Luogu4717 【模板】快速沃尔什变换（FWT）

　　https://www.cnblogs.com/RabbitHu/p/9182047.html

　　完全没有学证明的欲望因为这个实在太好写了而且FFT就算学过也忘得差不多了只会写板子

#include<iostream>
#include<cstdio>
#include<cmath>
#include<cstring>
#include<cstdlib>
#include<algorithm>
using namespace std;
#define N (1<<17)
#define P 998244353
#define inv2 499122177
int read()
{
    int x=,f=;char c=getchar();
    while (c<''||c>'') {if (c=='-') f=-;c=getchar();}
    while (c>=''&&c<='') x=(x<<)+(x<<)+(c^),c=getchar();
    return x*f;
}
int n,a[N],b[N],f[N],g[N];
void OR(int *a,int n,int op)
{
    for (int i=;i<=n;i<<=)
        for (int j=;j<n;j+=i)
            for (int k=j;k<j+(i>>);k++)
            {
                int x=a[k],y=a[k+(i>>)];
                if (op==) a[k]=x,a[k+(i>>)]=(x+y)%P;
                else a[k]=x,a[k+(i>>)]=(y-x+P)%P;
            }
}
void AND(int *a,int n,int op)
{
    for (int i=;i<=n;i<<=)
        for (int j=;j<n;j+=i)
            for (int k=j;k<j+(i>>);k++)
            {
                int x=a[k],y=a[k+(i>>)];
                if (op==) a[k]=(x+y)%P,a[k+(i>>)]=y;
                else a[k]=(x-y+P)%P,a[k+(i>>)]=y;
            }
}
void XOR(int *a,int n,int op)
{
    for (int i=;i<=n;i<<=)
        for (int j=;j<n;j+=i)
            for (int k=j;k<j+(i>>);k++)
            {
                int x=a[k],y=a[k+(i>>)];
                a[k]=(x+y)%P,a[k+(i>>)]=(x-y+P)%P;
                if (op==) a[k]=1ll*a[k]*inv2%P,a[k+(i>>)]=1ll*a[k+(i>>)]*inv2%P;
            }
}
void FWT(int *a,int *b,int n,int op)
{
    if (op==) OR(a,n,),OR(b,n,);
    else if (op==) AND(a,n,),AND(b,n,);
    else if (op==) XOR(a,n,),XOR(b,n,);
    for (int i=;i<n;i++) a[i]=1ll*a[i]*b[i]%P;
    if (op==) OR(a,n,);
    else if (op==) AND(a,n,);
    else if (op==) XOR(a,n,);
    for (int i=;i<n;i++) printf("%d ",f[i]);cout<<endl;
}
int main()
{
    freopen("FWT.in","r",stdin);
    freopen("FWT.out","w",stdout);
    n=<<read();
    for (int i=;i<n;i++) a[i]=read();
    for (int i=;i<n;i++) b[i]=read();
    memcpy(f,a,sizeof(f));memcpy(g,b,sizeof(g));
    FWT(f,g,n,);
    memcpy(f,a,sizeof(f));memcpy(g,b,sizeof(g));
    FWT(f,g,n,);
    memcpy(f,a,sizeof(f));memcpy(g,b,sizeof(g));
    FWT(f,g,n,);
    return ;
}