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
;
int a[] = new int
;
int b[] = new int
;
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;
}
}

View Code