test/yosupo/gcd_convolution.test.cpp

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Last update: 2024-01-07 22:37:45+09:00
Problem: https://judge.yosupo.jp/problem/gcd_convolution

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Code

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

#include "../../math/modint.hpp"
#include "../../convolution/gcd_lcm_convolution.hpp"


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

using mint = Modint<998244353>;

int main() {
    int N;
    cin >> N;
    vector<mint> a(N+1), b(N+1);
    for (int i = 1; i <= N; ++i) cin >> a[i];
    for (int i = 1; i <= N; ++i) cin >> b[i];
    auto c = gcd_convolution(a, b);
    for (int i = 1; i <= N; ++i) cout << c[i] << (i < N ? " " : "\n");
}

#line 1 "test/yosupo/gcd_convolution.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/gcd_convolution"

#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 2 "convolution/gcd_lcm_convolution.hpp"
#include <vector>

#line 3 "convolution/divisor_zeta_moebius_transform.hpp"

template <typename T>
void divisor_fzt(std::vector<T>& a) {
    const int n = a.size();
    std::vector<bool> sieve(n, true);
    for (int p = 2; p < n; ++p) {
        if (!sieve[p]) continue;
        for (int k = 1; k * p < n; ++k) {
            sieve[k * p] = false;
            a[k * p] += a[k];
        }
    }
}

template <typename T>
void divisor_fmt(std::vector<T>& a) {
    const int n = a.size();
    std::vector<bool> sieve(n, true);
    for (int p = 2; p < n; ++p) {
        if (!sieve[p]) continue;
        for (int k = (n - 1) / p; k > 0; --k) {
            sieve[k * p] = false;
            a[k * p] -= a[k];
        }
    }
}

template <typename T>
void multiple_fzt(std::vector<T>& a) {
    const int n = a.size();
    std::vector<bool> sieve(n, true);
    for (int p = 2; p < n; ++p) {
        if (!sieve[p]) continue;
        for (int k = (n - 1) / p; k > 0; --k) {
            sieve[k * p] = false;
            a[k] += a[k * p];
        }
    }
}

template <typename T>
void multiple_fmt(std::vector<T>& a) {
    const int n = a.size();
    std::vector<bool> sieve(n, true);
    for (int p = 2; p < n; ++p) {
        if (!sieve[p]) continue;
        for (int k = 1; k * p < n; ++k) {
            sieve[k * p] = false;
            a[k] -= a[k * p];
        }
    }
}
#line 5 "convolution/gcd_lcm_convolution.hpp"

/**
 * @brief GCD/LCM Convolution
 */

template <typename T>
std::vector<T> gcd_convolution(std::vector<T> a, std::vector<T> b) {
    const int n = std::max(a.size(), b.size());
    a.resize(n);
    b.resize(n);
    multiple_fzt(a);
    multiple_fzt(b);
    for (int i = 0; i < n; ++i) a[i] *= b[i];
    multiple_fmt(a);
    return a;
}

template <typename T>
std::vector<T> lcm_convolution(std::vector<T> a, std::vector<T> b) {
    const int n = std::max(a.size(), b.size());
    a.resize(n);
    b.resize(n);
    divisor_fzt(a);
    divisor_fzt(b);
    for (int i = 0; i < n; ++i) a[i] *= b[i];
    divisor_fmt(a);
    return a;
}
#line 5 "test/yosupo/gcd_convolution.test.cpp"


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

using mint = Modint<998244353>;

int main() {
    int N;
    cin >> N;
    vector<mint> a(N+1), b(N+1);
    for (int i = 1; i <= N; ++i) cin >> a[i];
    for (int i = 1; i <= N; ++i) cin >> b[i];
    auto c = gcd_convolution(a, b);
    for (int i = 1; i <= N; ++i) cout << c[i] << (i < N ? " " : "\n");
}