#663664 (C++17) No.1529 Constant Lcm

• 問題: No.1529 Constant Lcm
• ユーザー: KoD
• 提出日時: 2021-06-04 21:45:49
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 244 ms / 3,000 ms
• コード長: 7,166 bytes
• コンパイル時間: 2,160 ms
• コンパイル使用メモリ: 201,268 KB
• 最終ジャッジ日時: 2025-01-22 00:31:14
• ジャッジサーバーID （参考情報）: judge4 / judge4

ファイルパターン	結果
sample	AC * 2
other	AC * 24

ソースコード

#include <bits/stdc++.h>

using i32 = std::int32_t;
using u32 = std::uint32_t;
using i64 = std::int64_t;
using u64 = std::uint64_t;
using i128 = __int128_t;
using u128 = __uint128_t;
using isize = std::ptrdiff_t;
using usize = std::size_t;

class rep {
    struct Iter {
        usize itr;
        constexpr Iter(const usize pos) noexcept : itr(pos) {}
        constexpr void operator++() noexcept { ++itr; }
        constexpr bool operator!=(const Iter& other) const noexcept { return itr != other.itr; }
        constexpr usize operator*() const noexcept { return itr; }
    };
    const Iter first, last;

  public:
    explicit constexpr rep(const usize first, const usize last) noexcept : first(first), last(std::max(first, last)) {}
    constexpr Iter begin() const noexcept { return first; }
    constexpr Iter end() const noexcept { return last; }
};

constexpr u64 ceil_log2(const u64 x) {
    u64 e = 0;
    while (((u64)1 << e) < x) ++e;
    return e;
}

template <class F> class AutoReallocation {
    using R = typename decltype(std::declval<F>()((usize)0))::value_type;

    F func;
    mutable std::vector<R> data;

  public:
    explicit AutoReallocation(F&& f) : func(std::forward<F>(f)), data() {}

    void reserve(const usize size) const {
        if (data.size() < size) data = func(((usize)1 << ceil_log2(size)));
    }
    R operator[](const usize i) const {
        reserve(i + 1);
        return data[i];
    }
};

template <class F> decltype(auto) auto_realloc(F&& f) {
    using G = std::decay_t<F>;
    return AutoReallocation<G>(std::forward<G>(f));
}

struct PrimeSieve {
    static inline const auto min_prime = auto_realloc([](const usize n) {
        std::vector<usize> ret(n);
        std::iota(ret.begin(), ret.end(), (usize)0);
        std::vector<usize> list;
        for (const usize i : rep(2, n)) {
            if (ret[i] == i) list.push_back(i);
            for (const usize p : list) {
                if (p * i >= n || p > ret[i]) break;
                ret[p * i] = p;
            }
        }
        return ret;
    });
    static bool is_prime(const usize n) {
        if (n <= 1) return false;
        return min_prime[n] == n;
    }
    template <class T> static std::vector<std::pair<T, usize>> factorize(T x) {
        assert(x > 0);
        std::vector<std::pair<T, usize>> ret;
        while (x != 1) {
            const usize p = min_prime[x];
            ret.emplace_back((T)p, 0);
            while (min_prime[x] == p) {
                ret.back().second++;
                x /= p;
            }
        }
        return ret;
    }
};

template <class T> bool setmax(T& lhs, const T& rhs) {
    if (lhs < rhs) {
        lhs = rhs;
        return true;
    }
    return false;
}

template <class T> constexpr T totient(T x) {
    T ret = x;
    for (T i = 2; i * i <= x; ++i) {
        if (x % i == 0) {
            ret /= i;
            ret *= i - 1;
            while (x % i == 0) x /= i;
        }
    }
    if (x > 1) {
        ret /= x;
        ret *= x - 1;
    }
    return ret;
}

template <class T> constexpr T rem_euclid(T value, const T& mod) { return (value %= mod) >= 0 ? value : value + mod; }

template <u32 MOD, std::enable_if_t<((u32)1 <= MOD and MOD <= ((u32)1 << 31))>* = nullptr> class StaticModint {
    using Mint = StaticModint;

    static inline constexpr u32 PHI = totient(MOD);
    u32 v;

