【BZOJ】3527: [Zjoi2014]力

题目链接：http://www.lydsy.com/JudgeOnline/problem.php?id=3527

把${f_i}$消去之后换元就是卷积的形式，直接算就可以了。

---

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<vector>
#include<cstdlib>
#include<cmath>
#include<complex>
#include<cstring>
using namespace std;
#define maxn 1001000
#define llg long long 
#define Pi acos(-1.0)
#define yyj(a) freopen(a".in","r",stdin),freopen(a".out","w",stdout);
typedef complex<double> XU;

struct FFT
{
    llg rev[maxn],L,n;
    double c[maxn];
    void fft(XU *z,llg f)
    {
        for (llg i=0;i<n;i++) if (i<rev[i]) swap(z[i],z[rev[i]]);
        for (llg i=1;i<n;i*=2)
        {
            XU wn(cos(Pi/i),sin(Pi/i));
            for (llg p=i*2,j=0;j<n;j+=p)
            {
                XU w(1,0);
                for (llg k=0;k<i;k++,w*=wn)
                {
                    XU x=z[j+k],y=z[j+k+i]*w;
                    z[j+k]=x+y,z[j+k+i]=x-y;
                } 
            }
        }
        if (f==-1) reverse(z+1,z+n);
    }

    XU a[maxn],b[maxn];
    
    void work()
    {
        llg m=(n-1)*3;
        for (n=1;n<=m;n*=2) L++;
        for (llg i=0;i<n;i++) rev[i]=(rev[i/2]/2)|((i&1)<<(L-1));
        fft(a,1),fft(b,1);
        for (llg i=0;i<n;i++) a[i]*=b[i];
        fft(a,-1);
        for (llg i=0;i<n;i++) c[i]=(a[i].real()/n);
    }
}F1,F2;

double x[maxn];

int main()
{
    yyj("li");
    llg N;
    cin>>N;
    F1.n=N;
    for (llg i=0;i<N;i++) scanf("%lf",&x[i]),F1.a[i]=x[i];
    for (llg i=0;i<=N-2;i++) F1.b[i]=(double)-1.0/(double)(N-1-i)/(double)(N-1-i);
    for (llg i=N;i<=2*N-2;i++) F1.b[i]=(double)1.0/(double)(N-1-i)/(double)(N-1-i);
    F1.work();
    for (llg i=N-1;i<2*N-1;i++) printf("%.9lf
",F1.c[i]) ;
    return 0;
}