結果

問題 No.1218 Something Like a Theorem
ユーザー r1933r1933
提出日時 2020-09-04 22:06:38
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 4 ms / 2,000 ms
コード長 4,676 bytes
コンパイル時間 4,108 ms
コンパイル使用メモリ 216,008 KB
最終ジャッジ日時 2025-01-14 05:46:48
ジャッジサーバーID
（参考情報） 		judge1 / judge2
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ファイルパターン 結果
sample AC * 2
other AC * 16
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 # 

#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include "bits/stdc++.h"

// Begin Header {{{
using namespace std;

#ifndef DEBUG
#define dump(...)
#endif

#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define rep(i, b, e) for (intmax_t i = (b), i##_limit = (e); i < i##_limit; ++i)
#define repc(i, b, e) for (intmax_t i = (b), i##_limit = (e); i <= i##_limit; ++i)
#define repr(i, b, e) for (intmax_t i = (b), i##_limit = (e); i >= i##_limit; --i)
#define var(Type, ...) Type __VA_ARGS__; input(__VA_ARGS__)

constexpr size_t    operator""_zu(unsigned long long value) { return value; };
constexpr intmax_t  operator""_jd(unsigned long long value) { return value; };
constexpr uintmax_t operator""_ju(unsigned long long value) { return value; };

constexpr int INF = 0x3f3f3f3f;
constexpr intmax_t LINF = 0x3f3f3f3f3f3f3f3f_jd;

template <class T, class Compare = less<>>
using MaxHeap = priority_queue<T, vector<T>, Compare>;
template <class T, class Compare = greater<>>
using MinHeap = priority_queue<T, vector<T>, Compare>;

inline void input() {}
template <class Head, class... Tail>
inline void input(Head&& head, Tail&&... tail) {
    cin >> head;
    input(forward<Tail>(tail)...);
}

template <class Container, class Value = typename Container::value_type,
         enable_if_t<!is_same<Container, string>::value, nullptr_t> = nullptr>
 inline istream& operator>>(istream &is, Container &vs) {
     for (auto &v: vs) is >> v;
     return is;
 }

inline void output() { cout << "\n"; }
template <class Head, class... Tail>
inline void output(Head&& head, Tail&&... tail) {
    cout << head;
    if (sizeof...(tail)) cout << " ";
    output(forward<Tail>(tail)...);
}

template <class Container, class Value = typename Container::value_type,
         enable_if_t<!is_same<Container, string>::value, nullptr_t> = nullptr>
 inline ostream& operator<<(ostream &os, const Container &vs) {
     static constexpr const char *delim[] = {" ", ""};
     for (auto it = begin(vs); it != end(vs); ++it) {
         os << delim[it == begin(vs)] << *it;
     }
     return os;
 }

template <class Iterator>
inline void join(const Iterator &Begin, const Iterator &End, const string &delim = " ", const string &last = "\n") {
    for (auto it = Begin; it != End; ++it) {
        cout << ((it == Begin) ? "" : delim) << *it;
    }
    cout << last;
}

template <class T>
inline vector<T> makeVector(const T &initValue, size_t sz) {
    return vector<T>(sz, initValue);
}

template <class T, class... Args>
inline auto makeVector(const T &initValue, size_t sz, Args... args) {
    return vector<decltype(makeVector<T>(initValue, args...))>(sz, makeVector<T>(initValue, args...));
}

template <class Func>
class FixPoint : Func {
public:
    explicit constexpr FixPoint(Func&& f) noexcept : Func(forward<Func>(f)) {}

    template <class... Args>
    constexpr decltype(auto) operator()(Args&&... args) const {
        return Func::operator()(*this, std::forward<Args>(args)...);
    }
};

template <class Func>
static inline constexpr decltype(auto) makeFixPoint(Func&& f) noexcept {
    return FixPoint<Func>{forward<Func>(f)};
}

template <class Container>
struct reverse_t {
    Container &c;
    reverse_t(Container &c) : c(c) {}
    auto begin() { return c.rbegin(); }
    auto end() { return c.rend(); }
};

template <class Container>
auto reversed(Container &c) {
    return reverse_t<Container>(c);
}

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

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

template <class T>
inline T diff(const T &a, const T &b) noexcept {
    return a < b ? b - a : a - b;
}

void ioinit() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(10);
    clog << fixed << setprecision(10);
}
// }}} End Header

intmax_t power(intmax_t n, intmax_t p) {
    intmax_t ret = 1;
    for (; p > 0; p >>= 1) {
        if (p & 1) ret *= n;
        n *= n;
    }
    return ret;
}

signed main() {
    ioinit();

    var(intmax_t, n, z);

    const intmax_t Z = power(z, n);

    bool valid = false;
    rep(x, 1, z) {
        const intmax_t X = power(x, n);
        const intmax_t Y = Z - X;
        intmax_t ok = 1, ng = z;
        while (ng - ok > 1) {
            const intmax_t mid = (ng + ok) / 2;
            if (power(mid, n) <= Y) ok = mid;
            else ng = mid;
        }
        if (power(ok, n) == Y) {
            valid = true;
            break;
        }
    }

    cout << ((valid) ? "Yes" : "No") << "\n";
    return 0;
}
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