結果

問題 No.1396 Giri
ユーザー r1933r1933
提出日時 2021-02-14 22:18:28
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 619 ms / 2,000 ms
コード長 10,748 bytes
コンパイル時間 3,256 ms
コンパイル使用メモリ 229,004 KB
実行使用メモリ 93,796 KB
最終ジャッジ日時 2023-09-29 15:55:11
合計ジャッジ時間 9,534 ms
ジャッジサーバーID
（参考情報） 		judge12 / judge15
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
4,380 KB
testcase_01 AC 1 ms
4,380 KB
testcase_02 AC 618 ms
93,596 KB
testcase_03 AC 1 ms
4,380 KB
testcase_04 AC 2 ms
4,376 KB
testcase_05 AC 617 ms
93,544 KB
testcase_06 AC 1 ms
4,376 KB
testcase_07 AC 2 ms
4,376 KB
testcase_08 AC 2 ms
4,376 KB
testcase_09 AC 1 ms
4,376 KB
testcase_10 AC 1 ms
4,376 KB
testcase_11 AC 2 ms
4,376 KB
testcase_12 AC 1 ms
4,380 KB
testcase_13 AC 2 ms
4,376 KB
testcase_14 AC 2 ms
4,380 KB
testcase_15 AC 2 ms
4,376 KB
testcase_16 AC 2 ms
4,380 KB
testcase_17 AC 6 ms
4,376 KB
testcase_18 AC 33 ms
9,832 KB
testcase_19 AC 309 ms
50,240 KB
testcase_20 AC 431 ms
68,088 KB
testcase_21 AC 548 ms
84,656 KB
testcase_22 AC 607 ms
92,492 KB
testcase_23 AC 619 ms
93,796 KB
testcase_24 AC 615 ms
93,612 KB
testcase_25 AC 613 ms
93,600 KB
権限があれば一括ダウンロードができます
コンパイルメッセージ
main.cpp: 関数 ‘int main()’ 内:
main.cpp:13:64: 警告: ‘mxp’ may be used uninitialized [-Wmaybe-uninitialized]
   13 | #define rep(i, b, e) for (intmax_t i = (b), i##_limit = (e); i < i##_limit; ++i)
      |                                                                ^
main.cpp:361:14: 備考: ‘mxp’ はここで定義されています
  361 |     intmax_t mxp;
      |              ^~~

ソースコード

diff # 

#pragma GCC optimize("Ofast")
#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;
}

template <class T, class U>
inline istream& operator>>(istream &is, pair<T, U> &p) {
    is >> p.first >> p.second;
    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 = "\n", 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 &init_value, size_t sz) {
    return vector<T>(sz, init_value);
}

template <class T, class... Args>
inline auto makeVector(const T &init_value, size_t sz, Args... args) {
    return vector<decltype(makeVector<T>(init_value, args...))>(sz, makeVector<T>(init_value, 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 operator|=(vector<bool>::reference lhs, const bool rhs) {
    lhs = lhs | rhs;
}

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

// SmartSieve {{{
class SmartSieve {
    intmax_t L, R, M;
    vector<intmax_t> small; // 小さい篩 [2, sqrt(R))
    vector<vector<intmax_t>> large; // 大きい篩 [L, R)
    vector<intmax_t> aux; // aux[i] := large[i] の素因数の積

public:
    SmartSieve(intmax_t L, intmax_t R) : L(L), R(R), M(sqrt(R) + 1) {
        small.resize(M);
        iota(small.begin(), small.end(), 0);
        large.resize(R - L);
        aux.assign(R - L, 1);

        for (intmax_t i = 2; i * i < R; ++i) {
            if (small[i] < i) continue;

            for (intmax_t j = i * i; j < M; j += i) {
                if (small[j] == j) small[j] = i;
            }

            for (intmax_t j = (L + i - 1) / i * i; j < R; j += i) {
                intmax_t k = j;
                do {
                    if (aux[j - L] * aux[j - L] > R) break;

                    large[j - L].emplace_back(i);
                    aux[j - L] *= i;
                    k /= i;
                } while (k % i == 0);
            }
        }
    }

    bool isPrime(intmax_t n) const {
        assert(L <= n && n < R);
        if (n < M) return (2 <= n && small[n] == n);
        return (aux[n - L] == 1);
    }

    map<intmax_t, intmax_t> primeFactor(intmax_t n) {
        assert(L <= n && n < R);
        map<intmax_t, intmax_t> ret;
        for (const auto& e: large[n - L]) ret[e]++;
        n /= aux[n - L];
        if (n >= M) {
            ret[n]++;
            return ret;
        }
        while (n > 1) {
            ret[small[n]]++;
            n /= small[n];
        }
        return ret;
    }
};
// }}}

