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Strange Optimization(扩展欧几里得)

發(fā)布時間：2024/4/14 编程问答 26 豆豆

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Strange Optimization
Accepted : 67	?	Submit : 289
Time Limit : 1000 MS	?	Memory Limit : 65536 KB

Strange Optimization

Bobo is facing a strange optimization problem. Given , he is going to find a real number such that is maximized, where . Help him!

Note: It can be proved that the result is always rational.

Input

The input contains zero or more test cases and is terminated by end-of-file.

Each test case contains two integers .

The number of tests cases does not exceed .

Output

For each case, output a fraction which denotes the result.

Sample Input

1 1 1 2

Sample Output

1/2 1/4

Note

For the first sample, maximizes the function

//題意還是很好懂的，只要明白擴展歐幾里得原理，這題很簡單，i/n - j/m 可以化為 ( mi - nj ) / ( n * m )

因為 i，j 為整數(shù)所以等于? k*gcd(n,m)/(n*m)

所以 f(t)的最大值為 1 / ( Lcm(n,m)*2 )

1 #include <iostream> 2 #include <stdio.h> 3 #include <string.h> 4 #include <algorithm> 5 using namespace std; 6 #define LL long long 7 8 LL gcd(LL a,LL b) 9 { 10 return b==0?a:gcd(b,a%b); 11 } 12 13 int main() 14 { 15 LL n,m; 16 while (scanf("%I64d%I64d",&n,&m)!=EOF) 17 { 18 LL p = gcd(n,m); 19 LL q = n*m*2; 20 LL yue = gcd(p,q); 21 printf("%I64d/%I64d\n",p/yue,q/yue); 22 } 23 return 0; 24 } View Code

轉載于:https://www.cnblogs.com/haoabcd2010/p/6861733.html

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