#recursion #datastructures #devstudy #average #sum

The goal is to find the average of an array of integers using recursion.

This is what I have from last attempt found here: https://write.as/effyverse/recursion-101

Attempt 1:

def average(arr)
count = arr.count
if count == 1
arr[0..count-1].sum/count
else
average(arr[0..count-2].sum / (count-1)) * arr[count-1]
end
end

a = [1,2,3,4,5]
p average(a) == 3

b = [0,10]
p average(b) == 5

c = [1]
p average(c) == 1

Mistakes made:

__Implementation Errors:
– I am calling my recursion function with the wrong input. Instead of passing in an array, I am passing in the average, fully computed.

__Understanding Errors:

• I originally thought that my next-to-last case is represented by arr[0..count-2].sum. This is wrong because my next-to-last case is actually the ARRAY object of arr[0..count-2] and NOT the sum of it. The sum aspect is a part of the function, not the input case. It makes no sense to view the input as a sum when the method input is the array of integers — this confusion of what my input cases are supposed to be informed the implementation error above.

• I originally thought that my base case would be the last input to be computed by the recursive function instead of thinking of it as the END of the recursive call, as the case where the recursion call is no longer needed.

Attempt 2:

Find average of array of numbers using recursion

def average(arr)
count = arr.count
if count == 0
0
elsif count == 1
arr[0]
else
sum_of_all_num = average(arr[0..count-2]) * (count-1) + arr[count-1]
avg = sum_of_all_num / count
end
end

p average([1]) == 1
p average([0,10]) == 5
p average([1,3,5,7]) == 4

Explanation of thought process for recursion call:

What is our function?
average = arr.sum / arr.count

What does this tell us?
arr.sum = average * arr.count

What do we know?
– If we remove the last case from our average function input and express it outside of the recursive function call, we have:
sum_excl_last_num = average(arr[0..count-2]) * (count-1)

• remembering that our goal is to find the average of all num so we need:
  sum_of_all_num = sum_excl_last_num + arr[count-1]

• calculate average:
  avg = sum_of_all_num / count

• refactor:
  sum_of_all_num = average(arr[0..count-2]) * (count-1) + arr[count-1]
avg = sum_of_all_num / count