modifying iterative function to be recursive

Question

I have an interative function that takes in a sequence of integers and returns the index position of a target item or returns where the target should be inserted.( if the item is not in the list )

The function works great but I am trying to figure out what is the leanest way to change this function from iterative to recursive implimentation without the aid of any auxilliary functions.

def binary_search(a_list, first, last, target):
    """a sequence of integers, index of first item, index of last item, target to search for """

    while first <= last:
        middle = (first + last) // 2
        if a_list[middle] == target:
            return middle
        if target < a_list[middle]:
            last = middle - 1
        else:
            first = middle + 1
    return first

print(binary_search([2, 5, 8, 11, 17], 0, 4, 5))

Answer 1

How about this:

def binary_search_recursive(a_list, first, last, target):
    middle = (first + last) // 2
    number = a_list[middle]

    if first > last:
        return first
    if number == target:
        return middle
    if target < number:
        return binary_search_recursive(a_list, first, middle-1, target)
    else:
        return binary_search_recursive(a_list, middle+1, last, target)

EDIT : there was a small bug in the code -- now corrected.