# 3-idiots

Time Limit: 10000/5000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 216    Accepted Submission(s): 73

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

Source

Recommend
liuyiding

4

1 3 3 4

num = {0   1   0    2    1}

num数组和num数组卷积的解决，其实就是从{1 3 3 4}取一个数，从{1 3 3 4}再取一个数，他们的和每个值各有多少个

{0 1 0 2 1}*{0 1 0 2 1} 卷积的结果应该是{0 0  1  0  4  2  4  4  1 }。

和为 4 的取法有四种：1+3， 1+3  ，3+1 ，3+1

和为 5 的取法有两种：1+4 ，4+1；

和为 6的取法有四种：3+3,3+3,3+3,3+3,3+3

和为 7 的取法有四种： 3+4,3+4,4+3,4+3

和为 8 的取法有 一种：4+4

        while( len < 2*len1 )len <<= 1;
for(int i = 0;i < len1;i++)
x1[i] = complex(num[i],0);
for(int i = len1;i < len;i++)
x1[i] = complex(0,0);
fft(x1,len,1);
for(int i = 0;i < len;i++)
x1[i] = x1[i]*x1[i];
fft(x1,len,-1);
for(int i = 0;i < len;i++)
num[i] = (long long)(x1[i].r+0.5);

        //减掉取两个相同的组合
for(int i = 0;i < n;i++)
num[a[i]+a[i]]--;

        //选择的无序，除以2
for(int i = 1;i <= len;i++)
{
num[i]/=2;
}

        sum[0] = 0;
for(int i = 1;i <= len;i++)
sum[i] = sum[i-1]+num[i];

a数组从小到大排好序。

cnt -= (long long)(n-1-i)*i;

cnt -= (n-1);

cnt -= (long long)(n-1-i)*(n-i-2)/2;

        long long cnt = 0;
for(int i = 0;i < n;i++)
{
cnt += sum[len]-sum[a[i]];
//减掉一个取大，一个取小的
cnt -= (long long)(n-1-i)*i;
//减掉一个取本身，另外一个取其它
cnt -= (n-1);
//减掉大于它的取两个的组合
cnt -= (long long)(n-1-i)*(n-i-2)/2;
}

#include <stdio.h>
#include <iostream>
#include <string.h>
#include <algorithm>
#include <math.h>
using namespace std;

const double PI = acos(-1.0);
struct complex
{
double r,i;
complex(double _r = 0,double _i = 0)
{
r = _r; i = _i;
}
complex operator +(const complex &b)
{
return complex(r+b.r,i+b.i);
}
complex operator -(const complex &b)
{
return complex(r-b.r,i-b.i);
}
complex operator *(const complex &b)
{
return complex(r*b.r-i*b.i,r*b.i+i*b.r);
}
};
void change(complex y[],int len)
{
int i,j,k;
for(i = 1, j = len/2;i < len-1;i++)
{
if(i < j)swap(y[i],y[j]);
k = len/2;
while( j >= k)
{
j -= k;
k /= 2;
}
if(j < k)j += k;
}
}
void fft(complex y[],int len,int on)
{
change(y,len);
for(int h = 2;h <= len;h <<= 1)
{
complex wn(cos(-on*2*PI/h),sin(-on*2*PI/h));
for(int j = 0;j < len;j += h)
{
complex w(1,0);
for(int k = j;k < j+h/2;k++)
{
complex u = y[k];
complex t = w*y[k+h/2];
y[k] = u+t;
y[k+h/2] = u-t;
w = w*wn;
}
}
}
if(on == -1)
for(int i = 0;i < len;i++)
y[i].r /= len;
}

const int MAXN = 400040;
complex x1[MAXN];
int a[MAXN/4];
long long num[MAXN];//100000*100000会超int
long long sum[MAXN];

int main()
{
int T;
int n;
scanf("%d",&T);
while(T--)
{
scanf("%d",&n);
memset(num,0,sizeof(num));
for(int i = 0;i < n;i++)
{
scanf("%d",&a[i]);
num[a[i]]++;
}
sort(a,a+n);
int len1 = a[n-1]+1;
int len = 1;
while( len < 2*len1 )len <<= 1;
for(int i = 0;i < len1;i++)
x1[i] = complex(num[i],0);
for(int i = len1;i < len;i++)
x1[i] = complex(0,0);
fft(x1,len,1);
for(int i = 0;i < len;i++)
x1[i] = x1[i]*x1[i];
fft(x1,len,-1);
for(int i = 0;i < len;i++)
num[i] = (long long)(x1[i].r+0.5);
len = 2*a[n-1];
//减掉取两个相同的组合
for(int i = 0;i < n;i++)
num[a[i]+a[i]]--;
//选择的无序，除以2
for(int i = 1;i <= len;i++)
{
num[i]/=2;
}
sum[0] = 0;
for(int i = 1;i <= len;i++)
sum[i] = sum[i-1]+num[i];
long long cnt = 0;
for(int i = 0;i < n;i++)
{
cnt += sum[len]-sum[a[i]];
//减掉一个取大，一个取小的
cnt -= (long long)(n-1-i)*i;
//减掉一个取本身，另外一个取其它
cnt -= (n-1);
//减掉大于它的取两个的组合
cnt -= (long long)(n-1-i)*(n-i-2)/2;
}
//总数
long long tot = (long long)n*(n-1)*(n-2)/6;
printf("%.7lf\n",(double)cnt/tot);
}
return 0;
}

posted on 2013-07-24 14:18 kuangbin 阅读(...) 评论(...) 编辑 收藏

• 随笔 - 940
• 文章 - 0
• 评论 - 573
• 引用 - 0

JAVASCRIPT: