「BZOJ3527」[Zjoi2014]力

把式子化简后发现是几个卷积形式

#include<bits/stdc++.h>
#define db double
using namespace std;
const int N=400000;
const db PI=acos(-1);
struct Complex{
    db real,image;
    Complex(db _real=0,db _image=0):real(_real),image(_image){}
    Complex operator+(Complex k){return Complex(real+k.real,image+k.image);}
    Complex operator-(Complex k){return Complex(real-k.real,image-k.image);}
    Complex operator*(Complex k){return Complex(real*k.real-image*k.image,real*k.image+image*k.real);}
    Complex operator/(int k){return Complex(real/k,image/k);}
}a[N],b[N],c[N];
int on,n,m,maxp,rev[N];
void fft(Complex* x,int iff){
    for(int i=0;i<n;i++) if(rev[i]>i) swap(x[i],x[rev[i]]);
    for(int len=1;len<=n;len<<=1){
        Complex wn(cos(2*PI/len),iff*sin(2*PI/len));
        for(int now=0;now<n-1;now+=len){
            Complex w(1,0);
            for(int i=0;i<(len>>1);i++,w=w*wn){
                Complex t1=x[now+i],t2=w*x[now+(len>>1)+i];
                x[now+i]=t1+t2,x[now+(len>>1)+i]=t1-t2;
            }
        }
    }
    if(iff==-1) for(int i=0;i<n;i++) x[i]=x[i]/n;
    return;
}
int main(){
    db ans;
    scanf("%d",&on),on--;
    for(int i=0;i<=on;i++){
        if(i) c[i].real=1.0/i/i;
        scanf("%lf",&a[i].real),b[on-i].real=a[i].real;
    }
    m=on<<1;
    for(n=1;n<=m;n<<=1) maxp++;
    for(int i=1;i<n;i++) rev[i]=(rev[i>>1]>>1)|(i&1)<<(maxp-1);
    fft(a,1);fft(b,1);fft(c,1);
    for(int i=0;i<n;i++) a[i]=a[i]*c[i],b[i]=b[i]*c[i];
    fft(a,-1);fft(b,-1);
    for(int i=0;i<=on;i++){
        ans=a[i].real-b[on-i].real;
        printf("%lf
",ans);
    }
    return 0;
}