FFT

Posted 2022-02-24 cbdsopa的博客

建议全文背诵

3->2优化

#include<bits/stdc++.h>
using namespace std;
#define LL long long 
#define file(a) freopen(#a".in","r",stdin),freopen(#a".out","w",stdout)
#define endless() fclose(stdin),fclose(stdout)
#define ReadOnly(a) freopen(#a,"r",stdin)
inline int read()
	int s=0,f=1;char ch=getchar();
	while(ch<\'0\'||\'9\'<ch) if(ch==\'-\') f=-1;ch=getchar();
	while(\'0\'<=ch&&ch<=\'9\') s=s*10+(ch^48);ch=getchar();
	return s*f;

const int N=1e6+5e5+3;
const double pi=acos(-1);
struct Complex
	double x,y;
	Complex(double _x=0,double _y=0)
		x=_x;y=_y;
	
	inline friend Complex operator+(Complex a,Complex b)
		return Complex(a.x+b.x,a.y+b.y);
	 
	inline friend Complex operator-(Complex a,Complex b)
		return Complex(a.x-b.x,a.y-b.y);
	
	inline friend Complex operator*(Complex a,Complex b)
		return Complex(a.x*b.x-a.y*b.y,a.x*b.y+a.y*b.x);
	
F[N<<1];
int rev[N<<1];int n,m;
inline void get_rev()
	for(int i=0;i<n;++i)
		rev[i]=(rev[i>>1]>>1)|((i&1)?n>>1:0);
	

inline void FFT(Complex *f,bool flag)
	for(int i=0;i<n;++i)
		if(i<rev[i]) swap(f[i],f[rev[i]]);
	
	for(int p=2;p<=n;p<<=1)//枚举区间长度
		int len=p>>1;//获取分治长度
		Complex w1n(cos(2*pi/p),sin(2*pi/p) );
		if(!flag) w1n.y*=-1;
		for(int k=0;k<n;k+=p)//枚举初始化位置
			Complex wxn(1,0);
			for(int l=k;l<k+len;++l)//枚举detail
				Complex tmp=wxn*f[len+l];
				f[len+l]=f[l]-tmp;
				f[l]=f[l]+tmp;
				wxn=wxn*w1n;//获取下一个单位根
			
		
	

int main(void)
	n=read();m=read();
	for(int i=0;i<=n;++i)
		F[i].x=read();
	
	for(int i=0;i<=m;++i)
		F[i].y=read();
	
	for(m+=n,n=1;n<=m;n<<=1);//补足2的幂次
	get_rev();//二进制翻转
	FFT(F,1);//DFT
	for(int i=0;i<n;++i) F[i]=F[i]*F[i];
	FFT(F,0);//IDFT
	for(int i=0;i<=m;++i)
		printf("%d ",(int)(F[i].y/n/2+0.49) );
	
	return 0;

原版，更加灵活

#include<bits/stdc++.h>
using namespace std;
#define LL long long 
#define file(a) freopen(#a".in","r",stdin),freopen(#a".out","w",stdout)
#define endless() fclose(stdin),fclose(stdout)
#define ReadOnly(a) freopen(#a,"r",stdin)
inline int read()
	int s=0,f=1;char ch=getchar();
	while(ch<\'0\'||\'9\'<ch) if(ch==\'-\') f=-1;ch=getchar();
	while(\'0\'<=ch&&ch<=\'9\') s=s*10+(ch^48);ch=getchar();
	return s*f;

const int N=1e6+5e5+3;
const double pi=acos(-1);
struct Complex
	double x,y;
	Complex(double _x=0,double _y=0)
		x=_x;y=_y;
	
	inline friend Complex operator+(Complex a,Complex b)
		return Complex(a.x+b.x,a.y+b.y);
	 
	inline friend Complex operator-(Complex a,Complex b)
		return Complex(a.x-b.x,a.y-b.y);
	
	inline friend Complex operator*(Complex a,Complex b)
		return Complex(a.x*b.x-a.y*b.y,a.x*b.y+a.y*b.x);
	
F[N<<1],P[N<<1];
int rev[N<<1];int n,m;
inline void get_rev()
	for(int i=0;i<n;++i)
		rev[i]=(rev[i>>1]>>1)|((i&1)?n>>1:0);
	

inline void FFT(Complex *f,bool flag)
	for(int i=0;i<n;++i)
		if(i<rev[i]) swap(f[i],f[rev[i]]);
	
	for(int p=2;p<=n;p<<=1)//枚举区间长度
		int len=p>>1;//获取分治长度
		Complex w1n(cos(2*pi/p),sin(2*pi/p) );
		if(!flag) w1n.y*=-1;
		for(int k=0;k<n;k+=p)//枚举初始化位置
			Complex wxn(1,0);
			for(int l=k;l<k+len;++l)//枚举detail
				Complex tmp=wxn*f[len+l];
				f[len+l]=f[l]-tmp;
				f[l]=f[l]+tmp;
				wxn=wxn*w1n;//获取下一个单位根
			
		
	

int main(void)
	n=read();m=read();
	for(int i=0;i<=n;++i)
		F[i].x=read();
	
	for(int i=0;i<=m;++i)
		P[i].x=read();
	
	for(m+=n,n=1;n<=m;n<<=1);//补足2的幂次
	get_rev();//二进制翻转
	FFT(F,1);FFT(P,1);//DFT
	for(int i=0;i<n;++i) F[i]=F[i]*P[i];
	FFT(F,0);//IDFT
	for(int i=0;i<=m;++i)
		printf("%d ",(int)(F[i].x/n+0.49) );
	
	return 0;