verify/yosupo/convolution/bitwise_xor_convolution.test.cpp

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Last update: 2024-10-31 23:18:18+07:00
Problem: https://judge.yosupo.jp/problem/bitwise_xor_convolution

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Code

#define PROBLEM "https://judge.yosupo.jp/problem/bitwise_xor_convolution"
#include "template.hpp"
#include "modular-arithmetic/montgomery-modint.hpp"
#include "convolution/xor-convolution.hpp"

using mint = mint998;

int main(){
    cin.tie(nullptr)->sync_with_stdio(false);
    int n;
    cin >> n;
    n=1<<n;
    vector<mint> a(n),b(n);
    for(auto &x:a)cin >> x;
    for(auto &x:b)cin >> x;
    auto c=xor_convolution(a,b);
    for(auto x:c)cout << x << " ";
}

#line 1 "verify/yosupo/convolution/bitwise_xor_convolution.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/bitwise_xor_convolution"
#line 1 "template.hpp"
#include<bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;

using ll = long long;
using db = long double;
using vi = vector<int>;
using vl = vector<ll>;
using vd = vector<db>;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pdd = pair<db,db>;
const int INF=INT_MAX/2;
const int MOD=998244353;
const int MOD2=1000000007;
const ll LINF=LLONG_MAX/2;
const db DINF=numeric_limits<db>::infinity();
const db EPS=1e-9;
const db PI=acos(db(-1));

template<class T>
using ordered_set = tree<T,null_type,less<T>,rb_tree_tag,tree_order_statistics_node_update>;
template<class T>
using ordered_multiset = tree<T,null_type,less_equal<T>,rb_tree_tag,tree_order_statistics_node_update>;

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
mt19937_64 rng64(chrono::steady_clock::now().time_since_epoch().count());
#line 2 "modular-arithmetic/montgomery-modint.hpp"

/**
 * Author: Teetat T.
 * Date: 2024-03-17
 * Description: modular arithmetic operators using Montgomery space
 */

template<uint32_t mod,uint32_t root=0>
struct MontgomeryModInt{
    using mint = MontgomeryModInt;
    using i32 = int32_t;
    using u32 = uint32_t;
    using u64 = uint64_t;

    static constexpr u32 get_r(){
        u32 res=1;
        for(i32 i=0;i<5;i++)res*=2-mod*res;
        return res;
    }

    static const u32 r=get_r();
    static const u32 n2=-u64(mod)%mod;
    static_assert(mod<(1<<30));
    static_assert((mod&1)==1);
    static_assert(r*mod==1);

    u32 x;

    constexpr MontgomeryModInt():x(0){}
    constexpr MontgomeryModInt(const int64_t &v):x(reduce(u64(v%mod+mod)*n2)){}

    static constexpr u32 get_mod(){return mod;}
    static constexpr mint get_root(){return mint(root);}
    explicit constexpr operator int64_t()const{return val();}

    static constexpr u32 reduce(const u64 &v){
        return (v+u64(u32(v)*u32(-r))*mod)>>32;
    }

    constexpr u32 val()const{
        u32 res=reduce(x);
        return res>=mod?res-mod:res;
    }

    constexpr mint inv()const{
        int a=val(),b=mod,u=1,v=0,q=0;
        while(b>0){
            q=a/b;
            a-=q*b;
            u-=q*v;
            swap(a,b);
            swap(u,v);
        }
        return mint(u);
    }

    constexpr mint &operator+=(const mint &rhs){
        if(i32(x+=rhs.x-2*mod)<0)x+=2*mod;
        return *this;
    }
    constexpr mint &operator-=(const mint &rhs){
        if(i32(x-=rhs.x)<0)x+=2*mod;
        return *this;
    }
    constexpr mint &operator*=(const mint &rhs){
        x=reduce(u64(x)*rhs.x);
        return *this;
    }
    constexpr mint &operator/=(const mint &rhs){
        return *this*=rhs.inv();
    }

    constexpr mint &operator++(){return *this+=mint(1);}
    constexpr mint &operator--(){return *this-=mint(1);}
    constexpr mint operator++(int){
        mint res=*this;
        return *this+=mint(1),res;
    }
    constexpr mint operator--(int){
        mint res=*this;
        return *this-=mint(1),res;
    }

    constexpr mint operator-()const{return mint()-mint(*this);};
    constexpr mint operator+()const{return mint(*this);};

    friend constexpr mint operator+(const mint &lhs,const mint &rhs){return mint(lhs)+=rhs;}
    friend constexpr mint operator-(const mint &lhs,const mint &rhs){return mint(lhs)-=rhs;}
    friend constexpr mint operator*(const mint &lhs,const mint &rhs){return mint(lhs)*=rhs;}
    friend constexpr mint operator/(const mint &lhs,const mint &rhs){return mint(lhs)/=rhs;}
    friend constexpr bool operator==(const mint &lhs,const mint &rhs){
        return (lhs.x>=mod?lhs.x-mod:lhs.x)==(rhs.x>=mod?rhs.x-mod:rhs.x);
    }
    friend constexpr bool operator!=(const mint &lhs,const mint &rhs){
        return (lhs.x>=mod?lhs.x-mod:lhs.x)!=(rhs.x>=mod?rhs.x-mod:rhs.x);
    }
    friend constexpr bool operator<(const mint &lhs,const mint &rhs){
        return (lhs.x>=mod?lhs.x-mod:lhs.x)<(rhs.x>=mod?rhs.x-mod:rhs.x); // for std::map
    }

    friend istream &operator>>(istream &is,mint &o){
        int64_t v;
        is >> v;
        o=mint(v);
        return is;
    }
    friend ostream &operator<<(ostream &os,const mint &o){
        return os << o.val();
    }
};
using mint998 = MontgomeryModInt<998244353,3>;
using mint107 = MontgomeryModInt<1000000007>;

#line 2 "convolution/xor-convolution.hpp"

/**
 * Author: Teetat T.
 * Date: 2024-07-29
 * Description: Bitwise XOR Convolution.
 * Fast Walsh-Hadamard Transform: $A^\prime[S]=\sum_T(-1)^{|S\&T|}A[T]$.
 * Time: $O(N\log N)$.
 */

template<class T>
void fwht(vector<T> &a){
    int n=(int)a.size();
    assert(n==(n&-n));
    for(int i=1;i<n;i<<=1){
        for(int j=0;j<n;j++){
            if(j&i){
                T &u=a[j^i],&v=a[j];
                tie(u,v)=make_pair(u+v,u-v);
            }
        }
    }
}

template<class T>
vector<T> xor_convolution(vector<T> a,vector<T> b){
    int n=(int)a.size();
    fwht(a);
    fwht(b);
    for(int i=0;i<n;i++)a[i]*=b[i];
    fwht(a);
    T div=T(1)/T(n);
    if(div==T(0)){
        for(auto &x:a)x/=n;
    }else{
        for(auto &x:a)x*=div;
    }
    return a;
}

#line 5 "verify/yosupo/convolution/bitwise_xor_convolution.test.cpp"

using mint = mint998;

int main(){
    cin.tie(nullptr)->sync_with_stdio(false);
    int n;
    cin >> n;
    n=1<<n;
    vector<mint> a(n),b(n);
    for(auto &x:a)cin >> x;
    for(auto &x:b)cin >> x;
    auto c=xor_convolution(a,b);
    for(auto x:c)cout << x << " ";
}