library_for_cpp

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:heavy_check_mark: verify/yosupo_library_checker/convolution/Bitwise_And_Convolution.test.cpp

Depends on

Code

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

#include"../../../template/template.hpp"
#include"../../../Algebra/modint.hpp"
#include"../../../Convolution/Bitwise_And_Convolution.hpp"

using mint = modint<998244353>;

int main() {
    int N; cin >> N;
    vector<mint> a(1 << N), b(1 << N);
    for (int i = 0; i < (1 << N); i++) {
        int x; scanf("%d", &x);
        a[i] = mint(x);
    }

    for (int j = 0; j < (1 << N); j++) {
        int y; scanf("%d", &y);
        b[j] = mint(y);
    }

    convolution::Bitwize_And_Convolution<mint> A(a), B(b);
    cout <<  (A * B).to_vector() << endl;
}
#line 1 "verify/yosupo_library_checker/convolution/Bitwise_And_Convolution.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/bitwise_and_convolution"

#line 2 "template/template.hpp"

using namespace std;

// intrinstic
#include <immintrin.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

// utility
#line 2 "template/utility.hpp"

using ll = long long;

// a ← max(a, b) を実行する. a が更新されたら, 返り値が true.
template<typename T, typename U>
inline bool chmax(T &a, const U b){
    return (a < b ? a = b, 1: 0);
}

// a ← min(a, b) を実行する. a が更新されたら, 返り値が true.
template<typename T, typename U>
inline bool chmin(T &a, const U b){
    return (a > b ? a = b, 1: 0);
}
#line 59 "template/template.hpp"

// math
#line 2 "template/math.hpp"

// 除算に関する関数

// floor(x / y) を求める.
template<typename T, typename U>
T div_floor(T x, U y){ return (x > 0 ? x / y: (x - y + 1) / y); }

// ceil(x / y) を求める.
template<typename T, typename U>
T div_ceil(T x, U y){ return (x > 0 ? (x + y - 1) / y: x / y) ;}

// x を y で割った余りを求める.
template<typename T, typename U>
T mod(T x, U y){
    T q = div_floor(x, y);
    return x - q * y ;
}

// x を y で割った商と余りを求める.
template<typename T, typename U>
pair<T, T> divmod(T x, U y){
    T q = div_floor(x, y);
    return {q, x - q * y};
}

// 四捨五入を求める.
template<typename T, typename U>
T round(T x, U y){
    T q, r;
    tie (q, r) = divmod(x, y);
    return (r >= div_ceil(y, 2)) ? q + 1 : q;
}

// 指数に関する関数

// x の y 乗を求める.
ll intpow(ll x, ll y){
    ll a = 1;
    while (y){
        if (y & 1) { a *= x; }
        x *= x;
        y >>= 1;
    }
    return a;
}

// x の y 乗を z で割った余りを求める.
ll modpow(ll x, ll y, ll z){
    ll a = 1;
    while (y){
        if (y & 1) { (a *= x) %= z; }
        (x *= x) %= z;
        y >>= 1;
    }
    return a;
}

// x の y 乗を z で割った余りを求める.
template<typename T, typename U>
T modpow(T x, U y, T z) {
    T a = 1;
    while (y) {
        if (y & 1) { (a *= x) %= z; }

        (x *= x) %= z;
        y >>= 1;
    }

    return a;
}

// vector の要素の総和を求める.
ll sum(vector<ll> &X){
    ll y = 0;
    for (auto &&x: X) { y+=x; }
    return y;
}

// vector の要素の総和を求める.
template<typename T>
T sum(vector<T> &X){
    T y = T(0);
    for (auto &&x: X) { y += x; }
    return y;
}

// a x + b y = gcd(a, b) を満たす整数の組 (a, b) に対して, (x, y, gcd(a, b)) を求める.
tuple<ll, ll, ll> Extended_Euclid(ll a, ll b) {
    ll s = 1, t = 0, u = 0, v = 1;
    while (b) {
        ll q;
        tie(q, a, b) = make_tuple(div_floor(a, b), b, mod(a, b));
        tie(s, t) = make_pair(t, s - q * t);
        tie(u, v) = make_pair(v, u - q * v);
    }

    return make_tuple(s, u, a);
}

// floor(sqrt(N)) を求める (N < 0 のときは, 0 とする).
ll isqrt(const ll &N) { 
    if (N <= 0) { return 0; }

    ll x = sqrt(N);
    while ((x + 1) * (x + 1) <= N) { x++; }
    while (x * x > N) { x--; }

    return x;
}

// floor(sqrt(N)) を求める (N < 0 のときは, 0 とする).
ll floor_sqrt(const ll &N) { return isqrt(N); }

