test/library-checker/Convolution/BitwiseXorConvolution.test.cpp

View this file on GitHub
Last update: 2025-11-24 18:49:07+09:00
Problem: https://judge.yosupo.jp/problem/bitwise_xor_convolution

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/bitwise_xor_convolution"
#include <bits/stdc++.h>

#define REP(i, n) for (int i = 0; i < (n); i++)

#include "library/bitwise/Xor.hpp"
#include "library/mod/Modint.hpp"

using mint = Mint<long long>;

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

    int n;
    std::cin >> n;
    int N = 1 << n;
    std::vector<mint> a(N), b(N);
    REP (i, N)
        std::cin >> a[i];
    REP (i, N)
        std::cin >> b[i];
    auto c = BitwiseXor::convolution(a, b);
    REP (i, N)
        std::cout << c[i] << "\n "[i + 1 < N];
}

#line 1 "test/library-checker/Convolution/BitwiseXorConvolution.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/bitwise_xor_convolution"
#include <bits/stdc++.h>

#define REP(i, n) for (int i = 0; i < (n); i++)

#line 2 "library/bitwise/Util.hpp"
namespace bitwise{
  static int log2(int N){
    int n=__builtin_ffs(N)-1;
    assert((1<<n)==N);
    return n;
  }
  static bool in(int S,int a){ return (S>>a)&1; }
}
#line 3 "library/bitwise/Xor.hpp"
#define REP_(i, n) for (int i = 0; i < (n); i++)
#define RREP_(i, n) for (int i = (n) - 1; i >= 0; i--)
struct BitwiseXor {
    template <typename T> static void zeta(std::vector<T> &A) {
        const int n = bitwise::log2(A.size());
        REP_(i, n)
        REP_(S, 1 << n) {
            if (bitwise::in(S, i))
                continue;
            T x = A[S], y = A[S | (1 << i)];
            A[S] -= y;
            A[S | (1 << i)] += x;
        }
    }
    template <typename T> static void mobius(std::vector<T> &A) {
        const int n = bitwise::log2(A.size());
        RREP_(i, n)
        REP_(S, 1 << n) {
            if (bitwise::in(S, i))
                continue;
            T x = A[S], y = A[S | (1 << i)];
            A[S] += y;
            A[S | (1 << i)] -= x;
        }
        T inv = T(1) / (1 << n);
        REP (S, 1 << n)
            A[S] *= inv;
    }
    template <typename T>
    static std::vector<T> convolution(std::vector<T> A, std::vector<T> B) {
        zeta(A);
        zeta(B);
        REP (S, A.size())
            A[S] *= B[S];
        mobius(A);
        return A;
    }
};
#undef REP_
#undef RREP_
#line 2 "library/math/ExtraGCD.hpp"
using ll = long long;
std::pair<ll, ll> ext_gcd(ll a, ll b) {
    if (b == 0)
        return {1, 0};
    auto [X, Y] = ext_gcd(b, a % b);
    // bX + (a%b)Y = gcd(a,b)
    // a%b = a - b(a/b)
    // ∴ aY + b(X-(a/b)Y) = gcd(a,b)
    ll x = Y, y = X - (a / b) * Y;
    return {x, y};
}
#line 3 "library/mod/Modint.hpp"
template <typename T, T MOD = 998244353> struct Mint {
    inline static constexpr T mod = MOD;
    T v;
    Mint() : v(0) {}
    Mint(signed v) : v(v) {}
    Mint(long long t) {
        v = t % MOD;
        if (v < 0)
            v += MOD;
    }

    static Mint raw(int v) {
        Mint x;
        x.v = v;
        return x;
    }

    Mint pow(long long k) const {
        Mint res(1), tmp(v);
        while (k) {
            if (k & 1)
                res *= tmp;
            tmp *= tmp;
            k >>= 1;
        }
        return res;
    }

    static Mint add_identity() { return Mint(0); }
    static Mint mul_identity() { return Mint(1); }

    // Mint inv()const{return pow(MOD-2);}
    Mint inv() const { return Mint(ext_gcd(v, mod).first); }

    Mint &operator+=(Mint a) {
        v += a.v;
        if (v >= MOD)
            v -= MOD;
        return *this;
    }
    Mint &operator-=(Mint a) {
        v += MOD - a.v;
        if (v >= MOD)
            v -= MOD;
        return *this;
    }
    Mint &operator*=(Mint a) {
        v = 1LL * v * a.v % MOD;
        return *this;
    }
    Mint &operator/=(Mint a) { return (*this) *= a.inv(); }

    Mint operator+(Mint a) const { return Mint(v) += a; }
    Mint operator-(Mint a) const { return Mint(v) -= a; }
    Mint operator*(Mint a) const { return Mint(v) *= a; }
    Mint operator/(Mint a) const { return Mint(v) /= a; }
#define FRIEND(op)                                                             \
    friend Mint operator op(int a, Mint b) { return Mint(a) op b; }
    FRIEND(+);
    FRIEND(-);
    FRIEND(*);
    FRIEND(/);
#undef FRIEND
    Mint operator+() const { return *this; }
    Mint operator-() const { return v ? Mint(MOD - v) : Mint(v); }

    bool operator==(const Mint a) const { return v == a.v; }
    bool operator!=(const Mint a) const { return v != a.v; }

    static Mint comb(long long n, int k) {
        Mint num(1), dom(1);
        for (int i = 0; i < k; i++) {
            num *= Mint(n - i);
            dom *= Mint(i + 1);
        }
        return num / dom;
    }

    friend std::ostream &operator<<(std::ostream &os, const Mint &m) {
        os << m.v;
        return os;
    }
    friend std::istream &operator>>(std::istream &is, Mint &m) {
        is >> m.v;
        m.v %= MOD;
        if (m.v < 0)
            m.v += MOD;
        return is;
    }
};
#line 8 "test/library-checker/Convolution/BitwiseXorConvolution.test.cpp"

using mint = Mint<long long>;

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

    int n;
    std::cin >> n;
    int N = 1 << n;
    std::vector<mint> a(N), b(N);
    REP (i, N)
        std::cin >> a[i];
    REP (i, N)
        std::cin >> b[i];
    auto c = BitwiseXor::convolution(a, b);
    REP (i, N)
        std::cout << c[i] << "\n "[i + 1 < N];
}