FFT
代码
1 #include<iostream> 2 #include<cstring> 3 #include<cstdio> 4 #include<cmath> 5 #include<algorithm> 6 #include<complex> 7 using namespace std; 8 const int N = 400005; 9 const double PI = acos(-1.0); 10 typedef complex<double> Comp; 11 Comp a[N],b[N]; 12 int len,l,n,i,v,c[N]; 13 long long ans[N]; 14 double Ans,nn; 15 void Rader(Comp *F,int len) 16 { 17 int j = len >> 1; 18 for (int i=1;i<len-1;i++) 19 { 20 if (i<j) swap(F[i],F[j]); 21 int k = len>>1; 22 while (j >= k) 23 { 24 j -= k; 25 k >>= 1; 26 } 27 if (j < k) j += k; 28 } 29 } 30 void FFT(Comp *F,int len,int on) 31 { 32 Rader(F,len); 33 for (int h=2;h<=len;h<<=1) 34 { 35 Comp wn(cos(-on*2*PI/h),sin(-on*2*PI/h)); 36 for (int j=0;j<len;j+=h) 37 { 38 Comp w(1,0); 39 for (int k=j;k<j+h/2;k++) 40 { 41 Comp u = F[k]; 42 Comp t = w*F[k + h / 2]; 43 F[k] = u + t; 44 F[k + h / 2] = u - t; 45 w = w * wn; 46 } 47 } 48 } 49 if (on == -1) 50 for (int i=0;i<len;i++) 51 F[i]/=len; 52 } 53 void Conv(Comp *a,Comp *b,int len) 54 { 55 FFT(a,len,1); 56 FFT(b,len,1); 57 for (int i=0;i<len;i++) 58 a[i] =a[i]*b[i]; 59 FFT(a,len,-1); 60 for (int i=0;i<len;i++) 61 ans[i]=a[i].real()+0.5; 62 } 63 int main() 64 { 65 int test; 66 scanf("%d",&test); 67 while (test) 68 { 69 test--; 70 scanf("%d",&n); 71 l=0; 72 memset(a,0,sizeof(a)); 73 memset(b,0,sizeof(b)); 74 for (i=1;i<=n;i++) 75 { 76 scanf("%d",&v); 77 c[i]=v; 78 int q=a[v].real()+1; 79 a[v].real(q); 80 b[v].real(q); 81 l=max(l,v); 82 } 83 len=1; 84 while (len<=l*2) len*=2; 85 Conv(a,b,len); 86 for (i=1;i<=n;i++) 87 ans[c[i]+c[i]]--; 88 for (i=0;i<len;i++) 89 ans[i]/=2; 90 for (i=1;i<len;i++) 91 ans[i]=ans[i-1]+ans[i]; 92 sort(c+1,c+1+n); 93 nn=n; 94 Ans=0; 95 for (i=1;i<=n;i++) 96 Ans+=(ans[len-1]-ans[c[i]]-(nn-1)-(nn-i)*(i-1)-(nn-i)*(nn-i-1)/2); 97 printf("%.7lf ",Ans/(nn*(nn-1)*(nn-2)/6)); 98 } 99 }