把式子化简后发现是几个卷积形式
1 #include<bits/stdc++.h> 2 #define db double 3 using namespace std; 4 const int N=400000; 5 const db PI=acos(-1); 6 struct Complex{ 7 db real,image; 8 Complex(db _real=0,db _image=0):real(_real),image(_image){} 9 Complex operator+(Complex k){return Complex(real+k.real,image+k.image);} 10 Complex operator-(Complex k){return Complex(real-k.real,image-k.image);} 11 Complex operator*(Complex k){return Complex(real*k.real-image*k.image,real*k.image+image*k.real);} 12 Complex operator/(int k){return Complex(real/k,image/k);} 13 }a[N],b[N],c[N]; 14 int on,n,m,maxp,rev[N]; 15 void fft(Complex* x,int iff){ 16 for(int i=0;i<n;i++) if(rev[i]>i) swap(x[i],x[rev[i]]); 17 for(int len=1;len<=n;len<<=1){ 18 Complex wn(cos(2*PI/len),iff*sin(2*PI/len)); 19 for(int now=0;now<n-1;now+=len){ 20 Complex w(1,0); 21 for(int i=0;i<(len>>1);i++,w=w*wn){ 22 Complex t1=x[now+i],t2=w*x[now+(len>>1)+i]; 23 x[now+i]=t1+t2,x[now+(len>>1)+i]=t1-t2; 24 } 25 } 26 } 27 if(iff==-1) for(int i=0;i<n;i++) x[i]=x[i]/n; 28 return; 29 } 30 int main(){ 31 db ans; 32 scanf("%d",&on),on--; 33 for(int i=0;i<=on;i++){ 34 if(i) c[i].real=1.0/i/i; 35 scanf("%lf",&a[i].real),b[on-i].real=a[i].real; 36 } 37 m=on<<1; 38 for(n=1;n<=m;n<<=1) maxp++; 39 for(int i=1;i<n;i++) rev[i]=(rev[i>>1]>>1)|(i&1)<<(maxp-1); 40 fft(a,1);fft(b,1);fft(c,1); 41 for(int i=0;i<n;i++) a[i]=a[i]*c[i],b[i]=b[i]*c[i]; 42 fft(a,-1);fft(b,-1); 43 for(int i=0;i<=on;i++){ 44 ans=a[i].real-b[on-i].real; 45 printf("%lf ",ans); 46 } 47 return 0; 48 }