// ceil(sqrt(N)) を求める (N < 0 のときは, 0 とする).
ll ceil_sqrt(const ll &N) {
    ll x = isqrt(N);
    return x * x == N ? x : x + 1;
}
#line 62 "template/template.hpp"

// inout
#line 1 "template/inout.hpp"
// 入出力
template<class... T>
void input(T&... a){ (cin >> ... >> a); }

void print(){ cout << "\n"; }

template<class T, class... Ts>
void print(const T& a, const Ts&... b){
    cout << a;
    (cout << ... << (cout << " ", b));
    cout << "\n";
}

template<typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &P){
    is >> P.first >> P.second;
    return is;
}

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

template<typename T>
vector<T> vector_input(int N, int index){
    vector<T> X(N+index);
    for (int i=index; i<index+N; i++) cin >> X[i];
    return X;
}

template<typename T>
istream &operator>>(istream &is, vector<T> &X){
    for (auto &x: X) { is >> x; }
    return is;
}

template<typename T>
ostream &operator<<(ostream &os, const vector<T> &X){
    int s = (int)X.size();
    for (int i = 0; i < s; i++) { os << (i ? " " : "") << X[i]; }
    return os;
}

template<typename T>
ostream &operator<<(ostream &os, const unordered_set<T> &S){
    int i = 0;
    for (T a: S) {os << (i ? " ": "") << a; i++;}
    return os;
}

template<typename T>
ostream &operator<<(ostream &os, const set<T> &S){
    int i = 0;
    for (T a: S) { os << (i ? " ": "") << a; i++; }
    return os;
}

template<typename T>
ostream &operator<<(ostream &os, const unordered_multiset<T> &S){
    int i = 0;
    for (T a: S) { os << (i ? " ": "") << a; i++; }
    return os;
}

template<typename T>
ostream &operator<<(ostream &os, const multiset<T> &S){
    int i = 0;
    for (T a: S) { os << (i ? " ": "") << a; i++; }
    return os;
}
#line 65 "template/template.hpp"

// macro
#line 2 "template/macro.hpp"

// マクロの定義
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if
#define unless(cond) if (!(cond))
#define until(cond) while (!(cond))
#define loop while (true)

// オーバーロードマクロ
#define overload2(_1, _2, name, ...) name
#define overload3(_1, _2, _3, name, ...) name
#define overload4(_1, _2, _3, _4, name, ...) name
#define overload5(_1, _2, _3, _4, _5, name, ...) name

// 繰り返し系
#define rep1(n) for (ll i = 0; i < n; i++)
#define rep2(i, n) for (ll i = 0; i < n; i++)
#define rep3(i, a, b) for (ll i = a; i < b; i++)
#define rep4(i, a, b, c) for (ll i = a; i < b; i += c)
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)

#define foreach1(x, a) for (auto &&x: a)
#define foreach2(x, y, a) for (auto &&[x, y]: a)
#define foreach3(x, y, z, a) for (auto &&[x, y, z]: a)
#define foreach4(x, y, z, w, a) for (auto &&[x, y, z, w]: a)
#define foreach(...) overload5(__VA_ARGS__, foreach4, foreach3, foreach2, foreach1)(__VA_ARGS__)
#line 68 "template/template.hpp"

// bitop
#line 2 "template/bitop.hpp"

// 非負整数 x の bit legnth を求める.
ll bit_length(ll x) {
    if (x == 0) { return 0; }
    return (sizeof(long) * CHAR_BIT) - __builtin_clzll(x);
}

// 非負整数 x の popcount を求める.
ll popcount(ll x) { return __builtin_popcountll(x); }

// 正の整数 x に対して, floor(log2(x)) を求める.
ll floor_log2(ll x) { return bit_length(x) - 1; }

// 正の整数 x に対して, ceil(log2(x)) を求める.
ll ceil_log2(ll x) { return bit_length(x - 1); }

// x の第 k ビットを取得する
int get_bit(ll x, int k) { return (x >> k) & 1; }

// x のビット列を取得する.
// k はビット列の長さとする.
vector<int> get_bits(ll x, int k) {
    vector<int> bits(k);
    rep(i, k) {
        bits[i] = x & 1;
        x >>= 1;
    }

    return bits;
}

// x のビット列を取得する.
vector<int> get_bits(ll x) { return get_bits(x, bit_length(x)); }
#line 2 "Algebra/modint.hpp"

