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！

 

 1 import java.math.*;

 2 import java.util.*;

 3 

 4 public class Main {

 5     public static void main(String arg[]){

 6         Scanner cin = new Scanner(System.in);

 7         int n = cin.nextInt();

 8         int an[] = new int[n];

 9         int a[] = new int[n];

10         int b[] = new int[n];

11         int i,j,k;

12         for (i=0;i<n;i++)

13             an[i] = cin.nextInt();

14         Arrays.sort(an);

15         for (i=1,j=1;i<n;i++)

16             if (an[i]!=an[i-1])

17                 an[j++] = an[i];

18         for (i=1,k=0;i<j;i++){

19             a[k] = (an[i] - an[i-1])*2;

20             b[k] = an[i] * an[i-1];

21             int t = gcd(a[k],b[k]);

22             a[k] /= t;

23             b[k++] /= t;

24         }

25         BigInteger ans1 = BigInteger.valueOf(a[0]),ans2 = BigInteger.valueOf(b[0]),ans;

26         for (i=1;i<k;i++){

27             ans1 = ans1.gcd(BigInteger.valueOf(a[i]));

28             ans = ans2.multiply(BigInteger.valueOf(b[i]));

29             ans2 = ans.divide(ans2.gcd(BigInteger.valueOf(b[i])));

30         }

31         ans = ans2.gcd(ans1);

32         System.out.println(ans2.divide(ans)+" "+ans1.divide(ans));

33     }

34     public static int gcd(int a,int b){

35         int t;

36         if (a<b){

37             t = a;

38             a = b;

39             b = t;

40         }

41         while(true){

42             if (b==0) break;

43             t = a;

44             a = b;

45             b = t%b;

46         }

47         return a;

48     }

49 }

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