Sums of Parts Python 3

Question

Let us consider this example (array written in general format):

ls = [0, 1, 3, 6, 10]

Its following parts:

ls = [0, 1, 3, 6, 10]
ls = [1, 3, 6, 10]
ls = [3, 6, 10]
ls = [6, 10]
ls = [10]
ls = []

The corresponding sums are (put together in a list): [20, 20, 19, 16, 10, 0]

The function parts_sums (or its variants in other languages) will take as parameter a list ls and return a list of the sums of its parts as defined above.

I have tried like this but is not executed in given Execution Time.How can I speed up this code:

def parts_sums(ls):
    sums=[]
    if len(ls)==0:
        return[0]
    else:
        while len(ls)!=0:
            sums.append(sum(ls))
            ls.pop(0)
        sums.append(0)
        return sums

Answer 1

Here's an iterative, O(n) solution.

def parts_sums(ls):
    sums = [0] * (len(ls) + 1)
    for i, e in enumerate(reversed(ls)):
        sums[len(ls) - i - 1] += sums[len(ls) - i] + e
    return sums