FWT模板

Posted 2021-10-12 goto_1600

//#pragma GCC target("avx")
//#pragma GCC optimize(2)
//#pragma GCC optimize(3)
//#pragma GCC optimize("Ofast")
// created by myq
#include<iostream>
#include<cstdlib>
#include<string>
#include<cstring>
#include<cstdio>
#include<algorithm>
#include<climits>
#include<cmath>
#include<cctype>
#include<stack>
#include<queue>
#include<list>
#include<vector>
#include<set>
#include<map>
#include<sstream>
#include<unordered_map>
#include<unordered_set>
using namespace std;
typedef long long ll;
#define x first
#define y second
typedef pair<int,int> pii;
const int N = 1<<17;
const int mod=998244353;
inline int read()
{
	int res=0;
	int f=1;
	char c=getchar();
	while(c>'9' ||c<'0')
	{
		if(c=='-')	f=-1;
		c=getchar();
	}
	while(c>='0'&&c<='9')
	{
		res=(res<<3)+(res<<1)+c-'0';
	}
	return res;
 }
 #define int long long
 int n;
 int len;
 int a[N];
 int b[N];
  int ca[N];
 int cb[N];
 int qmi(int a,int b){
 	int res=1;
 	while(b){
 		if(b&1)	res=res*a%mod;
 		b>>=1;
 		a=a*a%mod;
	 }
	 return res;
 }
 int inv2=qmi(2,mod-2);
void fwt_xor(int f[],int inv=1)//^
{
	for(int mid=1;mid<len;mid*=2){
		for(int i=0;i<len;i+=2*mid){
			for(int k=0;k<mid;k++){
				int j=i+mid;
				int x=f[i+k];
				int y=f[j+k];
				f[i+k]=((x+y)%mod+mod)%mod;
				f[j+k]=((x-y)%mod+mod)%mod;
				if(inv==-1)
				{
					f[i+k]=f[i+k]*inv2%mod;
					f[j+k]=f[j+k]*inv2%mod;
				}
			}
			
		}
	}	
}
void fwt_and(int f[],int x=1){//&
	for(int mid=1;mid<len;mid*=2){
		for(int i=0;i<len;i+=2*mid){
			for(int k=0;k<mid;k++){
				int j=i+mid;
				f[i+k]=(f[i+k]+x*f[j+k]+mod)%mod;
			}
		}
	}	
}
void fwt_or(int f[],int x=1){//|
	for(int mid=1;mid<len;mid*=2){
		for(int i=0;i<len;i+=2*mid){
			for(int k=0;k<mid;k++){
				int j=i+mid;
				f[j+k]=(f[j+k]+f[i+k]*x+mod)%mod;
				}
			}
	}	
}
signed main()
{
	
	cin>>n;
	len=(1<<n);
	for(int i=0;i<1<<n;i++)	
		cin>>a[i];
	for(int i=0;i<1<<n;i++)
		cin>>b[i];
	memcpy(ca,a,sizeof a);
	memcpy(cb,b,sizeof b);
	fwt_or(a);
	fwt_or(b);
	for(int i=0;i<len;i++)
		a[i]=a[i]*b[i]%mod;
	fwt_or(a,-1);
	for(int i=0;i<len;i++)	cout<<a[i]<<" ";
	cout<<endl;
	memcpy(a,ca,sizeof a);
	memcpy(b,cb,sizeof b);
	fwt_and(a);
	fwt_and(b);
	for(int i=0;i<len;i++)
		a[i]=a[i]*b[i]%mod;
	fwt_and(a,-1);
	for(int i=0;i<len;i++)	cout<<a[i]<<" ";
	cout<<endl;
	memcpy(a,ca,sizeof a);
	memcpy(b,cb,sizeof b);
	fwt_xor(a);
	fwt_xor(b);
	for(int i=0;i<len;i++)
		a[i]=a[i]*b[i]%mod;
	fwt_xor(a,-1);
	for(int i=0;i<len;i++)	cout<<a[i]<<" ";
	cout<<endl;
	return 0;

}
/**
* In every life we have some trouble
* When you worry you make it double
* Don't worry,be happy.
**/