FFT（快速傅里叶变换）：HDU 4609 3-idiots

3-idiots

Time Limit: 10000/5000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 3560    Accepted Submission(s): 1241

Problem Description

　　King OMeGa catched three men who had been streaking in the street. Looking as idiots though, the three men insisted that it was a kind of performance art, and begged the king to free them. Out of hatred to the real idiots, the king wanted to check if they were lying. The three men were sent to the king's forest, and each of them was asked to pick a branch one after another. If the three branches they bring back can form a triangle, their math ability would save them. Otherwise, they would be sent into jail.
However, the three men were exactly idiots, and what they would do is only to pick the branches randomly. Certainly, they couldn't pick the same branch - but the one with the same length as another is available. Given the lengths of all branches in the forest, determine the probability that they would be saved.

 

Input

　　An integer T(T≤100) will exist in the first line of input, indicating the number of test cases.
Each test case begins with the number of branches N(3≤N≤10⁵).
The following line contains N integers a_i (1≤a_i≤10⁵), which denotes the length of each branch, respectively.

 

Output

　　Output the probability that their branches can form a triangle, in accuracy of 7 decimal places.

 

Sample Input

2

4

1 3 3 4

4

2 3 3 4

 

Sample Output

0.5000000

1.0000000

 

　　大家都去mod邝斌吧~

#include <algorithm>
#include <iostream>
#include <cstring>
#include <cstdio>
#include <cmath>
using namespace std;
const int maxn=500010;
const long double PI=acos(-1.0);
struct complex{
    long double r,i;
    complex(long double r_=0.0,long double i_=0.0){
        r=r_;i=i_;
    }
    complex operator +(complex &a){
        return complex(a.r+r,a.i+i);
    }
    complex operator -(complex &a){
        return complex(r-a.r,i-a.i);
    }
    complex operator *(complex a){
        return complex(r*a.r-i*a.i,i*a.r+a.i*r);
    }
}A[maxn];

void Rader(complex *a,int len){
    for(int i=1,j=len>>1;i<len-1;i++){
        if(i<j)swap(a[i],a[j]);
        int k=len>>1;
        while(j>=k){
            j-=k;
            k>>=1;
        }
        j+=k;
    }
}

void FFT(complex *a,int len,int on){
    Rader(a,len);
    for(int h=2;h<=len;h<<=1){
        complex wn(cos(-on*PI*2/h),sin(-on*PI*2/h));
        for(int j=0;j<len;j+=h){
            complex w(1.0,0);
            for(int k=j;k<j+(h>>1);k++){
                complex x=a[k];
                complex y=a[k+(h>>1)]*w;
                a[k]=x+y;
                a[k+(h>>1)]=x-y;
                w=w*wn;
            }    
        }
    }
    if(on==-1)
        for(int i=0;i<len;i++)
            a[i].r/=len;
}
int a[maxn];
long long num[maxn];
int main(){
#ifndef ONLINE_JUDGE
    //freopen("","r",stdin);
    //freopen("","w",stdout);
#endif
    int T,n,len=1;
    scanf("%d",&T);
    while(T--){
        scanf("%d",&n);
        memset(A,0,sizeof(A));
        memset(num,0,sizeof(num));
        while(len<=200000)len<<=1;
        for(int i=1;i<=n;i++)
            scanf("%d",&a[i]);
        sort(a+1,a+n+1);len=1;
        while(len<=a[n]*2)len<<=1;
        for(int i=1;i<=n;i++)    
            A[a[i]].r++;
        FFT(A,len,1);
        for(int i=0;i<len;i++)
            A[i]=A[i]*A[i];
        FFT(A,len,-1);
        for(int i=0;i<len;i++)
            num[i]=(long long)(A[i].r+0.5);
        for(int i=1;i<=n;i++)
            num[a[i]<<1]--;
        for(int i=0;i<len;i++)    
            num[i]>>=1;
        for(int i=1;i<len;i++)
            num[i]+=num[i-1];
        long long cnt=0;
        for(int i=1;i<=n;i++){
            cnt+=num[len-1]-num[a[i]];
            cnt-=(long long)(n-i)*(i-1);
            cnt-=n-1;
            cnt-=(long long)(n-i)*(n-i-1)/2;
        }
        long long tot=((long long)n*(n-1)*(n-2))/6;
        printf("%.7lf
",1.0*cnt/tot);
    }
    return 0;
}