結果

問題 No.1195 数え上げを愛したい（文字列編）
ユーザー square1001
提出日時 2020-08-22 14:17:54
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,474 ms / 3,000 ms
コード長 8,141 bytes
コンパイル時間 1,097 ms
コンパイル使用メモリ 89,328 KB
実行使用メモリ 18,984 KB
最終ジャッジ日時 2024-10-15 08:31:49
合計ジャッジ時間 11,310 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge2
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ファイルパターン 結果
other AC * 26
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ソースコード

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プレゼンテーションモードにする

#ifndef CLASS_FAST_MODINT
#define CLASS_FAST_MODINT
#include <vector>
#include <cstdint>
using singlebit = uint32_t;
using doublebit = uint64_t;
const int digit_level = 32;
static constexpr singlebit find_inv(singlebit n, int d = 6, singlebit x = 1) {
    return d == 0 ? x : find_inv(n, d - 1, x * (2 - x * n));
}
template <singlebit mod> class fast_modint {
    // Fast Modulo Integer, Assertion: mod < 2^(bits of singlebit - 1) and mod is prime
private:
    singlebit n;
    static constexpr singlebit r2 = (((doublebit(1) << digit_level) % mod) << digit_level) % mod;
    static constexpr singlebit ninv = singlebit(-1) * find_inv(mod);
    singlebit reduce(doublebit x) const {
        singlebit res = (x + doublebit(singlebit(x) * ninv) * mod) >> digit_level;
        return res < mod ? res : res - mod;
    }
public:
    fast_modint() : n(0) {};
    fast_modint(singlebit n_) { n = reduce(doublebit(n_) * r2); };
    static constexpr singlebit get_mod() { return mod; }
    singlebit get() const { return reduce(n); }
    bool operator==(const fast_modint& x) const { return n == x.n; }
    bool operator!=(const fast_modint& x) const { return n != x.n; }
    fast_modint& operator+=(const fast_modint& x) { n += x.n; n -= (n < mod ? 0 : mod); return *this; }
    fast_modint& operator-=(const fast_modint& x) { n += mod - x.n; n -= (n < mod ? 0 : mod); return *this; }
    fast_modint& operator*=(const fast_modint& x) { n = reduce(doublebit(n) * x.n); return *this; }
    fast_modint operator+(const fast_modint& x) const { return fast_modint(*this) += x; }
    fast_modint operator-(const fast_modint& x) const { return fast_modint(*this) -= x; }
    fast_modint operator*(const fast_modint& x) const { return fast_modint(*this) *= x; }
    fast_modint inv() const { return binpow(mod - 2); }
    fast_modint binpow(singlebit b) const {
        fast_modint ans(1), cur(*this);
        while (b > 0) {
            if (b & 1) ans *= cur;
            cur *= cur;
            b >>= 1;
        }
        return ans;
    }
};
template<typename modulo>
std::vector<modulo> get_modvector(std::vector<int> v) {
    std::vector<modulo> ans(v.size());
    for (int i = 0; i < v.size(); ++i) {
        ans[i] = modulo(v[i]);
    }
    return ans;
}
#endif // CLASS_FAST_MODINT
#ifndef CLASS_POLYNOMIAL_NTT
#define CLASS_POLYNOMIAL_NTT
template<singlebit mod, singlebit depth, singlebit primroot>
class polynomial_ntt {
public:
    using modulo = fast_modint<mod>;
    static void fourier_transform(std::vector<modulo>& v, bool inverse) {
        std::size_t s = v.size();
        for (std::size_t i = 0, j = 1; j < s - 1; ++j) {
            for (std::size_t k = s >> 1; k > (i ^= k); k >>= 1);
            if (i < j) std::swap(v[i], v[j]);
        }
        std::size_t sc = 0, sz = 1;
        while (sz < s) sz *= 2, ++sc;
        modulo root = modulo(primroot).binpow((mod - 1) >> sc);
        std::vector<modulo> pw(s + 1); pw[0] = 1;
        for (std::size_t i = 1; i <= s; i++) pw[i] = pw[i - 1] * root;
        std::size_t qs = s;
        for (std::size_t b = 1; b < s; b <<= 1) {
            qs >>= 1;
            for (std::size_t i = 0; i < s; i += b * 2) {
                for (std::size_t j = i; j < i + b; ++j) {
                    modulo delta = pw[(inverse ? b * 2 - j + i : j - i) * qs] * v[j + b];
                    v[j + b] = v[j] - delta;
                    v[j] += delta;
                }
            }
        }
        if (!inverse) return;
        modulo powinv = modulo((mod + 1) / 2).binpow(sc);
        for (std::size_t i = 0; i < s; ++i) {
            v[i] = v[i] * powinv;
        }
    }
    static std::vector<modulo> convolve(std::vector<modulo> v1, std::vector<modulo> v2) {
        std::size_t s1 = v1.size(), s2 = v2.size(), s = 1;
        while (s < s1 || s < s2) s *= 2;
        v1.resize(s * 2); fourier_transform(v1, false);
        v2.resize(s * 2); fourier_transform(v2, false);
        for (singlebit i = 0; i < s * 2; ++i) v1[i] *= v2[i];
        fourier_transform(v1, true);
        v1.resize(s1 + s2 - 1);
        return v1;
    }
};
#endif // CLASS_POLYNOMIAL_NTT
#ifndef CLASS_POLYNOMIAL_MOD
#define CLASS_POLYNOMIAL_MOD
#include <algorithm>
template<const singlebit mod, const singlebit depth, const singlebit primroot>
class polynomial_mod {
public:
    using modulo = fast_modint<mod>;
    using ntt = polynomial_ntt<mod, depth, primroot>;
