Strange Optimization(扩展欧几里得)

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

 

Strange Optimization Bobo is facing a strange optimization problem. Given n,m , he is going to find a real number α such that f(12+α) is maximized, where f(t)=mini,j∈Z|in−jm+t| . 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 n,m . 1≤n,m≤109 The number of tests cases does not exceed 104 . Output For each case, output a fraction p/q which denotes the result. Sample Input 1 1 1 2 Sample Output 1/2 1/4 Note For the first sample, α=0 maximizes the function

 

 

//题意还是很好懂的，只要明白扩展欧几里得原理，这题很简单，i/n - j/m 可以化为 ( mi - nj ) / ( n * m )

因为 i，j 为整数所以等于  k*gcd(n,m)/(n*m)

所以 f(t)的最大值为 1 / ( Lcm(n,m)*2 )

 1 #include 
 2 #include 
 3 #include <string.h>
 4 #include 
 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

 

转载于:https://www.cnblogs.com/haoabcd2010/p/6861733.html