bit/test/bitwise_xor_convolution.test.cpp

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• Last update: 2025-06-28 10:05:47+09:00
• Problem: https://judge.yosupo.jp/problem/bitwise_xor_convolution

Depends on

• bit/xor_convolution.hpp
• number_theory/mod_int.hpp
• number_theory/utils.hpp
• template/template.hpp

Code

#define PROBLEM "https://judge.yosupo.jp/problem/bitwise_xor_convolution"
#include "../../bit/xor_convolution.hpp"
#include "../../number_theory/mod_int.hpp"
#include "../../template/template.hpp"

int main() {
    using M = ModInt<998244353>;
    I32(n);
    V<M> a(1 << n), b(1 << n);
    REP(i, 1 << n) {
        cin >> a[i];
    }
    REP(i, 1 << n) {
        cin >> b[i];
    }
    V<M> c = bitwise_xor_convolution(a, b);
    REP(i, 1 << n) {
        cout << c[i] << " \n"[i + 1 == (1 << n)];
    }
}

#line 1 "bit/test/bitwise_xor_convolution.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/bitwise_xor_convolution"
#line 2 "bit/xor_convolution.hpp"
#include <cassert>
#include <type_traits>
#include <vector>
template <typename T>
void hadamard(int n, std::vector<T> &a) {
    for (int d = 0; d < n; ++d) {
        for (int i = 0; i < (1 << n); ++i) {
            if ((i & (1 << d)) == 0) {
                T x = a[i], y = a[i ^ (1 << d)];
                a[i] = x + y;
                a[i ^ (1 << d)] = x - y;
            }
        }
    }
}
template <typename T>
std::vector<T> bitwise_xor_convolution(std::vector<T> a, std::vector<T> b) {
    assert(a.size() == b.size() && a.size() > 0);
    int n = __builtin_ctz((unsigned)a.size());
    assert((int)a.size() == (1 << n));
    hadamard(n, a);
    hadamard(n, b);
    for (int i = 0; i < (1 << n); ++i) {
        a[i] *= b[i];
    }
    hadamard(n, a);
    if constexpr (std::is_integral_v<T>) {
        for (int i = 0; i < (1 << n); ++i) {
            a[i] /= 1 << n;
        }
    } else {
        T inv = T(1 << n).inv();
        for (int i = 0; i < (1 << n); ++i) {
            a[i] *= inv;
        }
    }
    return a;
}
#line 2 "number_theory/mod_int.hpp"

#line 4 "number_theory/mod_int.hpp"
#include <iostream>
#line 2 "number_theory/utils.hpp"

#include <utility>

constexpr bool is_prime(unsigned n) {
    if (n == 0 || n == 1) {
        return false;
    }
    for (unsigned i = 2; i * i <= n; ++i) {
        if (n % i == 0) {
            return false;
        }
    }
    return true;
}

constexpr unsigned mod_pow(unsigned x, unsigned y, unsigned mod) {
    unsigned ret = 1, self = x;
    while (y != 0) {
        if (y & 1) {
            ret = (unsigned)((unsigned long long)ret * self % mod);
        }
        self = (unsigned)((unsigned long long)self * self % mod);
        y /= 2;
    }
    return ret;
}

template <unsigned mod>
constexpr unsigned primitive_root() {
    static_assert(is_prime(mod), "`mod` must be a prime number.");
    if (mod == 2) {
        return 1;
    }

    unsigned primes[32] = {};
    int it = 0;
    {
        unsigned m = mod - 1;
        for (unsigned i = 2; i * i <= m; ++i) {
            if (m % i == 0) {
                primes[it++] = i;
                while (m % i == 0) {
                    m /= i;
                }
            }
        }
        if (m != 1) {
            primes[it++] = m;
        }
    }
    for (unsigned i = 2; i < mod; ++i) {
        bool ok = true;
        for (int j = 0; j < it; ++j) {
            if (mod_pow(i, (mod - 1) / primes[j], mod) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return i;
    }
    return 0;
}

// y >= 1
template <typename T>
constexpr T safe_mod(T x, T y) {
    x %= y;
    if (x < 0) {
        x += y;
    }
    return x;
}

// y != 0
template <typename T>
constexpr T floor_div(T x, T y) {
    if (y < 0) {
        x *= -1;
        y *= -1;
    }
    if (x >= 0) {
        return x / y;
    } else {
        return -((-x + y - 1) / y);
    }
}

