浅析错排问题

描述

In order to happy everyone, organizer HRW held an open up partythere have specific requirements for this activity is this:
First of all, all person in the party will have to write a note to his name into the box;Then, after all the note added is completed, each taking a note from the box;Finally, if made note of your name, then "Congratulations, won the party!"
Oh, my God!
Now to the question, you can calculate the probability of this happening?Don‘t count? Don‘t you want said by others as a  DouBi?!  AC it！

输入

Input file contains several test cases. Each test case consists of a integer numbers n on a line(one≤n≤ten ).The last test case is followed by a line that contains one zeroes. This line must not be processed.

输出

print the the probability
See the following example.

样例输入

2
3
0

样例输出

Case [1]: 50.00%.
Case [2]: 33.33%.

提示

要用到错排公式，计算所有人都抽到自己名字的概率

来源

原创

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#include<stdio.h>
int main()
{
    double a[55];
    double b[55];
    a[0]=1;
    for(int i=1;i<=22;i++)
        a[i]=a[i-1]*i;
    b[1]=0;
    b[2]=1;
    b[3]=2;
    for(int i=4;i<=22;i++)
        b[i]=(i-1)*(b[i-1]+b[i-2]);
        int n,d=1;
    while(~scanf("%d",&n),n)
    {
        printf("Case [%d]: ",d++);
        if(n==1)
            printf("100.00%%.\n");
        else
        {
            printf("%.2lf%%.\n",100*b[n]/a[n]);
        }
    }
}