fft模板

Posted 2020-10-21 position

#include<bits/stdc++.h>
using namespace std;
const int maxn=3000005;
const double pi=acos(-1.0);
inline int read(){
	int x=0,f=1;
	char ch=getchar();
	while(ch<‘0‘||ch>‘9‘){if(ch==‘-‘)f=-1;ch=getchar();}
	while(ch>=‘0‘&&ch<=‘9‘){x=x*10+ch-‘0‘;ch=getchar();}
	return x*f;
}
struct Complex{//复数类
	double r,i;
	Complex(){}
	Complex(double a,double b):r(a),i(b){}
	Complex operator+(const Complex &a)const{
		return Complex(r+a.r,i+a.i);
	}
	Complex operator-(const Complex &a)const{
		return Complex(r-a.r,i-a.i);
	}
	Complex operator*(const Complex &a)const{
		return Complex(r*a.r-i*a.i,r*a.i+i*a.r);
	}
}a[maxn],b[maxn];
int r[maxn],n,m;
void fft(Complex *a,int x){//x=1,DFT;x=-1,IDFT
	for(int i=0;i<n;i++) if(i<r[i]) swap(a[i],a[r[i]]);//翻转操作
	for(int i=1;i<n;i<<=1){
		Complex wn(cos(pi/i),x*sin(pi/i));//旋转因子
		for(int j=0;j<n;j+=(i<<1)){
			Complex w(1,0);//单位复数根
			for(int k=0;k<i;k++){ //蝴蝶变换
				Complex t=w*a[j+k+i];
				a[j+k+i]=a[j+k]-t;
				a[j+k]=a[j+k]+t;
				w=w*wn;
			}
		}
	}
	if(x==-1) for(int i=0;i<=n;i++) a[i].r=a[i].r/n;
}
int main(){
	n=read(),m=read();
	for(int i=0;i<=n;i++) a[i].r=read(),a[i].i=0;
	for(int i=0;i<=m;i++) b[i].r=read(),b[i].i=0;
	m+=n;int l=0;
	for(n=1;n<=m;n<<=1) ++l;
	for(int i=0;i<n;i++) r[i]=(r[i>>1]>>1)|((i&1)<<(l-1));//长度为l的二进制位翻转
	fft(a,1);fft(b,1);//求点值
	for(int i=0;i<=n;i++) a[i]=a[i]*b[i];
	fft(a,-1);//求系数
	for(int i=0;i<=m;i++)
		printf("%d ",(int)(a[i].r+0.5));
}