verify/library_checker/convolution/lcm_convolution.test.cpp

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• Last update: 2025-02-22 22:56:16+09:00
• Problem: https://judge.yosupo.jp/problem/lcm_convolution

Depends on

• lcm_convolution (src/convolution/lcm_convolution.hpp)
• Divisor/MultipleTransform (src/math/divisor_multiple_transform.hpp)
• EratosthenesSieve (src/math/eratosthenes_sieve.hpp)
• StaticModint (src/template/static_modint.hpp)
• template (src/template/template.hpp)

Code

#define PROBLEM "https://judge.yosupo.jp/problem/lcm_convolution"
#include "../../../src/template/template.hpp"
#include "../../../src/template/static_modint.hpp"
#include "../../../src/convolution/lcm_convolution.hpp"
using mint = modint998244353;
int main(void) {
    int n;
    cin >> n;
    vector<mint> a(n + 1), b(n + 1);
    rep(i, 1, n + 1) cin >> a[i];
    rep(i, 1, n + 1) cin >> b[i];
    vector<mint> c = lcm_convolution(a, b);
    rep(i, 1, n + 1) cout << c[i] << " \n"[i == n];
}

#line 1 "verify/library_checker/convolution/lcm_convolution.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/lcm_convolution"
#line 2 "src/template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using P = pair<long long, long long>;
#define rep(i, a, b) for(long long i = (a); i < (b); ++i)
#define rrep(i, a, b) for(long long i = (a); i >= (b); --i)
constexpr long long inf = 4e18;
struct SetupIO {
    SetupIO() {
        ios::sync_with_stdio(0);
        cin.tie(0);
        cout << fixed << setprecision(30);
    }
} setup_io;
#line 3 "src/template/static_modint.hpp"
template <uint32_t m>
struct StaticModint {
    using mint = StaticModint;
    static constexpr uint32_t mod() {
        return m;
    }
    static constexpr mint raw(const uint32_t v) {
        mint a;
        a._v = v;
        return a;
    }
    constexpr StaticModint()
        : _v(0) {}
    template <class T>
    constexpr StaticModint(const T& v) {
        static_assert(is_integral_v<T>);
        if constexpr(is_signed_v<T>) {
            int64_t x = int64_t(v % int64_t(m));
            if(x < 0) x += m;
            _v = uint32_t(x);
        } else _v = uint32_t(v % m);
    }
    constexpr uint32_t val() const {
        return _v;
    }
    constexpr mint& operator++() {
        return *this += 1;
    }
    constexpr mint& operator--() {
        return *this -= 1;
    }
    constexpr mint operator++(int) {
        mint res = *this;
        ++*this;
        return res;
    }
    constexpr mint operator--(int) {
        mint res = *this;
        --*this;
        return res;
    }
    constexpr mint& operator+=(mint rhs) {
        if(_v >= m - rhs._v) _v -= m;
        _v += rhs._v;
        return *this;
    }
    constexpr mint& operator-=(mint rhs) {
        if(_v < rhs._v) _v += m;
        _v -= rhs._v;
        return *this;
    }
    constexpr mint& operator*=(mint rhs) {
        return *this = *this * rhs;
    }
    constexpr mint& operator/=(mint rhs) {
        return *this *= rhs.inv();
    }
    constexpr mint operator+() const {
        return *this;
    }
    constexpr mint operator-() const {
        return mint{} - *this;
    }
    constexpr mint pow(long long n) const {
        assert(0 <= n);
        if(n == 0) return 1;
        mint x = *this, r = 1;
        while(1) {
            if(n & 1) r *= x;
            n >>= 1;
            if(n == 0) return r;
            x *= x;
        }
    }
    constexpr mint inv() const {
        if constexpr(prime) {
            assert(_v);
            return pow(m - 2);
        } else {
            const auto eg = inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }
    friend constexpr mint operator+(mint lhs, mint rhs) {
        return lhs += rhs;
    }
    friend constexpr mint operator-(mint lhs, mint rhs) {
        return lhs -= rhs;
    }
    friend constexpr mint operator*(mint lhs, mint rhs) {
        return uint64_t(lhs._v) * rhs._v;
    }
    friend constexpr mint operator/(mint lhs, mint rhs) {
        return lhs /= rhs;
    }
    friend constexpr bool operator==(mint lhs, mint rhs) {
        return lhs._v == rhs._v;
    }
    friend constexpr bool operator!=(mint lhs, mint rhs) {
        return lhs._v != rhs._v;
    }
    friend istream& operator>>(istream& in, mint& x) {
        long long a;
        in >> a;
        x = a;
        return in;
    }
    friend ostream& operator<<(ostream& out, const mint& x) {
        return out << x.val();
    }