// y != 0
template <typename T>
constexpr T ceil_div(T x, T y) {
    if (y < 0) {
        x *= -1;
        y *= -1;
    }
    if (x >= 0) {
        return (x + y - 1) / y;
    } else {
        return -(-x / y);
    }
}

// b >= 1
// returns (g, x) s.t. g = gcd(a, b), a * x = g (mod b), 0 <= x < b / g
// from ACL
template <typename T>
std::pair<T, T> extgcd(T a, T b) {
    a = safe_mod(a, b);
    T s = b, t = a, m0 = 0, m1 = 1;
    while (t) {
        T u = s / t;
        s -= t * u;
        m0 -= m1 * u;
        std::swap(s, t);
        std::swap(m0, m1);
    }
    if (m0 < 0) {
        m0 += b / s;
    }
    return std::pair<T, T>(s, m0);
}

// b >= 1
// returns (g, x, y) s.t. g = gcd(a, b), a * x + b * y = g, 0 <= x < b / g, |y| < max(2, |a| / g)
template <typename T>
std::tuple<T, T, T> extgcd2(T a, T b) {
    T _a = safe_mod(a, b);
    T quot = (a - _a) / b;
    T x00 = 0, x01 = 1, y0 = b;
    T x10 = 1, x11 = -quot, y1 = _a;
    while (y1) {
        T u = y0 / y1;
        x00 -= u * x10;
        x01 -= u * x11;
        y0 -= u * y1;
        std::swap(x00, x10);
        std::swap(x01, x11);
        std::swap(y0, y1);
    }
    if (x00 < 0) {
        x00 += b / y0;
        x01 -= a / y0;
    }
    return std::tuple<T, T, T>(y0, x00, x01);
}

// gcd(x, m) == 1
template <typename T>
T inv_mod(T x, T m) {
    return extgcd(x, m).second;
}
#line 7 "number_theory/mod_int.hpp"

template <unsigned mod>
struct ModInt {
    static_assert(mod != 0, "`mod` must not be equal to 0.");
    static_assert(mod < (1u << 31),
                  "`mod` must be less than (1u << 31) = 2147483648.");

    unsigned val;

    static constexpr unsigned get_mod() { return mod; }

    constexpr ModInt() : val(0) {}
    template <typename T, std::enable_if_t<std::is_signed_v<T>> * = nullptr>
    constexpr ModInt(T x)
        : val((unsigned)((long long)x % (long long)mod + (x < 0 ? mod : 0))) {}
    template <typename T, std::enable_if_t<std::is_unsigned_v<T>> * = nullptr>
    constexpr ModInt(T x) : val((unsigned)(x % mod)) {}

    static constexpr ModInt raw(unsigned x) {
        ModInt<mod> ret;
        ret.val = x;
        return ret;
    }

    constexpr unsigned get_val() const { return val; }

    constexpr ModInt operator+() const { return *this; }
    constexpr ModInt operator-() const { return ModInt<mod>(0u) - *this; }

    constexpr ModInt &operator+=(const ModInt &rhs) {
        val += rhs.val;
        if (val >= mod) val -= mod;
        return *this;
    }
    constexpr ModInt &operator-=(const ModInt &rhs) {
        val -= rhs.val;
        if (val >= mod) val += mod;
        return *this;
    }
    constexpr ModInt &operator*=(const ModInt &rhs) {
        val = (unsigned long long)val * rhs.val % mod;
        return *this;
    }
    constexpr ModInt &operator/=(const ModInt &rhs) {
        val = (unsigned long long)val * rhs.inv().val % mod;
        return *this;
    }

    friend constexpr ModInt operator+(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) += rhs;
    }
    friend constexpr ModInt operator-(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) -= rhs;
    }
    friend constexpr ModInt operator*(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) *= rhs;
    }
    friend constexpr ModInt operator/(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) /= rhs;
    }

    constexpr ModInt pow(unsigned long long x) const {
        ModInt<mod> ret = ModInt<mod>::raw(1);
        ModInt<mod> self = *this;
        while (x != 0) {
            if (x & 1) ret *= self;
            self *= self;
            x >>= 1;
        }
        return ret;
    }
    constexpr ModInt inv() const {
        static_assert(is_prime(mod), "`mod` must be a prime number.");
        assert(val != 0);
        return this->pow(mod - 2);
    }

    friend std::istream &operator>>(std::istream &is, ModInt<mod> &x) {
        long long val;
        is >> val;
        x.val = val % mod + (val < 0 ? mod : 0);
        return is;
    }

