FWT

前言

没有前言

讲解

暂时不打算讲解

放一个巨佬的博客供膜拜

再来一个外校的巨佬

练习

板题(洛谷)

代码

板题代码

//12252024832524
#include <cstdio>
#include <cstring>
#include <algorithm>
#define TT template<typename T>
using namespace std; 

typedef long long LL;
const int MAXN = 1 << 17 | 5;
const int MOD = 998244353;
const int inv2 = 499122177;
int n,N;
int a[MAXN],b[MAXN],a1[MAXN],b1[MAXN];

LL Read()
{
	LL x = 0,f = 1;char c = getchar();
	while(c > '9' || c < '0'){if(c == '-')f = -1;c = getchar();}
	while(c >= '0' && c <= '9'){x = (x*10) + (c^48);c = getchar();}
	return x * f;
}
TT void Put1(T x)
{
	if(x > 9) Put1(x/10);
	putchar(x%10^48);
}
TT void Put(T x,char c = -1)
{
	if(x < 0) putchar('-'),x = -x;
	Put1(x);
	if(c >= 0) putchar(c);
}
TT T Max(T x,T y){return x > y ? x : y;}
TT T Min(T x,T y){return x < y ? x : y;}
TT T Abs(T x){return x < 0 ? -x : x;}

int qpow(int x,int y)
{
	int ret = 1;
	while(y){if(y & 1) ret = 1ll * ret * x % MOD;x = 1ll * x * x % MOD;y >>= 1;}
	return ret;
}
void Add(int &x){if(x >= MOD) x -= MOD;}
void Del(int &x){if(x < 0) x += MOD;}
void fwtor(int *a,int opt)
{
	for(int i = 1;i < N;i <<= 1)//块长
		for(int p = i << 1,j = 0;j < N;j += p)//第几个块 
			for(int k = 0;k < i;++ k)//块内第几个 
				if(opt == 1) Add(a[i+j+k] += a[j+k]);
				else Del(a[i+j+k] -= a[j+k]);
}
void fwtand(int *a,int opt)
{
	for(int i = 1;i < N;i <<= 1)//块长
		for(int p = i << 1,j = 0;j < N;j += p)//第几个块 
			for(int k = 0;k < i;++ k)//块内第几个 
				if(opt == 1) Add(a[j+k] += a[i+j+k]);
				else Del(a[j+k] -= a[i+j+k]);
}
void fwtxor(int *a,int opt)
{
	for(int i = 1;i < N;i <<= 1)//块长
		for(int p = i << 1,j = 0;j < N;j += p)//第几个块 
			for(int k = 0;k < i;++ k)//块内第几个 
			{
				int x = a[j+k],y = a[i+j+k];
				if(opt == 1) Add(a[j+k] = x+y),Del(a[i+j+k] = x-y);
				else a[j+k] = 1ll * (x + y) * inv2 % MOD,a[i+j+k] = 1ll * (x - y) * inv2 % MOD;
			}
}

int main()
{
//	freopen(".in","r",stdin);
//	freopen(".out","w",stdout);
	n = Read(); N = 1 << n;
	for(int i = 0;i < N;++ i) a[i] = Read();
	for(int i = 0;i < N;++ i) b[i] = Read();
	//or
	for(int i = 0;i < N;++ i) a1[i] = a[i],b1[i] = b[i];
	fwtor(a1,1);
	fwtor(b1,1);
	for(int i = 0;i < N;++ i) a1[i] = 1ll * a1[i] * b1[i] % MOD;
	fwtor(a1,-1);
	for(int i = 0;i < N;++ i) Del(a1[i]),Put(a1[i],i == N - 1 ? '
' : ' ');
	//and
	for(int i = 0;i < N;++ i) a1[i] = a[i],b1[i] = b[i];
	fwtand(a1,1);
	fwtand(b1,1);
	for(int i = 0;i < N;++ i) a1[i] = 1ll * a1[i] * b1[i] % MOD;
	fwtand(a1,-1);
	for(int i = 0;i < N;++ i) Del(a1[i]),Put(a1[i],i == N - 1 ? '
' : ' ');
	//xor
	fwtxor(a,1);
	fwtxor(b,1);
	for(int i = 0;i < N;++ i) a[i] = 1ll * a[i] * b[i] % MOD;
	fwtxor(a,-1);
	for(int i = 0;i < N;++ i) Del(a[i]),Put(a[i],i == N - 1 ? '
' : ' ');
	return 0;
}