結果

問題 No.2954 Calculation of Exponentiation
ユーザー Tatsu_mrTatsu_mr
提出日時 2024-11-08 23:49:23
言語 C++23
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 7,616 bytes
コンパイル時間 3,568 ms
コンパイル使用メモリ 262,664 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2024-11-08 23:49:34
合計ジャッジ時間 4,592 ms
ジャッジサーバーID
（参考情報） 		judge3 / 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
5,248 KB
testcase_01 AC 2 ms
5,248 KB
testcase_02 AC 2 ms
5,248 KB
testcase_03 AC 2 ms
5,248 KB
testcase_04 AC 2 ms
5,248 KB
testcase_05 AC 2 ms
5,248 KB
testcase_06 AC 2 ms
5,248 KB
testcase_07 AC 2 ms
5,248 KB
testcase_08 AC 2 ms
5,248 KB
testcase_09 AC 2 ms
5,248 KB
testcase_10 AC 2 ms
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testcase_11 AC 2 ms
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testcase_12 AC 2 ms
5,248 KB
testcase_13 AC 2 ms
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testcase_14 AC 2 ms
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testcase_15 AC 2 ms
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testcase_16 AC 2 ms
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testcase_17 AC 2 ms
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testcase_18 AC 2 ms
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testcase_19 AC 2 ms
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testcase_20 AC 2 ms
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testcase_21 AC 2 ms
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testcase_22 AC 2 ms
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testcase_23 AC 2 ms
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testcase_24 AC 2 ms
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testcase_25 AC 2 ms
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testcase_26 AC 2 ms
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testcase_27 AC 2 ms
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testcase_28 AC 2 ms
5,248 KB
testcase_29 AC 2 ms
5,248 KB
testcase_30 AC 2 ms
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ソースコード

diff # 

#include <bits/stdc++.h>
#define For(i, a, b) for(int i = a; i < b; i++)
#define rep(i, n) For(i, 0, n)
#define rFor(i, a, b) for(int i = a; i >= b; i--)
#define ALL(v) (v).begin(), (v).end()
#define rALL(v) (v).rbegin(), (v).rend()
using namespace std;

using lint = long long;
using ld = long double;

int INF = 2000000000;
lint LINF = 1000000000000000000;

struct Fraction {
    using lint = long long;
    
    private:
    lint gcd(lint x, lint y) {
        if (y == 0) {
            return x;
        }
        return gcd(y, x % y);
    }
    
    void reduce() {
        if (p != 0) {
            lint g = gcd(abs(p), abs(q));
            p /= g;
            q /= g;
        } else {
            q = 1;
        }
    }
    
    int comp(lint a, lint b, lint c, lint d) const {
        if (a == c && b == d) {
            return 0;
        }
        return (a * d < c * b ? -1 : 1);
    }

    public:
    lint p, q;
    
    Fraction() : p(0), q(1) {}
    Fraction(lint p_, lint q_) : p(p_), q(q_) {
        assert(q_ != 0);
        if (q < 0) {
            p = -p;
            q = -q;
        }
        reduce();
    }
    Fraction(lint p_) : p(p_), q(1) {}
    
    Fraction &operator+=(const Fraction &a) {
        lint np = p * a.q + q * a.p;
        lint nq = q * a.q;
        *this = Fraction(np, nq);
        return *this;
    }
    
    Fraction &operator-=(const Fraction &a) {
        lint np = p * a.q - q * a.p;
        lint nq = q * a.q;
        *this = Fraction(np, nq);
        return *this;
    }
    
    Fraction &operator*=(const Fraction &a) {
        lint np = p * a.p;
        lint nq = q * a.q;
        *this = Fraction(np, nq);
        return *this;
    }
    
    Fraction &operator/=(const Fraction &a) {
        assert(a.p != 0);
        lint np = p * a.q;
        lint nq = q * a.p;
        *this = Fraction(np, nq);
        return *this;
    }
    
    Fraction operator+(const Fraction &a) {
        return Fraction(*this) += a;
    }
    
    Fraction operator-(const Fraction &a) {
        return Fraction(*this) -= a;
    }
    
    Fraction operator*(const Fraction &a) {
        return Fraction(*this) *= a;
    }
    
    Fraction operator/(const Fraction &a) {
        return Fraction(*this) /= a;
    }
    