   private:
    uint32_t _v = 0;
    static constexpr bool prime = []() -> bool {
        if(m == 1) return 0;
        if(m == 2 or m == 7 or m == 61) return 1;
        if(m % 2 == 0) return 0;
        uint32_t d = m - 1;
        while(d % 2 == 0) d /= 2;
        for(uint32_t a : {2, 7, 61}) {
            uint32_t t = d;
            mint y = mint(a).pow(t);
            while(t != m - 1 && y != 1 && y != m - 1) {
                y *= y;
                t <<= 1;
            }
            if(y != m - 1 && t % 2 == 0) return 0;
        }
        return 1;
    }();
    static constexpr pair<int32_t, int32_t> inv_gcd(const int32_t a, const int32_t b) {
        if(a == 0) return {b, 0};
        int32_t s = b, t = a, m0 = 0, m1 = 1;
        while(t) {
            const int32_t u = s / t;
            s -= t * u;
            m0 -= m1 * u;
            swap(s, t);
            swap(m0, m1);
        }
        if(m0 < 0) m0 += b / s;
        return {s, m0};
    }
};
using modint998244353 = StaticModint<998244353>;
using modint1000000007 = StaticModint<1000000007>;
#line 3 "src/math/eratosthenes_sieve.hpp"
struct EratosthenesSieve {
    vector<int> primes, min_factor, moebius, euler;
    EratosthenesSieve(const int N)
        : primes(), min_factor(N + 1), moebius(N + 1, 1), euler(N + 1), N(N) {
        assert(N >= 1);
        iota(min_factor.begin(), min_factor.end(), 0);
        min_factor[0] = min_factor[1] = -1;
        iota(euler.begin(), euler.end(), 0);
        for(int i = 2; i <= N; ++i) {
            if(min_factor[i] < i) continue;
            primes.emplace_back(i);
            moebius[i] = -1;
            euler[i] = euler[i] / i * (i - 1);
            for(int j = i * 2; j <= N; j += i) {
                if(min_factor[j] == j) min_factor[j] = i;
                if((j / i) % i == 0) moebius[j] = 0;
                else moebius[j] = -moebius[j];
                euler[j] = euler[j] / i * (i - 1);
            }
        }
    }
    vector<pair<int, int>> prime_factors(int n) const {
        assert(1 <= n and n <= N);
        vector<pair<int, int>> res;
        while(n > 1) {
            const int p = min_factor[n];
            int exp = 0;
            while(min_factor[n] == p) {
                n /= p;
                ++exp;
            }
            res.emplace_back(p, exp);
        }
        return res;
    }
    vector<int> divisor(const int n) const {
        assert(1 <= n and n <= n);
        vector<int> res({1});
        const auto pf = prime_factors(n);
        for(const auto& p : pf) {
            const int s = (int)res.size();
            for(int i = 0; i < s; ++i) {
                int v = 1;
                for(int j = 0; j < p.second; ++j) {
                    v *= p.first;
                    res.push_back(res[i] * v);
                }
            }
        }
        sort(res.begin(), res.end());
        return res;
    }

   private:
    int N;
};
#line 4 "src/math/divisor_multiple_transform.hpp"
struct DivisorTransform {
    template <typename T>
    static void zeta_transform(vector<T>& f) {
        const int N = f.size() - 1;
        const auto sieve = EratosthenesSieve(N).primes;
        for(const auto& p : sieve) {
            for(int k = 1; k * p <= N; ++k) f[k * p] += f[k];
        }
    }
    template <typename T>
    static void moebius_transform(vector<T>& g) {
        const int N = g.size() - 1;
        const auto sieve = EratosthenesSieve(N).primes;
        for(const auto& p : sieve) {
            for(int k = N / p; k > 0; --k) g[k * p] -= g[k];
        }
    }
};
struct MultipleTransform {
    template <typename T>
    static void zeta_transform(vector<T>& f) {
        const int N = f.size() - 1;
        const auto sieve = EratosthenesSieve(N).primes;
        for(const auto& p : sieve) {
            for(int k = N / p; k > 0; --k) f[k] += f[k * p];
        }
    }
    template <typename T>
    static void moebius_transform(vector<T>& g) {
        const int N = g.size() - 1;
        const auto sieve = EratosthenesSieve(N).primes;
        for(const auto& p : sieve) {
            for(int k = 1; k * p <= N; ++k) g[k] -= g[k * p];
        }
    }
};
#line 4 "src/convolution/lcm_convolution.hpp"
template <typename mint>
vector<mint> lcm_convolution(const vector<mint>& a, const vector<mint>& b) {
    assert(a.size() == b.size());
    auto s = a, t = b;
    DivisorTransform::zeta_transform(s);
    DivisorTransform::zeta_transform(t);
    for(int i = 0; i < (int)a.size(); ++i) s[i] *= t[i];
    DivisorTransform::moebius_transform(s);
    return s;
}
#line 5 "verify/library_checker/convolution/lcm_convolution.test.cpp"
using mint = modint998244353;
int main(void) {
    int n;
    cin >> n;
    vector<mint> a(n + 1), b(n + 1);
    rep(i, 1, n + 1) cin >> a[i];
    rep(i, 1, n + 1) cin >> b[i];
    vector<mint> c = lcm_convolution(a, b);
    rep(i, 1, n + 1) cout << c[i] << " \n"[i == n];
}

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