poj 3101 Astronomy

2个星球周期为a,b。则相差半周的长度为a*b/(2*abs(a-b)),对于n个只需求这n个

分数的最小公倍数即可！

公式：

分数的最小公倍数 = 分子的最小公倍数/分母的最大公约数

由于涉及到大数所以用java写的方便！

 import java.math.*;
 import java.util.*;

 public class Main {
     public static void main(String arg[]){
         Scanner cin = new Scanner(System.in);
         int n = cin.nextInt();
         int an[] = new int[n];
         int a[] = new int[n];
         int b[] = new int[n];
         int i,j,k;
         for (i=0;i<n;i++)
             an[i] = cin.nextInt();
         Arrays.sort(an);
         for (i=1,j=1;i<n;i++)
             if (an[i]!=an[i-1])
                 an[j++] = an[i];
         for (i=1,k=0;i<j;i++){
             a[k] = (an[i] - an[i-1])*2;
             b[k] = an[i] * an[i-1];
             int t = gcd(a[k],b[k]);
             a[k] /= t;
             b[k++] /= t;
         }
         BigInteger ans1 = BigInteger.valueOf(a[0]),ans2 = BigInteger.valueOf(b[0]),ans;
         for (i=1;i<k;i++){
             ans1 = ans1.gcd(BigInteger.valueOf(a[i]));
             ans = ans2.multiply(BigInteger.valueOf(b[i]));
             ans2 = ans.divide(ans2.gcd(BigInteger.valueOf(b[i])));
         }
         ans = ans2.gcd(ans1);
         System.out.println(ans2.divide(ans)+" "+ans1.divide(ans));
     }
     public static int gcd(int a,int b){
         int t;
         if (a<b){
             t = a;
             a = b;
             b = t;
         }
         while(true){
             if (b==0) break;
             t = a;
             a = b;
             b = t%b;
         }
         return a;
     }
 }