    Fraction operator-() {
        p = -p;
        return *this;
    }
    
    bool operator==(const Fraction &a) const {
        return comp(p, q, a.p, a.q) == 0;
    }
    
    bool operator!=(const Fraction &a) const {
        return comp(p, q, a.p, a.q) != 0;
    }
    
    bool operator<(const Fraction &a) const {
        return comp(p, q, a.p, a.q) == -1;
    }
    
    bool operator>(const Fraction &a) const {
        return comp(p, q, a.p, a.q) == 1;
    }
    
    bool operator<=(const Fraction &a) const {
        return comp(p, q, a.p, a.q) <= 0;
    }
    
    bool operator>=(const Fraction &a) const {
        return comp(p, q, a.p, a.q) >= 0;
    }
    
    friend ostream &operator<<(ostream &os, Fraction a) {
        return os << a.p << "/" << a.q;
    }
};

namespace fastprime {

template <class T>
T modpow(T a, T b, T mod) {
    T cur = a % mod, res = 1 % mod;
    while (b) {
        if (b & 1) {
            res = (res * cur) % mod;
        }
        cur = (cur * cur) % mod;
        b >>= 1;
    }
    return res;
}

bool MillerRabin(long long n) {
    if (n <= 1) {
        return false;
    }
    if (n == 2 || n == 7 || n == 61) {
        return true;
    }
    if (n % 2 == 0) {
        return false;
    }
    
    vector<long long> A;
    if (n < 4759123141) {
        A = {2, 7, 61};
    } else {
        A = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
    }
    long long s = 0, d = n - 1;
    while (d % 2 == 0) {
        s++;
        d >>= 1;
    }
    for (auto a : A) {
        if (a % n == 0) {
            return true;
        }
        long long x = modpow<__int128_t>(a, d, n);
        if (x == 1) {
            continue;
        }
        bool ok = false;
        for (int i = 0; i < s; i++) {
            if (x == n - 1) {
                ok = true;
                break;
            }
            x = (__int128_t)x * x % n;
        }
        if (!ok) {
            return false;
        }
    }
    return true;
}

long long gcd(long long x, long long y) {
    if (y == 0) {
        return x;
    }
    return gcd(y, x % y);
}

unsigned int xorshift() {
    static unsigned int x = 123456789, y = 362436069, z = 521288629, w = 88675123;
    unsigned int t = (x ^ (x << 11));
    x = y;
    y = z;
    z = w;
    return (w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)));
}

long long Pollard(long long n) {
    if (n % 2 == 0) {
        return 2LL;
    }
    if (MillerRabin(n)) {
        return n;
    }
    
    long long i = 0;
    while (true) {
        i++;
        long long r = xorshift();
        auto f = [&](long long x) {
            return (__int128_t(x) * x + r) % n;
        };
        long long x = i, y = f(x);
        while (true) {
            long long p = gcd(abs(y - x + n), 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> l = prime_factorize(p);
    vector<long long> r = prime_factorize(n / p);
    for (auto x : r) {
        l.emplace_back(x);
    }
    sort(l.begin(), l.end());
    return l;
}

vector<long long> divisors(long long n) {
    if (n == 1) {
        return {1LL};
    }
    auto divisor_dfs = [&](auto divisor_dfs, vector<pair<long long, long long>> &p, long long t, int cur, vector<long long> &res) -> void {
        if (cur == p.size()) {
            res.emplace_back(t);
            return;
        }
        divisor_dfs(divisor_dfs, p, t, cur + 1, res);
        for (int i = 0; i < p[cur].second; i++) {
            t *= p[cur].first;
            divisor_dfs(divisor_dfs, p, t, cur + 1, res);
        }
    };
    
    vector<long long> res, pf = prime_factorize(n);
    
    vector<pair<long long, long long>> p;
    long long cnt = 1, now = pf[0];
    for (int i = 1; i < (int)pf.size(); i++) {
        if (pf[i] == now) {
            cnt++;
        } else {
            p.emplace_back(now, cnt);
            now = pf[i];
            cnt = 1;
        }
    }
    p.emplace_back(now, cnt);
    
    divisor_dfs(divisor_dfs, p, 1, 0, res);
    sort(res.begin(), res.end());
    return res;
}

} // namespace fastprime

using namespace fastprime;

template <class T>
vector<pair<T, int>> RLE(vector<T> v) {
    vector<pair<T, int>> res;
    for (auto x : v) {
        if (res.size() == 0 || res.back().first != x) {
            res.emplace_back(x, 1);
        } else {
            res.back().second++;
        }
    }
    return res;
}

int main() {
    ld a, b;
    cin >> a >> b;
    if (b == 0.0000) {
        cout << "Yes" << endl;
        return 0;
    }
    lint ap, aq, bp, bq;
    if (b >= 0) {
        ap = a * 10000, aq = 10000;
        bp = b * 10000, bq = 10000;
    } else {
        b *= -1;
        ap = a * 10000, aq = 10000;
        bp = b * 10000, bq = 10000;
        swap(ap, aq);
    }
    Fraction A(ap, aq), B(bp, bq);
    if (A.q != 1) {
        cout << "No" << endl;
        return 0;
    }
    auto d = RLE(prime_factorize(A.p));
    for (auto [fi, se] : d) {
        if (B.q != 0 && se % B.q != 0) {
            cout << "No" << endl;
            return 0;
        }
    }
    cout << "Yes" << endl;
}
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