protected:
    std::size_t sz;
    std::vector<modulo> a;
public:
    explicit polynomial_mod() : sz(1), a(std::vector<modulo>({ modulo() })) {};
    explicit polynomial_mod(std::size_t sz_) : sz(sz_), a(std::vector<modulo>(sz_, modulo())) {};
    explicit polynomial_mod(std::vector<modulo> a_) : sz(a_.size()), a(a_) {};
    polynomial_mod& operator=(const polynomial_mod& p) {
        sz = p.sz;
        a = p.a;
        return (*this);
    }
    std::size_t size() const { return sz; }
    std::size_t degree() const { return sz - 1; }
    modulo operator[](std::size_t idx) const {
        return a[idx];
    }
    modulo& operator[](std::size_t idx) {
        return a[idx];
    }
    bool operator==(const polynomial_mod& p) const {
        for (std::size_t i = 0; i < sz || i < p.sz; ++i) {
            if ((i < sz ? a[i] : modulo(0)) != (i < p.sz ? p.a[i] : modulo(0))) {
                return false;
            }
        }
        return true;
    }
    bool operator!=(const polynomial_mod& p) const {
        return !(operator==(p));
    }
    polynomial_mod resize_transform(std::size_t d) const {
        // Resize polynomial to d: in other words, f(x) := f(x) mod x^d
        polynomial_mod ans(*this);
        ans.sz = d;
        ans.a.resize(d, modulo(0));
        return ans;
    }
    polynomial_mod star_transform() const {
        // f*(x) = x^degree * f(1/x)
        polynomial_mod ans(*this);
        std::reverse(ans.a.begin(), ans.a.end());
        return ans;
    }
    polynomial_mod inverse(std::size_t d) const {
        // Find g(x) where g(x) * f(x) = 1 (mod x^d)
        polynomial_mod ans(std::vector<modulo>({ a[0].inv() }));
        while (ans.size() < d) {
            polynomial_mod nxt({ modulo(2) });
            nxt -= ans * resize_transform(ans.size() * 2);
            nxt *= ans;
            ans = nxt.resize_transform(ans.size() * 2);
        }
        ans = ans.resize_transform(d);
        return ans;
    }
    polynomial_mod& operator+=(const polynomial_mod& p) {
        sz = std::max(sz, p.sz);
        a.resize(sz);
        for (std::size_t i = 0; i < sz; ++i) a[i] += p.a[i];
        return (*this);
    }
    polynomial_mod& operator-=(const polynomial_mod& p) {
        sz = std::max(sz, p.sz);
        a.resize(sz);
        for (std::size_t i = 0; i < sz; ++i) a[i] -= p.a[i];
        return (*this);
    }
    polynomial_mod& operator*=(const polynomial_mod& p) {
        a = ntt::convolve(a, p.a);
        sz += p.sz - 1;
        return (*this);
    }
    polynomial_mod& operator/=(const polynomial_mod& p) {
        std::size_t dn = degree(), dm = p.degree();
        if (dn < dm) (*this) = polynomial_mod();
        else {
            polynomial_mod gstar = p.star_transform().inverse(dn - dm + 1);
            polynomial_mod qstar = (gstar * (*this).star_transform()).resize_transform(dn - dm + 1);
            (*this) = qstar.star_transform();
        }
        return (*this);
    }
    polynomial_mod& operator%=(const polynomial_mod& p) {
        (*this) -= polynomial_mod(*this) / p * p;
        (*this) = (*this).resize_transform(p.size() - 1);
        return (*this);
    }
    polynomial_mod operator+() const {
        return polynomial_mod(*this);
    }
    polynomial_mod operator-() const {
        return polynomial_mod() - polynomial_mod(*this);
    }
    polynomial_mod operator+(const polynomial_mod& p) const {
        return polynomial_mod(*this) += p;
    }
    polynomial_mod operator-(const polynomial_mod& p) const {
        return polynomial_mod(*this) -= p;
    }
    polynomial_mod operator*(const polynomial_mod& p) const {
        return polynomial_mod(*this) *= p;
    }
    polynomial_mod operator/(const polynomial_mod& p) const {
        return polynomial_mod(*this) /= p;
    }
    polynomial_mod operator%(const polynomial_mod& p) const {
        return polynomial_mod(*this) %= p;
    }
};
#endif // CLASS_POLYNOMIAL_MOD
#include <queue>
#include <string>
#include <iostream>
using namespace std;
using poly = polynomial_mod<998244353, 23, 3>;
using mint = poly::modulo;
int main() {
    string str;
    cin >> str;
    vector<int> cnt(26);
    for (int i = 0; i < str.size(); ++i) {
        ++cnt[str[i] - 'a'];
    }
    queue<poly> que;
    for (int i = 0; i < 26; ++i) {
        vector<mint> vec(cnt[i] + 1);
        vec[0] = 1;
        for (int j = 1; j <= cnt[i]; ++j) {
            vec[j] = vec[j - 1] * mint(j).inv();
        }
        que.push(poly(vec));
    }
    while (que.size() >= 2) {
        poly pl = que.front(); que.pop();
        poly pr = que.front(); que.pop();
        que.push(pl * pr);
    }
    poly p = que.front();
    mint ans = 0; mint fact = 1;
    for (int i = 0; i < p.size(); ++i) {
        ans += p[i] * fact;
        fact *= i + 1;
    }
    cout << (ans - 1).get() << endl;
    return 0;
}
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