
                if (y_max < m) break;
                // y_max < m * (n + 1)
                // floor(y_max / m) <= n
                n = (unsigned long long)(y_max / m);
                b = (unsigned long long)(y_max % m);
                std::swap(m, a);
            }
            return ans;
        }

    }  // namespace internal

}  // namespace atcoder

namespace atcoder {

    namespace internal {

#ifndef _MSC_VER
        template <class T>
        using is_signed_int128 =
            typename std::conditional<std::is_same<T, __int128_t>::value ||
            std::is_same<T, __int128>::value,
            std::true_type,
            std::false_type>::type;

        template <class T>
        using is_unsigned_int128 =
            typename std::conditional<std::is_same<T, __uint128_t>::value ||
            std::is_same<T, unsigned __int128>::value,
            std::true_type,
            std::false_type>::type;

        template <class T>
        using make_unsigned_int128 =
            typename std::conditional<std::is_same<T, __int128_t>::value,
            __uint128_t,
            unsigned __int128>;

        template <class T>
        using is_integral = typename std::conditional<std::is_integral<T>::value ||
            is_signed_int128<T>::value ||
            is_unsigned_int128<T>::value,
            std::true_type,
            std::false_type>::type;

        template <class T>
        using is_signed_int = typename std::conditional<(is_integral<T>::value&&
            std::is_signed<T>::value) ||
            is_signed_int128<T>::value,
            std::true_type,
            std::false_type>::type;

        template <class T>
        using is_unsigned_int =
            typename std::conditional<(is_integral<T>::value&&
                std::is_unsigned<T>::value) ||
            is_unsigned_int128<T>::value,
            std::true_type,
            std::false_type>::type;

        template <class T>
        using to_unsigned = typename std::conditional<
            is_signed_int128<T>::value,
            make_unsigned_int128<T>,
            typename std::conditional<std::is_signed<T>::value,
            std::make_unsigned<T>,
            std::common_type<T>>::type>::type;

#else

        template <class T> using is_integral = typename std::is_integral<T>;

        template <class T>
        using is_signed_int =
            typename std::conditional<is_integral<T>::value&& std::is_signed<T>::value,
            std::true_type,
            std::false_type>::type;

        template <class T>
        using is_unsigned_int =
            typename std::conditional<is_integral<T>::value&&
            std::is_unsigned<T>::value,
            std::true_type,
            std::false_type>::type;

        template <class T>
        using to_unsigned = typename std::conditional<is_signed_int<T>::value,
            std::make_unsigned<T>,
            std::common_type<T>>::type;

#endif

        template <class T>
        using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

        template <class T>
        using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

        template <class T> using to_unsigned_t = typename to_unsigned<T>::type;

    }  // namespace internal

}  // namespace atcoder

namespace atcoder {

    namespace internal {

        struct modint_base {};
        struct static_modint_base : modint_base {};

        template <class T> using is_modint = std::is_base_of<modint_base, T>;
        template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;

    }  // namespace internal

    template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
    struct static_modint : internal::static_modint_base {
        using mint = static_modint;

    public:
        static constexpr int mod() { return m; }
        static mint raw(int v) {
            mint x;
            x._v = v;
            return x;
        }

        static_modint() : _v(0) {}
        template <class T, internal::is_signed_int_t<T>* = nullptr>
        static_modint(T v) {
            long long x = (long long)(v % (long long)(umod()));
            if (x < 0) x += umod();
            _v = (unsigned int)(x);
        }
        template <class T, internal::is_unsigned_int_t<T>* = nullptr>
        static_modint(T v) {
            _v = (unsigned int)(v % umod());
        }

        unsigned int val() const { return _v; }

        mint& operator++() {
            _v++;
            if (_v == umod()) _v = 0;
            return *this;
        }
        mint& operator--() {
            if (_v == 0) _v = umod();
            _v--;
            return *this;
        }
        mint operator++(int) {
            mint result = *this;
            ++* this;
            return result;
        }
        mint operator--(int) {
            mint result = *this;
            --* this;
            return result;
        }

        mint& operator+=(const mint& rhs) {
            _v += rhs._v;
            if (_v >= umod()) _v -= umod();
            return *this;
        }
        mint& operator-=(const mint& rhs) {
            _v -= rhs._v;
            if (_v >= umod()) _v += umod();
            return *this;
        }
        mint& operator*=(const mint& rhs) {
            unsigned long long z = _v;
            z *= rhs._v;
            _v = (unsigned int)(z % umod());
            return *this;
        }
        mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

        mint operator+() const { return *this; }
        mint operator-() const { return mint() - *this; }

        mint pow(long long n) const {
            assert(0 <= n);
            mint x = *this, r = 1;
            while (n) {
                if (n & 1) r *= x;
                x *= x;
                n >>= 1;
            }
            return r;
        }
        mint inv() const {
            if (prime) {
                assert(_v);
                return pow(umod() - 2);
            }
            else {
                auto eg = internal::inv_gcd(_v, m);
                assert(eg.first == 1);
                return eg.second;
            }
        }

        friend mint operator+(const mint& lhs, const mint& rhs) {
            return mint(lhs) += rhs;
        }
        friend mint operator-(const mint& lhs, const mint& rhs) {
            return mint(lhs) -= rhs;
        }
        friend mint operator*(const mint& lhs, const mint& rhs) {
            return mint(lhs) *= rhs;
        }
        friend mint operator/(const mint& lhs, const mint& rhs) {
            return mint(lhs) /= rhs;
        }
        friend bool operator==(const mint& lhs, const mint& rhs) {
            return lhs._v == rhs._v;
        }
        friend bool operator!=(const mint& lhs, const mint& rhs) {
            return lhs._v != rhs._v;
        }

