uva 11673 Garbage Remembering Exam （概率）

题目链接： http://vjudge.net/problem/viewProblem.action?id=42000

该过程为随即过程，因此总期望值等于个单词对应的期望值，即它们wasted的概率

 1 #include <stdio.h>

 2 #include <cstring>

 3 #include <cstdlib>

 4 #include <algorithm>

 5 #include <cmath>

 6            

 7 using namespace std;

 8 #define lson o<<1

 9 #define rson o<<1|1

10 #define max(a,b) (a)>(b)?(a):(b)

11 #define min(a,b) (a)<(b)?(a):(b)

12 #define INF 200000000

13 #define N 100010           

14 typedef long long ll;

15 long double lg[N];

16 

17 void init (){

18      lg[1]=0;

19     for(int i=2;i<N;i++){

20        lg[i]=(long double)log(i)+lg[i-1];

21     }     

22 }      

23 int main(){

24    int n,k,cs=1;

25    init();

26    while(scanf("%d%d",&n,&k) && n){

27       long double p,ans=0;

28       int up,down,put=2*k;

29       if(2*k>n-1)put=n-1;

30       long double l0=lg[n-1]-lg[n-1-put];

31       for(int i=1;i<=n;i++){

32           up=max(i-1-k,0);

33           down=max(n-i-k,0);

34           if(up+down>=put)p=exp(lg[up+down]-lg[up+down-put]-l0);

35           else p=0;

36           ans+=1-p;

37       }

38       printf("Case %d: %.4lf\n",cs++,(double)ans);

39    }

40    return 0;

41 }