// ModInt {{{
template <intmax_t Modulo>
class ModInt {
public:
    using value_type = intmax_t;

private:
    static constexpr value_type cmod = Modulo; // compile-time
    static value_type rmod; // runtime
    value_type value = 0;

    static constexpr value_type inverse(value_type n, value_type m) {
        value_type a = n;
        value_type b = m;
        value_type x = 0;
        value_type y = 1;
        for (value_type u = y, v = x; a;) {
            const value_type t = b / a;
            swap(x -= t * u, u);
            swap(y -= t * v, v);
            swap(b -= t * a, a);
        }
        if ((x %= m) < 0) x += m;
        return x;
    }

    static value_type normalize(intmax_t n, value_type m) {
        if (n >= m) {
            n %= m;
        } else if (n < 0) {
            if ((n %= m) < 0) n += m;
        }
        return n;
    }

public:
    ModInt() = default;
    ModInt(intmax_t n) : value(normalize(n, getModulo())) {}

    template <typename T>
        constexpr explicit operator T() const { return static_cast<T>(value); }

    ModInt& operator=(intmax_t n) {
        value = normalize(n, getModulo());
        return *this;
    }

    ModInt& operator+=(const ModInt& other) {
        if ((value += other.value) >= getModulo()) value -= getModulo();
        return *this;
    }
    ModInt& operator-=(const ModInt& other) {
        if ((value -= other.value) < 0) value += getModulo();
        return *this;
    }
    ModInt& operator*=(const ModInt& other) {
        value = (value * other.value) % getModulo();
        return *this;
    }
    ModInt& operator/=(const ModInt& other) {
        value = (value * inverse(other.value, getModulo())) % getModulo();
        return *this;
    }

    ModInt& operator++() {
        if (++value == getModulo()) value = 0;
        return *this;
    }
    ModInt& operator--() {
        if (value-- == 0) value = getModulo() - 1;
        return *this;
    }

    ModInt operator++(int) {
        const ModInt tmp(*this);
        ++*this;
        return tmp;
    }
    ModInt operator--(int) {
        const ModInt tmp(*this);
        --*this;
        return tmp;
    }

    friend ModInt operator+(ModInt lhs, const ModInt& rhs) { return lhs += rhs; }
    friend ModInt operator-(ModInt lhs, const ModInt& rhs) { return lhs -= rhs; }
    friend ModInt operator*(ModInt lhs, const ModInt& rhs) { return lhs *= rhs; }
    friend ModInt operator/(ModInt lhs, const ModInt& rhs) { return lhs /= rhs; }

    ModInt operator+() const { return *this; }
    ModInt operator-() const {
        if (value == 0) return *this;
        return ModInt(getModulo() - value);
    }

    friend bool operator==(const ModInt& lhs, const ModInt& rhs) {
        return lhs.value == rhs.value;
    }
    friend bool operator!=(const ModInt& lhs, const ModInt& rhs) {
        return !(lhs == rhs);
    }

    friend ostream& operator<<(ostream& os, const ModInt& n) {
        return os << n.value;
    }
    friend istream& operator>>(istream& is, ModInt& n) {
        is >> n.value;
        n.value = normalize(n.value, getModulo());
        return is;
    }

    static value_type getModulo() { return ((cmod > 0) ? cmod : rmod); }

    template <int M = Modulo, typename T = typename enable_if<(M <= 0)>::type>
        static T setModulo(value_type m) { rmod = m; }
};

template <intmax_t M>
constexpr typename ModInt<M>::value_type ModInt<M>::cmod;
template <intmax_t M>
typename ModInt<M>::value_type ModInt<M>::rmod;
// }}}

// constexpr intmax_t MOD = intmax_t(1e9) + 7;
constexpr intmax_t MOD = 998244353;
using Mint = ModInt<MOD>;

vector<bool> sieve(intmax_t MAX) {
    vector<bool> is_prime(MAX + 1, true);
    is_prime[0] = is_prime[1] = false;

    for (intmax_t i = 2; i * i <= MAX; ++i) {
        if (is_prime[i]) {
            for (intmax_t j = 2; i * j <= MAX; ++j) {
                is_prime[i * j] = false;
            }
        }
    }

    return is_prime;
}

template <class T>
T power(const T& b, const intmax_t& e) {
    T ret = 1;
    T n = b;
    for (intmax_t p = abs(e); p > 0; p >>= 1) {
        if (p & 1) ret *= n;
        n *= n;
    }
    if (e < 0) return T(1) / ret;
    return ret;
}

int main() {
    ioinit();

    var(intmax_t, N);

    auto prime = sieve(N + 1);
    intmax_t mxp;
    repr(i, N, 1) {
        if (prime[i]) {
            mxp = i;
            break;
        }
    }

    SmartSieve sieve(1, N + 1);
    vector<intmax_t> mxl(N + 1); // mxl[p] := mxp より小さい整数について、素因数 p の個数の max
    vector<intmax_t> mxr(N + 1); // mxr[p] := mxp より大きい整数について、素因数 p の個数の max
    rep(i, 1, mxp) {
        for (const auto [p, c]: sieve.primeFactor(i)) {
            chmax(mxl[p], c);
        }
    }
    repc(i, mxp + 1, N) {
        for (const auto [p, c]: sieve.primeFactor(i)) {
            chmax(mxr[p], c);
        }
    }

    Mint res = 1;
    repc(i, 1, N) {
        res *= power<Mint>(i, max(mxl[i], mxr[i]));
    }

    output(res);
    return 0;
}
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