generating all possible fractions and determining their ranking may not be the most efficient thing to do considering the input size

try another algorithm

I have implemented the Brute Force Solution, but it Times Out as expected! What is the algorithm for quickly generating the ranking and fetching the desired position? Any help is appreciated!

mmm, recursion!

You bough a Sword (Recursion) to a Fist (Iterative) Fight. But this is really good!

Nice and readable. However, could be easily done in O(1) space without creating a separate resulting array.

Default method signature for Python was:
def reverse() with the missing argument (n).
Please fix this!

Isn't a ceiling function preferred since we are talking about population, where heads should be rounded up instead of down.