#line 4 "Algebra/modint.hpp"

template<int M>
class modint {
    public:
    static constexpr int Mod = M; 
    int64_t x;

    public:
    // 初期化
    constexpr modint(): x(0) {}
    constexpr modint(int64_t a): x((a % Mod + Mod) % Mod) {}

    // マイナス元
    modint operator-() const { return modint(-x); }

    // 加法
    modint& operator+=(const modint &b){
        if ((x += b.x) >= Mod) x -= Mod;
        return *this;
    }

    friend modint operator+(const modint &x, const modint &y) { return modint(x) += y; }

    // 減法
    modint& operator-=(const modint &b){
        if ((x += Mod - b.x) >= Mod) x -= Mod;
        return *this;
    }

    friend modint operator-(const modint &x, const modint &y) { return modint(x) -= y; }

    // 乗法
    modint& operator*=(const modint &b){
        (x *= b.x) %= Mod;
        return *this;
    }

    friend modint operator*(const modint &x, const modint &y) { return modint(x) *= y; }
    friend modint operator*(const int &x, const modint &y) { return modint(x) *= y; }
    friend modint operator*(const ll &x, const modint &y) { return modint(x) *= y; }

    // 除法
    modint& operator/=(const modint &b){ return (*this) *= b.inverse(); }

    friend modint operator/(const modint &x, const modint &y) { return modint(x) /= y; }

    modint inverse() const {
        int64_t s = 1, t = 0;
        int64_t a = x, b = Mod;

        while (b > 0) {
            int64_t q = a / b;

            a -= q * b; swap(a, b);
            s -= q * t; swap(s, t);
        }

        assert (a == 1);

        return modint(s);
    }

    // 比較
    friend bool operator==(const modint &a, const modint &b) { return (a.x == b.x); }
    friend bool operator==(const modint &a, const int &b) { return a.x == mod(b, Mod); }
    friend bool operator!=(const modint &a, const modint &b) { return (a.x != b.x); }

    // 入力
    friend istream &operator>>(istream &is, modint &a) {
        is >> a.x;
        a.x = (a.x % Mod + Mod) % Mod;
        return is;
    }

    // 出力
    friend ostream &operator<<(ostream &os, const modint &a) { return os << a.x; }

    bool is_zero() const { return x == 0; }
    bool is_member(ll a) const { return x == (a % Mod + Mod) % Mod; }
};

template<int Mod>
modint<Mod> pow(modint<Mod> x, long long n) {
    if (n < 0) { return pow(x, -n).inverse(); }

    auto res = modint<Mod>(1);
    for (; n; n >>= 1) {
        if (n & 1) { res *= x; }
        x *= x;
    }

    return res;
}
#line 2 "Convolution/Bitwise_And_Convolution.hpp"

#line 2 "Convolution/Commutative_Idempotent_Monoid_Convolution_Base.hpp"

#line 2 "Convolution/Convolution_Base.hpp"

#line 4 "Convolution/Convolution_Base.hpp"

namespace convolution {
    template<typename R>
    class Convolution_Base {
        protected:
        std::vector<R> data;

        public:
        Convolution_Base() = default;
        Convolution_Base(std::vector<R> data_in): data(std::move(data_in)) {}
        
        Convolution_Base(size_t n): data(std::vector<R>(n)) {} 
        
        // 加法 (+=)
        Convolution_Base& operator+=(const Convolution_Base<R> &B) {
            if(data.size() != B.data.size()) { throw std::length_error("Convolution operands must have the same size."); }

            for (size_t i = 0; i < data.size(); i++) { data[i] += B.data[i]; }
            return *this;
        }

        // 減法 (-=)
        Convolution_Base& operator-=(const Convolution_Base<R> &B) {
            if(data.size() != B.data.size()) { throw std::length_error("Convolution operands must have the same size."); }
            for (size_t i = 0; i < data.size(); i++) { data[i] -= B.data[i]; }
            return *this;
        }