  public:
    static constexpr u32 mod() noexcept { return MOD; }

    template <class T, std::enable_if_t<std::is_signed_v<T> and std::is_integral_v<T>>* = nullptr>
    static constexpr T normalize(const T x) noexcept {
        return rem_euclid<std::common_type_t<T, i64>>(x, MOD);
    }
    template <class T, std::enable_if_t<std::is_unsigned_v<T> and std::is_integral_v<T>>* = nullptr>
    static constexpr T normalize(const T x) noexcept {
        return x % MOD;
    }

    constexpr StaticModint() noexcept : v(0) {}
    template <class T> constexpr StaticModint(const T x) noexcept : v(normalize(x)) {}
    template <class T> static constexpr Mint raw(const T x) noexcept {
        Mint ret;
        ret.v = x;
        return ret;
    }

    constexpr u32 get() const noexcept { return v; }
    constexpr Mint neg() const noexcept { return raw(v == 0 ? 0 : MOD - v); }
    constexpr Mint inv() const noexcept { return pow(PHI - 1); }
    constexpr Mint pow(u64 exp) const noexcept {
        Mint ret(1), mult(*this);
        for (; exp > 0; exp >>= 1) {
            if (exp & 1) ret *= mult;
            mult *= mult;
        }
        return ret;
    }

    constexpr Mint operator-() const noexcept { return neg(); }
    constexpr Mint operator~() const noexcept { return inv(); }

    constexpr Mint operator+(const Mint& rhs) const noexcept { return Mint(*this) += rhs; }
    constexpr Mint& operator+=(const Mint& rhs) noexcept {
        if ((v += rhs.v) >= MOD) v -= MOD;
        return *this;
    }

    constexpr Mint operator-(const Mint& rhs) const noexcept { return Mint(*this) -= rhs; }
    constexpr Mint& operator-=(const Mint& rhs) noexcept {
        if (v < rhs.v) v += MOD;
        v -= rhs.v;
        return *this;
    }

    constexpr Mint operator*(const Mint& rhs) const noexcept { return Mint(*this) *= rhs; }
    constexpr Mint& operator*=(const Mint& rhs) noexcept {
        v = (u64)v * rhs.v % MOD;
        return *this;
    }

    constexpr Mint operator/(const Mint& rhs) const noexcept { return Mint(*this) /= rhs; }
    constexpr Mint& operator/=(const Mint& rhs) noexcept { return *this *= rhs.inv(); }

    constexpr bool operator==(const Mint& rhs) const noexcept { return v == rhs.v; }
    constexpr bool operator!=(const Mint& rhs) const noexcept { return v != rhs.v; }
    friend std::ostream& operator<<(std::ostream& stream, const Mint& rhs) { return stream << rhs.v; }
};

using Modint1000000007 = StaticModint<1000000007>;
using Modint998244353 = StaticModint<998244353>;

template <class T> using Vec = std::vector<T>;

using Fp = Modint998244353;

void main_() {
    usize N;
    std::cin >> N;
    Vec<usize> max(N);
    for (const auto i : rep(1, N / 2 + 1)) {
        const auto left = PrimeSieve::factorize(i);
        const auto right = PrimeSieve::factorize(N - i);
        usize l = 0, r = 0;
        while (l < left.size() or r < right.size()) {
            if (l < left.size() and r < right.size() and left[l].first == right[r].first) {
                setmax(max[left[l].first], left[l].second + right[r].second);
                l += 1;
                r += 1;
            } else {
                if (r == right.size() or (l < left.size() and left[l].first < right[r].first)) {
                    setmax(max[left[l].first], left[l].second);
                    l += 1;
                } else {
                    setmax(max[right[r].first], right[r].second);
                    r += 1;
                }
            }
        }
    }
    Fp ans = 1;
    for (const auto i : rep(1, N)) {
        // std::cerr << i << ' ' << max[i] << std::endl;
        ans *= Fp(i).pow(max[i]);
    }
    std::cout << ans << '\n';
}

int main() {
    std::ios_base::sync_with_stdio(false);
    std::cin.tie(nullptr);
    main_();
    return 0;
}