Map each list value to its corresponding percentile

Question

I\'d like to create a function that takes a (sorted) list as its argument and outputs a list containing each element\'s corresponding percentile.

For example,

Answer 1

In terms of complexity, I think reptilicus's answer is not optimal. It takes O(n^2) time.

Here is a solution that takes O(n log n) time.

def list_to_percentiles(numbers):
    pairs = zip(numbers, range(len(numbers)))
    pairs.sort(key=lambda p: p[0])
    result = [0 for i in range(len(numbers))]
    for rank in xrange(len(numbers)):
        original_index = pairs[rank][1]
        result[original_index] = rank * 100.0 / (len(numbers)-1)
    return result

I'm not sure, but I think this is the optimal time complexity you can get. The rough reason I think it's optimal is because the information of all of the percentiles is essentially equivalent to the information of the sorted list, and you can't get better than O(n log n) for sorting.

EDIT: Depending on your definition of "percentile" this may not always give the correct result. See BrenBarn's answer for more explanation and for a better solution which makes use of scipy/numpy.