hdu5810——Balls and Boxes（数学推导）-白红宇

hdu5810——Balls and Boxes（数学推导）

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发布时间：2019-05-10

本文共 1379 字，大约阅读时间需要 4 分钟。

Problem Description

Mr. Chopsticks is interested in random phenomena, and he conducts an experiment to study randomness. In the experiment, he throws n balls into m boxes in such a manner that each ball has equal probability of going to each boxes. After the experiment, he calculated the statistical variance V as

V=∑mi=1(Xi−X¯)2m

where Xi is the number of balls in the ith box, and X¯ is the average number of balls in a box.

Your task is to find out the expected value of V.

Input

The input contains multiple test cases. Each case contains two integers n and m (1 <= n, m <= 1000 000 000) in a line.

The input is terminated by n = m = 0.

Output

For each case, output the result as A/B in a line, where A/B should be an irreducible fraction. Let B=1 if the result is an integer.

Sample Input

2 1

2 2

0 0

Sample Output

0/1

1/2

反正最后推出来是n*(m-1)/m*m，恩

#include 
   
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     #include 
     
      #include 
      
       #include 
       
        #include 
        
         #include 
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           #include 
           
            #include 
            
             #define INF 0x3f3f3f3f#define MAXN 1010#define mod 1000000007using namespace std;long long gcd(long long a,long long b){ if(b==0) return a; else return gcd(b,a%b);}int main(){ long long a,b; while(~scanf("%I64d%I64d",&a,&b)) { if(a==0&&b==0) break; long long fz=a*(b-1); long long fm=b*b; long long c=gcd(fz,fm); if(fm==0) fm++; printf("%I64d/%I64d\n",fz/c,fm/c); } return 0;}

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