BZOJ2720 列队春游 [期望][数学]

2720: [Violet 5]列队春游

Time Limit: 5 Sec  Memory Limit: 128 MB
Submit: 215  Solved: 152
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Description

Input

Output

Sample Input

Sample Output

HINT

Source

#include<bits/stdc++.h>int i,n,s,x,c[1001]; double ans;int main(){      scanf("%d",&n);       for(i=1;i<=n;i++)scanf("%d",&x),c[x]++;n++;      for(i=0;i<=1000;i++)          if(c[i])ans+=1.0*c[i]*n/(n-s),s+=c[i];      printf("%.2lf\n",ans);}

考虑对i有贡献的j，
j< i则共有s个，
j>=i则共有n-s+1个，j必须在i中
则共有\( (n-s)! \)种排列，剩余s-1个\( P^{s-1}_n \)种排列。
=>\( \frac {C*S*(n-s)!P^{s-1}_n }{n!} \) = \( \frac{C*S(n-s)!n! }{n!(n-s+1)!} \)
=>\( \frac{C*S}{n*S+1} \)
加上自己的贡献：
\( \frac{C*S}{n*s+1}+\)=\( \frac{C*S}{n*s+1} + \frac{C*(n*s+1)}{n*s+1} \)
=>\( \frac{C*(n+1)}{n-s+1} \)