HDU4609 计数问题+FFT

题目大意：

给出n(1e5)条线段(长度为整数，<=1e5)，求任取3条线段能组成一个三角形的概率。

用cnt[i]记录长度为i的线段的个数，通过卷积可以计算出两条线段长度之和为i的方案数sum[i]：先用FFT计算出cnt[i]的卷积sum[i]，为取两条线段长度和为i的排列数（包括自己和自己），去掉自己和自己的方案数，再对所有sum[i]除以2即为所求方案数。

之后对所有线段a[i]有大到小排列，考虑第i条线段是三角形最长边的情况（长度相同则将编号大的视为更长，就没有长度相同的情况了。实际计算时无影响）。首先是sum[i + 1] + sum[i + 2] + ... + sum[len - 1]，即其他两边之和要大于他的方案数。然后去掉：1.另两边有一条比他大，有一条比他小。 2.两条都比他长。 3.有一条是他自己。这三种情况。

要注意有些地方爆int。还有len的计算要注意边界（一直wa，wa了半天）。

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
using namespace std;

const double pi = acos(-);

struct Complex{
    double real, imag;
    Complex (){}
    Complex (double _real, double _imag){
        real = _real;
        imag = _imag;
    }
};

Complex operator + (Complex x, Complex y){
    return Complex(x.real + y.real, x.imag + y.imag);
}

Complex operator - (Complex x, Complex y){
    return Complex(x.real - y.real, x.imag - y.imag);
}

Complex operator * (Complex x, Complex y){
    return Complex(x.real * y.real - x.imag * y.imag, x.real * y.imag + x.imag * y.real);
}

Complex operator / (Complex x, double y){
    return Complex(x.real / y, x.imag / y);
}

int reverse(int x, int len){
    int t = ;
    for (int i = ; i < len; i <<= ){
        t <<= ;
        if (x & i) t |= ;
    }
    return t;
}

Complex A[];
void FFT(Complex *a, int n, int DFT){
    for (int i = ; i < n; ++i) A[reverse(i, n)] = a[i];
    for (int i = ; i <= n; i <<= ){
        Complex wn = Complex(cos( * pi / i), DFT * sin( * pi / i));
        for (int j = ; j < n; j += i){
            Complex w = Complex(, );
            for (int k = ; k < (i >> ); ++k){
                Complex x = A[j + k];
                Complex y = w * A[j + k + (i >> )];
                A[j + k] = x + y;
                A[j + k + (i >> )] = x - y;
                w = w * wn;
            }
        }
    }
    if (DFT == -) for (int i = ; i < n; ++i) A[i] = A[i] / n;
    for (int i = ; i < n; ++i) a[i] = A[i];
}

int T, n;
int a[];
int cnt[];
Complex B[];
long long sum[];

int main(){

    scanf("%d", &T);
    while (T--){
        scanf("%d", &n);
        int maxL = ;
        memset(cnt, , sizeof(cnt));
        memset(sum, , sizeof(sum));
        for (int i = ; i < n; ++i){
            scanf("%d", a + i);
            if (a[i] > maxL) maxL = a[i];
            ++cnt[a[i]];
        }
        int len = ;
        while (len <= maxL * ) len <<= ;
        for (int i = ; i <= maxL; ++i) B[i] = Complex(cnt[i], );
        for (int i = maxL + ; i < len; ++i) B[i] = Complex(, );
        FFT(B, len, );
        for (int i = ; i < len; ++i) B[i] = B[i] * B[i];
        FFT(B, len, -);
        for (int i = ; i < len; ++i) sum[i] = (long long)(B[i].real + 0.5);
        for (int i = ; i < n; ++i) --sum[a[i] + a[i]];
        for (int i = ; i < len; ++i) sum[i] >>= ;
        for (int i = len - ; i >= ; --i) sum[i] += sum[i + ];
        sort(a, a + n);
        long long ans = ;
        for (int i = ; i < n; ++i){
            long long tmp = sum[a[i] + ];
            tmp -= ((long long)n - i - ) * i;
            tmp -= ((long long)n - i - ) * (n - i - ) / 2LL;
            tmp -= n - ;
            ans += tmp;
        }
        double Ans = (double)ans * 6.0 / n / (n - ) / (n - );
        printf("%.7f\n", Ans);
    }

    return ;
}