        // スカラー倍 (*=)
        Convolution_Base& operator*=(const R &a) {
            for (size_t i = 0; i < data.size(); i++) { data[i] *= a; }
            return *this;
        }

        virtual Convolution_Base<R>& operator*=(const Convolution_Base<R> &B) = 0;

        inline size_t size() const { return data.size(); }

        inline R& operator[](size_t k) { return data[k]; }
        inline const R& operator[](size_t k) const { return data[k]; }

        const std::vector<R>& to_vector() const { return data; }
    };
}
#line 4 "Convolution/Commutative_Idempotent_Monoid_Convolution_Base.hpp"

namespace convolution {
    template<typename R>
    class Commutative_Idempotent_Monoid_Convolution_Base: public Convolution_Base<R> {
        // 型エイリアス
        using Base = Convolution_Base<R>;
        using Self = Commutative_Idempotent_Monoid_Convolution_Base<R>;

        using Base::Base;

        public:
        virtual void zeta_transform(std::vector<R> &f) const = 0;
        virtual void mobius_transform(std::vector<R> &g) const = 0;

        Self& operator*=(const Base &B) override {
            if (this->data.size() != B.to_vector().size()) {
                throw std::length_error("Convolution operands must have the same size.");
            }

            std::vector<R> f_copy(this->data); 
            std::vector<R> g_copy(B.to_vector()); 

            this->zeta_transform(f_copy);
            this->zeta_transform(g_copy); 

            for (size_t i = 0; i < f_copy.size(); i++) { 
                f_copy[i] *= g_copy[i]; 
            }

            this->mobius_transform(f_copy);
            this->data = std::move(f_copy);
            return *this;
        }

        void zeta() { zeta_transform(this->data); }
        void mobius() { mobius_transform(this->data); }
    };
}
#line 4 "Convolution/Bitwise_And_Convolution.hpp"

namespace convolution {
    template<typename R>
    class Bitwize_And_Convolution: public Commutative_Idempotent_Monoid_Convolution_Base<R> {
        using Base = Convolution_Base<R>;
        using ImplBase = Commutative_Idempotent_Monoid_Convolution_Base<R>;
        using ImplBase::ImplBase;

        // 加法 (+)
        friend Bitwize_And_Convolution operator+(const Bitwize_And_Convolution &lhs, const Bitwize_And_Convolution &rhs) {
            Bitwize_And_Convolution temp(lhs);
            temp += rhs;
            return temp;
        }

        // 減法 (-)
        friend Bitwize_And_Convolution operator-(const Bitwize_And_Convolution &lhs, const Bitwize_And_Convolution &rhs) {
            Bitwize_And_Convolution temp(lhs);
            temp -= rhs;
            return temp;
        }

        // 乗法 (*)
        friend Bitwize_And_Convolution operator*(const Bitwize_And_Convolution &lhs, const Bitwize_And_Convolution &rhs) { 
            Bitwize_And_Convolution temp(lhs);
            temp *= rhs;
            return temp;
        }

        // スカラー倍 (a * rhs)
        friend Bitwize_And_Convolution operator*(const R &a, const Bitwize_And_Convolution &rhs) {
            Bitwize_And_Convolution temp(rhs);
            temp *= a;
            return temp;
        }

        // スカラー倍 (lhs * a)
        friend Bitwize_And_Convolution operator*(const Bitwize_And_Convolution &lhs, const R &a) {
            Bitwize_And_Convolution temp(lhs);
            temp *= a;
            return temp;
        }

        void zeta_transform(std::vector<R> &f) const override {
            int m = floor_log2(f.size());

            for (size_t i = 0; i < m; i++) {
                for (int S = 0; S < (1 << m); S++) {
                    if (get_bit(S, i)) { continue; }

                    f[S] += f[S | (1 << i)];
                }
            }
        }

        void mobius_transform(std::vector<R> &g) const override {
            int m = floor_log2(g.size());

            for (size_t i = 0; i < m; i++) {
                for (int S = 0; S < (1 << m); S++) {
                    if (get_bit(S, i)) { continue; }

                    g[S] -= g[S | (1 << i)];
                }
            }
        }
    };
}
#line 6 "verify/yosupo_library_checker/convolution/Bitwise_And_Convolution.test.cpp"

using mint = modint<998244353>;

int main() {
    int N; cin >> N;
    vector<mint> a(1 << N), b(1 << N);
    for (int i = 0; i < (1 << N); i++) {
        int x; scanf("%d", &x);
        a[i] = mint(x);
    }

    for (int j = 0; j < (1 << N); j++) {
        int y; scanf("%d", &y);
        b[j] = mint(y);
    }

    convolution::Bitwize_And_Convolution<mint> A(a), B(b);
    cout <<  (A * B).to_vector() << endl;
}
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