UVA 题目10288 Coupons（期望）

Coupons in cereal boxes are numbered 1 to n, and a set of one of each is required for a prize (a cereal
box, of course). With one coupon per box, how many boxes on average are required to make a complete
set of n coupons?
Input
Input consists of a sequence of lines each containing a single positive integer n, 1 ≤ n ≤ 33, giving the
size of the set of coupons. Input is terminated by end of file.
Output
For each input line, output the average number of boxes required to collect the complete set of n
coupons. If the answer is an integer number, output the number. If the answer is not integer, then
output the integer part of the answer followed by a space and then by the proper fraction in the format
shown below. The fractional part should be irreducible. There should be no trailing spaces in any line
of output.
Sample Input
2
5
17
Sample Output
3
5
11 --
12
340463
58 ------

720720

题目大意：n个球放在n个盒子里，每次取每个盒子的概率一样，问取出n个球的期望是多少

ac代码

#include<stdio.h>#include<algorithm>#include<stdlib.h>#include<iostream>#include<math.h>#define LL long longusing namespace std;LL gcd(LL a,LL b){    if(a<b)    {        swap(a,b);    }    if(b==0)        return a;    return gcd(b,a%b);}int fun(LL x){    int ans=0;    while(x)    {        x/=10;        ans++;    }    return ans;}int main(){    LL n;    while(scanf("%lld",&n)!=EOF)    {        LL i;        LL fz=n,fm=n;        for(i=1;i<n;i++)        {            fz=fz*(n-i)+n*fm;            fm=fm*(n-i);            LL Gcd=gcd(fm,fz);            fm/=Gcd;            fz/=Gcd;        }        if(fm==1)        {            printf("%lld\n",fz);        }        else        {            LL fi;            fi=fz/fm;            fz%=fm;            int c1=fun(fi);            int c2=max(fun(fz),fun(fm));            for(i=0;i<c1;i++)                printf(" ");            printf(" %lld\n",fz);            printf("%lld ",fi);            for(i=0;i<c2;i++)                printf("-");            printf("\n");            for(i=0;i<c1;i++)                printf(" ");            printf(" %lld\n",fm);        }    }}