test/yosupo/bitwise_xor_convolution.cpp

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• Last update: 2021-03-04 05:51:44+09:00
• Link: https://judge.yosupo.jp/problem/bitwise_xor_convolution

Depends on

• cpp_src/math/Modular.hpp
• cpp_src/other/FWT.hpp

Code

//#pragma GCC optimize("Ofast")
//#pragma GCC optimize("unroll-loops")
#define PROBLEM "https://judge.yosupo.jp/problem/bitwise_xor_convolution"

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

using ll = long long;
using pii = pair<int, int>;
template <class T>
using V = vector<T>;
template <class T>
using VV = V<V<T>>;

#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fi first
#define se second
#define rep(i, n) rep2(i, 0, n)
#define rep2(i, m, n) for (int i = m; i < (n); i++)
#define per(i, b) per2(i, 0, b)
#define per2(i, a, b) for (int i = int(b) - 1; i >= int(a); i--)
#define ALL(c) (c).begin(), (c).end()
#define SZ(x) ((int)(x).size())

constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }

template <class T, class U>
void chmin(T& t, const U& u) {
    if (t > u) t = u;
}
template <class T, class U>
void chmax(T& t, const U& u) {
    if (t < u) t = u;
}

template <class T, class U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
    os << "(" << p.first << "," << p.second << ")";
    return os;
}

template <class T>
ostream& operator<<(ostream& os, const vector<T>& v) {
    os << "{";
    rep(i, v.size()) {
        if (i) os << ",";
        os << v[i];
    }
    os << "}";
    return os;
}

#ifdef LOCAL
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
    cerr << " " << H;
    debug_out(T...);
}
#define debug(...) \
    cerr << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl
#else
#define debug(...) (void(0))
#define dump(x) (void(0))
#endif

#define call_from_test
#include "../../cpp_src/math/Modular.hpp"
#include "../../cpp_src/other/FWT.hpp"
#undef call_from_test

using Mint = ModInt<998244353>;

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

    int N;
    cin >> N;
    V<Mint> a(1 << N), b(1 << N);
    rep(i, 1 << N) cin >> a[i];
    rep(i, 1 << N) cin >> b[i];

    xor_fwt(a, false);
    xor_fwt(b, false);
    rep(i, 1 << N) a[i] *= b[i];
    xor_fwt(a, true);
    rep(i, 1 << N) { cout << a[i] << (i + 1 == (1 << N) ? '\n' : ' '); }

    return 0;
}

#line 1 "test/yosupo/bitwise_xor_convolution.cpp"
//#pragma GCC optimize("Ofast")
//#pragma GCC optimize("unroll-loops")
#define PROBLEM "https://judge.yosupo.jp/problem/bitwise_xor_convolution"

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

using ll = long long;
using pii = pair<int, int>;
template <class T>
using V = vector<T>;
template <class T>
using VV = V<V<T>>;

#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fi first
#define se second
#define rep(i, n) rep2(i, 0, n)
#define rep2(i, m, n) for (int i = m; i < (n); i++)
#define per(i, b) per2(i, 0, b)
#define per2(i, a, b) for (int i = int(b) - 1; i >= int(a); i--)
#define ALL(c) (c).begin(), (c).end()
#define SZ(x) ((int)(x).size())

constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }

template <class T, class U>
void chmin(T& t, const U& u) {
    if (t > u) t = u;
}
template <class T, class U>
void chmax(T& t, const U& u) {
    if (t < u) t = u;
}

template <class T, class U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
    os << "(" << p.first << "," << p.second << ")";
    return os;
}

template <class T>
ostream& operator<<(ostream& os, const vector<T>& v) {
    os << "{";
    rep(i, v.size()) {
        if (i) os << ",";
        os << v[i];
    }
    os << "}";
    return os;
}

#ifdef LOCAL
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
    cerr << " " << H;
    debug_out(T...);
}
#define debug(...) \
    cerr << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl
#else
#define debug(...) (void(0))
#define dump(x) (void(0))
#endif

#define call_from_test
#line 1 "cpp_src/math/Modular.hpp"
template <unsigned int MOD>
struct ModInt {
    using uint = unsigned int;
    using ull = unsigned long long;
    using M = ModInt;

    uint v;

