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:heavy_check_mark: test/yosupo/exp_of_formal_power_series.test.cpp

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Code

#define PROBLEM "https://judge.yosupo.jp/problem/exp_of_formal_power_series"

#include "../../math/modint.hpp"
#include "../../math/polynomial.cpp"

#include <bits/stdc++.h>
using namespace std;


using mint = Modint<998244353>;

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    int N;
    cin >> N;
    Polynomial<mint> f(N);
    for (int i = 0; i < N; ++i) cin >> f[i];
    auto g = f.exp();
    for (int i = 0; i < N; ++i) cout << g[i] << (i < N - 1 ? " " : "\n");
}
#line 1 "test/yosupo/exp_of_formal_power_series.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/exp_of_formal_power_series"

#line 2 "math/modint.hpp"
#include <algorithm>
#include <iostream>

/**
 * @brief Mod int
 */
template <int m>
class Modint {
    using mint = Modint;
    static_assert(m > 0, "Modulus must be positive");

   public:
    static constexpr int mod() { return m; }

    constexpr Modint(long long y = 0) : x(y >= 0 ? y % m : (y % m + m) % m) {}

    constexpr int val() const { return x; }

    constexpr mint& operator+=(const mint& r) {
        if ((x += r.x) >= m) x -= m;
        return *this;
    }
    constexpr mint& operator-=(const mint& r) {
        if ((x += m - r.x) >= m) x -= m;
        return *this;
    }
    constexpr mint& operator*=(const mint& r) {
        x = static_cast<int>(1LL * x * r.x % m);
        return *this;
    }
    constexpr mint& operator/=(const mint& r) { return *this *= r.inv(); }

    constexpr bool operator==(const mint& r) const { return x == r.x; }

    constexpr mint operator+() const { return *this; }
    constexpr mint operator-() const { return mint(-x); }

    constexpr friend mint operator+(const mint& l, const mint& r) {
        return mint(l) += r;
    }
    constexpr friend mint operator-(const mint& l, const mint& r) {
        return mint(l) -= r;
    }
    constexpr friend mint operator*(const mint& l, const mint& r) {
        return mint(l) *= r;
    }
    constexpr friend mint operator/(const mint& l, const mint& r) {
        return mint(l) /= r;
    }

    constexpr mint inv() const {
        int a = x, b = m, u = 1, v = 0;
        while (b > 0) {
            int t = a / b;
            std::swap(a -= t * b, b);
            std::swap(u -= t * v, v);
        }
        return mint(u);
    }

    constexpr mint pow(long long n) const {
        mint ret(1), mul(x);
        while (n > 0) {
            if (n & 1) ret *= mul;
            mul *= mul;
            n >>= 1;
        }
        return ret;
    }

    friend std::ostream& operator<<(std::ostream& os, const mint& r) {
        return os << r.x;
    }

    friend std::istream& operator>>(std::istream& is, mint& r) {
        long long t;
        is >> t;
        r = mint(t);
        return is;
    }

   private:
    int x;
};
#line 3 "math/polynomial.cpp"
#include <cassert>
#include <vector>

#line 2 "convolution/ntt.hpp"
#include <bit>
#line 4 "convolution/ntt.hpp"

constexpr int get_primitive_root(int mod) {
    if (mod == 167772161) return 3;
    if (mod == 469762049) return 3;
    if (mod == 754974721) return 11;
    if (mod == 998244353) return 3;
    if (mod == 1224736769) return 3;
}

template <typename mint>
void ntt(std::vector<mint>& a) {
    constexpr int mod = mint::mod();
    constexpr mint primitive_root = get_primitive_root(mod);

    const int n = a.size();
    for (int m = n; m > 1; m >>= 1) {
        mint omega = primitive_root.pow((mod - 1) / m);
        for (int s = 0; s < n / m; ++s) {
            mint w = 1;
            for (int i = 0; i < m / 2; ++i) {
                mint l = a[s * m + i];
                mint r = a[s * m + i + m / 2];
                a[s * m + i] = l + r;
                a[s * m + i + m / 2] = (l - r) * w;
                w *= omega;
            }
        }
    }
}

template <typename mint>
void intt(std::vector<mint>& a) {
    constexpr int mod = mint::mod();
    constexpr mint primitive_root = get_primitive_root(mod);

    const int n = a.size();
    for (int m = 2; m <= n; m <<= 1) {
        mint omega = primitive_root.pow((mod - 1) / m).inv();
        for (int s = 0; s < n / m; ++s) {
            mint w = 1;
            for (int i = 0; i < m / 2; ++i) {
                mint l = a[s * m + i];
                mint r = a[s * m + i + m / 2] * w;
                a[s * m + i] = l + r;
                a[s * m + i + m / 2] = l - r;
                w *= omega;
            }
        }
    }
}

