Question

I have a problem: i need to find an average of the list using this scheme:

First of all, we find an average of two elements, three elements….. len(list) elements and form a new list using averages. The use .pop() and find all averages again. Function should stop when len(list) == 2. Recursion should be used.

Example:
list: [-1, 4, 8, 1]

1 step:

• find an average of [-1, 4], [-1, 4, 8], [-1, 4, 8, 1]
• Then we form a new list: [1.5, 3.66..., 3] (averages)
• Then find averages of new list: [1.5, 3.66...], [1.5, 3.66..., 3]
• Then we form a new list: [2.5833.., 7.222...] (averages)
• When len(list) == 2, find an average of this two elements.

Answer is 2.652777.

What should i write:

jada = []

while True:    
    print 'Lst elements:'    
    a = input()
    if (a == ''):    
        break    
    jada.append(a)

print 'Lst is:' + str(Jada)

def keskmine(Jada):
    for i in range(len(Jada) - 1):
        ...

    jada.pop()
    return keskmine(Jada)

Actually, this is a part of a homework, but i don’t know how to solve it.

Answer 1

In short, you’re finding the “running average” from a list of numbers.

Using recursion would be helpful here. Return the only element when “len(lst) == 1” otherwise, compute the running average and recurse.

There are two parts in this assignment. First, you need to transform lists like [-1, 4, 8, 1] to lists like [1.5, 3.66, 3] (find the running averages). Second, you need to repeat this process with the result of the running averages until your list’s length is 2 (or 1).

You can tackle the first problem (find the running averages) independently from the second. Finding the running average is simple, you first keep track of the running sum (e.g. if the list is [-1, 4, 8, 1] the running sum is [-1, 3, 11, 12]) and divide each elements by their respective running index (i.e. just [1, 2, 3, 4]), to get [-1/1, 3/2, 11/3, 12/4] = [-1, 1.5, 3.66, 3]. Then you can discard the first element to get [1.5, 3.66, 3].

The second problem can be easily solved using recursion. Recursion is just another form of looping, all recursive code can be transformed to a regular for/while-loops code and all looping code can be transformed to recursive code. However, some problems have a tendency towards a more “natural” solution in either recursion or looping. In my opinion, the second problem (repeating the process of taking running averages) is more naturally solved using recursion. Let’s assume you have solved the first problem (of finding the running average) and we have a function runavg(lst) to solve the first problem. We want to write a function which repeatedly find the running average of lst, or return the average when the lst’s length is 2.