    private:
        unsigned int _v;
        static constexpr unsigned int umod() { return m; }
        static constexpr bool prime = internal::is_prime<m>;
    };

    template <int id> struct dynamic_modint : internal::modint_base {
        using mint = dynamic_modint;

    public:
        static int mod() { return (int)(bt.umod()); }
        static void set_mod(int m) {
            assert(1 <= m);
            bt = internal::barrett(m);
        }
        static mint raw(int v) {
            mint x;
            x._v = v;
            return x;
        }

        dynamic_modint() : _v(0) {}
        template <class T, internal::is_signed_int_t<T>* = nullptr>
        dynamic_modint(T v) {
            long long x = (long long)(v % (long long)(mod()));
            if (x < 0) x += mod();
            _v = (unsigned int)(x);
        }
        template <class T, internal::is_unsigned_int_t<T>* = nullptr>
        dynamic_modint(T v) {
            _v = (unsigned int)(v % mod());
        }

        unsigned int val() const { return _v; }

        mint& operator++() {
            _v++;
            if (_v == umod()) _v = 0;
            return *this;
        }
        mint& operator--() {
            if (_v == 0) _v = umod();
            _v--;
            return *this;
        }
        mint operator++(int) {
            mint result = *this;
            ++* this;
            return result;
        }
        mint operator--(int) {
            mint result = *this;
            --* this;
            return result;
        }

        mint& operator+=(const mint& rhs) {
            _v += rhs._v;
            if (_v >= umod()) _v -= umod();
            return *this;
        }
        mint& operator-=(const mint& rhs) {
            _v += mod() - rhs._v;
            if (_v >= umod()) _v -= umod();
            return *this;
        }
        mint& operator*=(const mint& rhs) {
            _v = bt.mul(_v, rhs._v);
            return *this;
        }
        mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

        mint operator+() const { return *this; }
        mint operator-() const { return mint() - *this; }

        mint pow(long long n) const {
            assert(0 <= n);
            mint x = *this, r = 1;
            while (n) {
                if (n & 1) r *= x;
                x *= x;
                n >>= 1;
            }
            return r;
        }
        mint inv() const {
            auto eg = internal::inv_gcd(_v, mod());
            assert(eg.first == 1);
            return eg.second;
        }

        friend mint operator+(const mint& lhs, const mint& rhs) {
            return mint(lhs) += rhs;
        }
        friend mint operator-(const mint& lhs, const mint& rhs) {
            return mint(lhs) -= rhs;
        }
        friend mint operator*(const mint& lhs, const mint& rhs) {
            return mint(lhs) *= rhs;
        }
        friend mint operator/(const mint& lhs, const mint& rhs) {
            return mint(lhs) /= rhs;
        }
        friend bool operator==(const mint& lhs, const mint& rhs) {
            return lhs._v == rhs._v;
        }
        friend bool operator!=(const mint& lhs, const mint& rhs) {
            return lhs._v != rhs._v;
        }

    private:
        unsigned int _v;
        static internal::barrett bt;
        static unsigned int umod() { return bt.umod(); }
    };
    template <int id> internal::barrett dynamic_modint<id>::bt(998244353);

    using modint998244353 = static_modint<998244353>;
    using modint1000000007 = static_modint<1000000007>;
    using modint = dynamic_modint<-1>;

    namespace internal {

        template <class T>
        using is_static_modint = std::is_base_of<internal::static_modint_base, T>;

        template <class T>
        using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;

        template <class> struct is_dynamic_modint : public std::false_type {};
        template <int id>
        struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};

        template <class T>
        using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;

    }  // namespace internal

}  // namespace atcoder


using namespace atcoder;

vector <int> prime;
bool isprime[10001];
int g[10001];

int main(void)
{
    cin.tie(0);
    ios::sync_with_stdio(false);
    
    memset(isprime, true, sizeof(isprime));

    for (int i = 2; i <= 10000; i++)
    {
        if (isprime[i])
        {
            prime.push_back(i);
            for (int j = 2 * i; j <= 10000; j += i)
            {
                isprime[j] = false;
            }
        }
    }

    g[0] = 0;
    g[1] = 1;
    g[2] = 2;

    for (int i = 3; i <= 10000; i++)
    {
        set <int> S;
        S.insert(g[i - 1]);
        S.insert(g[i - 2]);
        for (int j = 0; ; j++)
        {
            if (S.find(j) == S.end())
            {
                g[i] = j;
                break;
            }
        }
    }
    int n, t;
    int grundy = 0;

    cin >> n;

    for (int i = 0; i < n; i++)
    {
        cin >> t;
        for (int j = 0; j < prime.size(); j++)
        {
            if (t == 1 && prime[j] * prime[j] < t)
            {
                break;
            }
            int cnt = 0;
            while (1)
            {
                if (t % prime[j] != 0) break;
                t /= prime[j];
                cnt++;
            }
            grundy ^= g[cnt];
        }
        if (t > 1)
        {
            grundy ^= g[1];
        }
    }

    if (grundy > 0)
    {
        cout << "Alice" << '\n';
    }
    else
    {
        cout << "Bob" << '\n';
    }
    return 0;
}
yukicoder

結果

テストケース

ソースコード