template <typename mint>
std::vector<mint> convolution(std::vector<mint> a, std::vector<mint> b) {
    const int size = a.size() + b.size() - 1;
    const int n = std::bit_ceil((unsigned int)size);
    a.resize(n);
    b.resize(n);
    ntt(a);
    ntt(b);
    for (int i = 0; i < n; ++i) a[i] *= b[i];
    intt(a);
    a.resize(size);
    mint n_inv = mint(n).inv();
    for (int i = 0; i < size; ++i) a[i] *= n_inv;
    return a;
}
#line 7 "math/polynomial.cpp"

template <typename mint>
class Polynomial : public std::vector<mint> {
    using Poly = Polynomial;

   public:
    using std::vector<mint>::vector;
    using std::vector<mint>::operator=;

    Poly pre(int size) const {
        return Poly(this->begin(),
                    this->begin() + std::min((int)this->size(), size));
    }

    Poly rev(int deg = -1) const {
        auto ret = *this;
        if (deg != -1) ret.resize(deg, 0);
        return Poly(ret.rbegin(), ret.rend());
    }

    void trim() {
        while (!this->empty() && this->back() == 0) this->pop_back();
    }

    // --- unary operation ---

    Poly& operator-() const {
        auto ret = *this;
        for (auto& x : ret) x = -x;
        return ret;
    }

    // -- binary operation with scalar ---

    Poly& operator+=(const mint& rhs) {
        if (this->empty()) this->resize(1);
        (*this)[0] += rhs;
        return *this;
    }

    Poly& operator-=(const mint& rhs) {
        if (this->empty()) this->resize(1);
        (*this)[0] -= rhs;
        return *this;
    }

    Poly& operator*=(const mint& rhs) {
        for (auto& x : *this) x *= rhs;
        return *this;
    }

    Poly& operator/=(const mint& rhs) { return *this *= rhs.inv(); }

    Poly operator+(const mint& rhs) const { return Poly(*this) += rhs; }
    Poly operator-(const mint& rhs) const { return Poly(*this) -= rhs; }
    Poly operator*(const mint& rhs) const { return Poly(*this) *= rhs; }
    Poly operator/(const mint& rhs) const { return Poly(*this) /= rhs; }

    // --- binary operation with polynomial ---

    Poly& operator+=(const Poly& rhs) {
        if (this->size() < rhs.size()) this->resize(rhs.size());
        for (int i = 0; i < (int)rhs.size(); ++i) (*this)[i] += rhs[i];
        return *this;
    }

    Poly& operator-=(const Poly& rhs) {
        if (this->size() < rhs.size()) this->resize(rhs.size());
        for (int i = 0; i < (int)rhs.size(); ++i) (*this)[i] -= rhs[i];
        return *this;
    }

    Poly& operator*=(const Poly& rhs) {
        *this = convolution(*this, rhs);
        return *this;
        // // naive convolution O(N^2)
        // std::vector<mint> res(this->size() + rhs.size() - 1);
        // for (int i = 0; i < (int)this->size(); ++i) {
        //     for (int j = 0; j < (int)rhs.size(); ++j) {
        //         res[i + j] += (*this)[i] * rhs[j];
        //     }
        // }
        // return *this = res;
    }

    Poly& operator/=(const Poly& rhs) {
        if (this->size() < rhs.size()) {
            this->clear();
            return *this;
        }
        int n = this->size() - rhs.size() + 1;
        return *this = (rev().pre(n) * rhs.rev().inv(n)).pre(n).rev(n);
    }

    Poly& operator%=(const Poly& rhs) {
        *this -= *this / rhs * rhs;
        trim();
        return *this;
    }

    std::pair<Poly, Poly> divmod(const Poly& rhs) {
        auto q = *this / rhs;
        auto r = *this - q * rhs;
        r.trim();
        return {q, r};
    }

    Poly operator+(const Poly& rhs) const { return Poly(*this) += rhs; }
    Poly operator-(const Poly& rhs) const { return Poly(*this) -= rhs; }
    Poly operator*(const Poly& rhs) const { return Poly(*this) *= rhs; }
    Poly operator/(const Poly& rhs) const { return Poly(*this) /= rhs; }
    Poly operator%(const Poly& rhs) const { return Poly(*this) %= rhs; }