    friend std::ostream &operator<<(std::ostream &os, const ModInt<mod> &x) {
        os << x.val;
        return os;
    }

    friend bool operator==(const ModInt &lhs, const ModInt &rhs) {
        return lhs.val == rhs.val;
    }

    friend bool operator!=(const ModInt &lhs, const ModInt &rhs) {
        return lhs.val != rhs.val;
    }
};

template <unsigned mod>
void debug(ModInt<mod> x) {
    std::cerr << x.val;
}
#line 2 "template/template.hpp"
#include <bits/stdc++.h>
#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i)
#define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER2(i, n) for (i32 i = (i32)(n)-1; i >= 0; --i)
#define PER3(i, m, n) for (i32 i = (i32)(n)-1; i >= (i32)(m); --i)
#define PER(...) OVERRIDE(__VA_ARGS__, PER3, PER2)(__VA_ARGS__)
#define ALL(x) begin(x), end(x)
#define LEN(x) (i32)(x.size())
using namespace std;
using u32 = unsigned int;
using u64 = unsigned long long;
using i32 = signed int;
using i64 = signed long long;
using f64 = double;
using f80 = long double;
using pi = pair<i32, i32>;
using pl = pair<i64, i64>;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = V<V<T>>;
template <typename T>
using VVV = V<V<V<T>>>;
template <typename T>
using VVVV = V<V<V<V<T>>>>;
template <typename T>
using PQR = priority_queue<T, V<T>, greater<T>>;
template <typename T>
bool chmin(T &x, const T &y) {
    if (x > y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
    if (x < y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T>
i32 lob(const V<T> &arr, const T &v) {
    return (i32)(lower_bound(ALL(arr), v) - arr.begin());
}
template <typename T>
i32 upb(const V<T> &arr, const T &v) {
    return (i32)(upper_bound(ALL(arr), v) - arr.begin());
}
template <typename T>
V<i32> argsort(const V<T> &arr) {
    V<i32> ret(arr.size());
    iota(ALL(ret), 0);
    sort(ALL(ret), [&](i32 i, i32 j) -> bool {
        if (arr[i] == arr[j]) {
            return i < j;
        } else {
            return arr[i] < arr[j];
        }
    });
    return ret;
}
#ifdef INT128
using u128 = __uint128_t;
using i128 = __int128_t;
#endif
[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;
struct SetUpIO {
    SetUpIO() {
#ifdef FAST_IO
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
#endif
        cout << fixed << setprecision(15);
    }
} set_up_io;
void scan(char &x) { cin >> x; }
void scan(u32 &x) { cin >> x; }
void scan(u64 &x) { cin >> x; }
void scan(i32 &x) { cin >> x; }
void scan(i64 &x) { cin >> x; }
void scan(f64 &x) { cin >> x; }
void scan(string &x) { cin >> x; }
template <typename T>
void scan(V<T> &x) {
    for (T &ele : x) {
        scan(ele);
    }
}
void read() {}
template <typename Head, typename... Tail>
void read(Head &head, Tail &...tail) {
    scan(head);
    read(tail...);
}
#define CHAR(...)     \
    char __VA_ARGS__; \
    read(__VA_ARGS__);
#define U32(...)     \
    u32 __VA_ARGS__; \
    read(__VA_ARGS__);
#define U64(...)     \
    u64 __VA_ARGS__; \
    read(__VA_ARGS__);
#define I32(...)     \
    i32 __VA_ARGS__; \
    read(__VA_ARGS__);
#define I64(...)     \
    i64 __VA_ARGS__; \
    read(__VA_ARGS__);
#define F64(...)     \
    f64 __VA_ARGS__; \
    read(__VA_ARGS__);
#define STR(...)        \
    string __VA_ARGS__; \
    read(__VA_ARGS__);
#define VEC(type, name, size) \
    V<type> name(size);       \
    read(name);
#define VVEC(type, name, size1, size2)    \
    VV<type> name(size1, V<type>(size2)); \
    read(name);
#line 5 "bit/test/bitwise_xor_convolution.test.cpp"

int main() {
    using M = ModInt<998244353>;
    I32(n);
    V<M> a(1 << n), b(1 << n);
    REP(i, 1 << n) {
        cin >> a[i];
    }
    REP(i, 1 << n) {
        cin >> b[i];
    }
    V<M> c = bitwise_xor_convolution(a, b);
    REP(i, 1 << n) {
        cout << c[i] << " \n"[i + 1 == (1 << n)];
    }
}

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