    ModInt(ll _v = 0) { set_norm(_v % MOD + MOD); }
    M& set_norm(uint _v) {  //[0, MOD * 2)->[0, MOD)
        v = (_v < MOD) ? _v : _v - MOD;
        return *this;
    }

    explicit operator bool() const { return v != 0; }
    explicit operator int() const { return v; }
    M operator+(const M& a) const { return M().set_norm(v + a.v); }
    M operator-(const M& a) const { return M().set_norm(v + MOD - a.v); }
    M operator*(const M& a) const { return M().set_norm(ull(v) * a.v % MOD); }
    M operator/(const M& a) const { return *this * a.inv(); }
    M& operator+=(const M& a) { return *this = *this + a; }
    M& operator-=(const M& a) { return *this = *this - a; }
    M& operator*=(const M& a) { return *this = *this * a; }
    M& operator/=(const M& a) { return *this = *this / a; }
    M operator-() const { return M() - *this; }
    M& operator++(int) { return *this = *this + 1; }
    M& operator--(int) { return *this = *this - 1; }

    M pow(ll n) const {
        if (n < 0) return inv().pow(-n);
        M x = *this, res = 1;
        while (n) {
            if (n & 1) res *= x;
            x *= x;
            n >>= 1;
        }
        return res;
    }

    M inv() const {
        ll a = v, b = MOD, p = 1, q = 0, t;
        while (b != 0) {
            t = a / b;
            swap(a -= t * b, b);
            swap(p -= t * q, q);
        }
        return M(p);
    }

    friend ostream& operator<<(ostream& os, const M& a) { return os << a.v; }
    friend istream& operator>>(istream& in, M& x) {
        ll v_;
        in >> v_;
        x = M(v_);
        return in;
    }

    bool operator<(const M& r) const { return v < r.v; }
    bool operator>(const M& r) const { return v < *this; }
    bool operator<=(const M& r) const { return !(r < *this); }
    bool operator>=(const M& r) const { return !(*this < r); }
    bool operator==(const M& a) const { return v == a.v; }
    bool operator!=(const M& a) const { return v != a.v; }

    static uint get_mod() { return MOD; }
};

// using Mint = ModInt<1000000007>;
// using Mint = ModInt<998244353>;
#line 1 "cpp_src/other/FWT.hpp"
//vector size : power of 2

template<class T>
void and_fwt(vector<T>& f) {
    int n = f.size();
    for (int d = 1; d < n; d <<= 1) {
        for (int i = 0; i < n; i += d * 2) {
            for (int j = 0; j < d; ++j) {
                T x = f[i+j], y = f[i+j+d];
                f[i+j] = x + y;
            }
        }
    }
}

template<class T>
void and_ifwt(vector<T>& f) {
    int n = f.size();
    for (int d = 1; d < n; d <<= 1) {
        for (int i = 0; i < n; i += d * 2) {
            for (int j = 0; j < d; ++j) {
                T x = f[i+j], y = f[i+j+d];
                f[i+j] = x - y;
            }
        }
    }
}

template <class T>
void xor_fwt(vector<T>& f, bool rev) {
    int n = f.size();
    for (int d = 1; d < n; d <<= 1) {
        for (int i = 0; i < n; i += d * 2) {
            for (int j = 0; j < d; ++j) {
                T x = f[i + j], y = f[i + j + d];
                f[i + j] = x + y;
                f[i + j + d] = x - y;
            }
        }
    }

    if (rev) {
        T r = T(1) / n;
        for (auto& x : f) x *= r;
    }
}
#line 73 "test/yosupo/bitwise_xor_convolution.cpp"
#undef call_from_test

using Mint = ModInt<998244353>;

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

    int N;
    cin >> N;
    V<Mint> a(1 << N), b(1 << N);
    rep(i, 1 << N) cin >> a[i];
    rep(i, 1 << N) cin >> b[i];

    xor_fwt(a, false);
    xor_fwt(b, false);
    rep(i, 1 << N) a[i] *= b[i];
    xor_fwt(a, true);
    rep(i, 1 << N) { cout << a[i] << (i + 1 == (1 << N) ? '\n' : ' '); }

    return 0;
}

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