    // --- shift operation ---

    Poly operator<<(int n) const {
        auto ret = *this;
        ret.insert(ret.begin(), n, 0);
        return ret;
    }

    Poly operator>>(int n) const {
        if ((int)this->size() <= n) return {};
        auto ret = *this;
        ret.erase(ret.begin(), ret.begin() + n);
        return ret;
    }

    // --- evaluation ---

    mint operator()(const mint& x) {
        mint y = 0, powx = 1;
        for (int i = 0; i < (int)this->size(); ++i) {
            for (auto c : *this) {
                y += c * powx;
                powx *= x;
            }
            return y;
        }
    }

    // --- other operations ---

    Poly inv(int deg = -1) const {
        assert((*this)[0] != mint(0));
        if (deg == -1) deg = this->size();
        Poly res = {(*this)[0].inv()};
        for (int d = 1; d < deg; d <<= 1) {
            auto f = pre(2 * d);
            auto g = res;
            f.resize(2 * d);
            g.resize(2 * d);

            // g_{n+1} = g_n * (2 - g_n * f) mod x^{2^{n+1}}

            ntt(f);
            ntt(g);
            for (int i = 0; i < 2 * d; ++i) f[i] *= g[i];
            intt(f);

            for (int i = 0; i < d; ++i) f[i] = 0;

            ntt(f);
            for (int i = 0; i < 2 * d; ++i) f[i] *= g[i];
            intt(f);

            res.resize(2 * d);
            auto coef = mint(2 * d).inv().pow(2);
            for (int i = d; i < 2 * d; ++i) res[i] = -f[i] * coef;
        }
        return res.pre(deg);
    }

    Poly exp(int deg = -1) const {
        assert((*this)[0] == mint(0));
        if (deg == -1) deg = this->size();
        Poly ret = {mint(1)};
        for (int i = 1; i < deg; i <<= 1) {
            ret = (ret * (this->pre(i << 1) + mint(1) - ret.log(i << 1)))
                      .pre(i << 1);
        }
        return ret;
    }

    Poly log(int deg = -1) const {
        assert((*this)[0] == mint(1));
        if (deg == -1) deg = this->size();
        return (diff() * inv(deg)).pre(deg - 1).integral();
    }

    Poly pow(long long k, int deg = -1) const {
        if (k == 0) return {1};
        if (deg == -1) deg = this->size();
        auto ret = *this;
        int cnt0 = 0;
        while (cnt0 < (int)ret.size() && ret[cnt0] == 0) ++cnt0;
        if (cnt0 > (deg - 1) / k) return {};
        ret = ret >> cnt0;
        deg -= cnt0 * k;
        ret = ((ret / ret[0]).log(deg) * k).exp(deg) * ret[0].pow(k);
        ret = ret << (cnt0 * k);
        return ret;
    }

    Poly diff() const {
        Poly ret(std::max(0, (int)this->size() - 1));
        for (int i = 1; i <= (int)ret.size(); ++i)
            ret[i - 1] = (*this)[i] * mint(i);
        return ret;
    }

    Poly integral() const {
        Poly ret(this->size() + 1);
        ret[0] = mint(0);
        for (int i = 0; i < (int)ret.size() - 1; ++i)
            ret[i + 1] = (*this)[i] / mint(i + 1);
        return ret;
    }

    Poly taylor_shift(long long c) const {
        const int n = this->size();
        std::vector<mint> fact(n, 1), fact_inv(n, 1);
        for (int i = 1; i < n; ++i) fact[i] = fact[i - 1] * i;
        fact_inv[n - 1] = mint(1) / fact[n - 1];
        for (int i = n - 1; i > 0; --i) fact_inv[i - 1] = fact_inv[i] * i;

        auto ret = *this;
        Poly e(n + 1);
        e[0] = 1;
        mint p = c;
        for (int i = 1; i < n; ++i) {
            ret[i] *= fact[i];
            e[i] = p * fact_inv[i];
            p *= c;
        }
        ret = (ret.rev() * e).pre(n).rev();
        for (int i = n - 1; i >= 0; --i) {
            ret[i] *= fact_inv[i];
        }
        return ret;
    }
};
#line 5 "test/yosupo/exp_of_formal_power_series.test.cpp"

#include <bits/stdc++.h>
using namespace std;


using mint = Modint<998244353>;

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    int N;
    cin >> N;
    Polynomial<mint> f(N);
    for (int i = 0; i < N; ++i) cin >> f[i];
    auto g = f.exp();
    for (int i = 0; i < N; ++i) cout << g[i] << (i < N - 1 ? " " : "\n");
}
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