洛谷 - P4717 模板快速莫比乌斯/沃尔什变换 (FMT/FWT)

Posted 2021-09-05 Frozen_Guardian

题目链接：点击查看

题目分析：看不懂原理我爪巴了

代码：

// Problem: P4717 【模板】快速莫比乌斯/沃尔什变换 (FMT/FWT)
// Contest: Luogu
// URL: https://www.luogu.com.cn/problem/P4717
// Memory Limit: 250 MB
// Time Limit: 1000 ms
// 
// Powered by CP Editor (https://cpeditor.org)

// #pragma GCC optimize(2)
// #pragma GCC optimize("Ofast","inline","-ffast-math")
// #pragma GCC target("avx,sse2,sse3,sse4,mmx")
#include<iostream>
#include<cstdio>
#include<string>
#include<ctime>
#include<cmath>
#include<cstring>
#include<algorithm>
#include<stack>
#include<climits>
#include<queue>
#include<map>
#include<set>
#include<sstream>
#include<cassert>
#include<bitset>
#include<list>
#include<unordered_map>
#define lowbit(x) (x&-x)
using namespace std;
typedef long long LL;
typedef unsigned long long ull;
template<typename T>
inline void read(T &x)
{
	T f=1;x=0;
	char ch=getchar();
	while(0==isdigit(ch)){if(ch=='-')f=-1;ch=getchar();}
	while(0!=isdigit(ch)) x=(x<<1)+(x<<3)+ch-'0',ch=getchar();
	x*=f;
}
template<typename T>
inline void write(T x)
{
	if(x<0){x=~(x-1);putchar('-');}
    if(x>9)write(x/10);
    putchar(x%10+'0');
}
const int inf=0x3f3f3f3f;
const int N=1e6+100;
const int mod=998244353;
int len;
LL a[N],b[N],A[N],B[N];
void FWTor(LL *f,int x)
{
	for(int mid=1;(mid<<1)<=len;mid<<=1)
	{
		int R=mid<<1;
		for(int i=0;i<len;i+=R)
			for(int j=0;j<mid;j++)
				f[i+j+mid]=(f[i+j+mid]+f[i+j]*x+mod)%mod;
	}
}
void FWTand(LL *f,int x)
{
	for(int mid=1;(mid<<1)<=len;mid<<=1)
	{
		int R=mid<<1;
		for(int i=0;i<len;i+=R)
			for(int j=0;j<mid;j++)
				f[i+j]=(f[i+j]+f[i+j+mid]*x+mod)%mod; 
	}
}
void FWTxor(LL *f,int x)
{
	for(int mid=1;(mid<<1)<=len;mid<<=1)
	{
		int R=mid<<1;
		for(int i=0;i<len;i+=R)
			for(int j=0;j<mid;j++)
			{
				f[i+j]=(f[i+j]+f[i+j+mid])%mod;
				f[i+j+mid]=(f[i+j]-f[i+j+mid]+mod-f[i+j+mid]+mod)%mod;
				f[i+j]=f[i+j]*x%mod;
				f[i+j+mid]=f[i+j+mid]*x%mod;
			}
	}
}
void copy() {
	for(int i=0;i<len;i++) {
		A[i]=a[i],B[i]=b[i];
	}
}
void merge() {
	for(int i=0;i<len;i++) {
		A[i]=A[i]*B[i]%mod;
	}
}
void print() {
	for(int i=0;i<len;i++) {
		printf("%lld ",A[i]);
	}
	puts("");
}
int main()
{
#ifndef ONLINE_JUDGE
//	freopen("data.in.txt","r",stdin);
//	freopen("data.out.txt","w",stdout);
#endif
//	ios::sync_with_stdio(false);
	read(len);
	len=1<<len;
	for(int i=0;i<len;i++) {
		read(a[i]);
	}
	for(int i=0;i<len;i++) {
		read(b[i]);
	}
	copy(),FWTor(A,1),FWTor(B,1),merge(),FWTor(A,-1),print();
	copy(),FWTand(A,1),FWTand(B,1),merge(),FWTand(A,-1),print();
	copy(),FWTxor(A,1),FWTxor(B,1),merge(),FWTxor(A,(mod+1)>>1),print();
	return 0;
}