如何将不适当的分数转换为 Java 中的带分数？

Question

I'm attempting the ccc j4 or s2 for the 2002 challenge. I currently have a function to simplify the fraction, but it gives it as a mixed number. The output of that function is a string, and I think I need another function to convert it into a mixed number. Any help would be appreciated. Thanks!

This is the function I used for converting:

public static long gcm(long a, long b) {
  return b == 0 ? a : gcm(b, a % b);
}

public static String asFraction(long a, long b) {
  long gcm = gcm(a, b);
  return (a / gcm) + "/" + (b / gcm);
}

It outputs an improper fraction, but I want a mixed number. How can I get this? PS English is not my first language.

Answer 1

Since this is part of a challenge, I'll refrain from providing the exact answer, but what I'd focus on is this: A mixed number is an integer followed by a proper fraction. You have an improper fraction. How do you convert improper fractions to mixed numbers?

Let's take a simple example, say, 11/4 . How would we write this as a mixed fraction? We'd write 2 3/4 , because:

• 2 is the largest integer smaller than 11/4.
• 2 is 8/4, leaving 3/4 for the proper fraction.
• Thus the integer part is 2 and the proper fraction is 3/4 , giving us the answer.

So, given an improper fraction n/d , one way to get a mixed number is to take k = floor[n/d] , and return k + (n - kd)/d .

Hope that helps!