Uva10976
It is easy to see that for every fraction in the form 1 k (k > 0), we can always find two positive integers x and y, x ≥ y, such that: 1 k = 1 x + 1 y Now our question is: can you write a program that counts how many such pairs of x and y there are for any given k?
Input Input contains no more than 100 lines, each giving a value of k (0 < k ≤ 10000).
Output
For each k, output the number of corresponding (x,y) pairs, followed by a sorted list of the values of x and y, as shown in the sample output.
Sample Input
2 12
Sample Output
2 1/2 = 1/6 + 1/3 1/2 = 1/4 + 1/4 8 1/12 = 1/156 + 1/13 1/12 = 1/84 + 1/14 1/12 = 1/60 + 1/15 1/12 = 1/48 + 1/16 1/12 = 1/36 + 1/18 1/12 = 1/30 + 1/20 1/12 = 1/28 + 1/21 1/12 = 1/24 + 1/24
1 #include <cstdio> 2 #include <iostream> 3 #include <queue> 4 #include <vector> 5 #include<string.h> 6 #include<map> 7 #include<bits/stdc++.h> 8 #define LL long long 9 #define maxn 1005 10 using namespace std; 11 //vector<int> m; 12 int main() 13 { 14 int k; 15 while(scanf("%d",&k)!=EOF) 16 //while(~scanf("%d",&k),k)这么写就WA,这是什么神奇的卡点,我表示很迷.jpg 17 { 18 int x[maxn],y[maxn]; 19 int ans=0; 20 for(int i=k+1;i<=2*k;i++)//枚举y 21 { 22 int m=(k*i)/(i-k); 23 if((k*i)%(i-k)==0&&m>=i) 24 { 25 x[ans]=m,y[ans]=i; 26 ans++; 27 } 28 } 29 printf("%d\n",ans); 30 for(int i=0;i<ans;i++) 31 printf("1/%d = 1/%d + 1/%d\n",k,x[i],y[i]); 32 } 33 return 0; 34 }
思路:
Cuz: x>=y 则1/x<=1/y 则1/k=1/x+1/y<=2/y
So: y<=2k && y>k,x>=y(由题目得)
x=(k*y)/(y-k),如果满足(k*y)%(y-k)则存在这样的正整数x。