Problem implementing Merge Sort from pseudo code python

Question

Im trying to implement merge sort in Python based on the following pseudo code. I know there are many implementations out there, but I have not been able to find one that followis this pattern with a for loop at the end as opposed to while loop(s). Also, setting the last values in the subarrays to infinity is something I haven't seen in other implementation. NOTE: The following pseudo code has 1 based index i.e. index starts at 1. So I think my biggest issue is getting the indexing right. Right now its just not sorting properly and its really hard to follow with the debugger. My implementation is at the bottom.

Current Output:

Input:  [9, 8, 7, 6, 5, 4, 3, 2, 1, 0]
Merge Sort:  [0, 0, 0, 3, 0, 5, 5, 5, 8, 0]

def merge_sort(arr, p, r):
    if p < r:
        q = (p + (r - 1)) // 2
        merge_sort(arr, p, q)
        merge_sort(arr, q + 1, r)
        merge(arr, p, q, r)

def merge(A, p, q, r):
    n1 = q - p + 1
    n2 = r - q

    L = [0] * (n1 + 1)
    R = [0] * (n2 + 1)

    for i in range(0, n1):
        L[i] = A[p + i]

    for j in range(0, n2):
        R[j] = A[q + 1 + j]

    L[n1] = 10000000 #dont know how to do infinity for integers
    R[n2] = 10000000 #dont know how to do infinity for integers

    i = 0
    j = 0

    for k in range(p, r):
        if L[i] <= R[j]:
            A[k] = L[i]
            i += 1
        else:
            A[k] = R[j]
            j += 1

    return A

Answer 1

First of all you need to make sure if the interval represented by p and r is open or closed at its endpoints. The pseudocode (for loops include last index) establishes that the interval is closed at both endpoints: [p, r].

With last observation in mind you can note that for k in range(p, r): doesn't check last number so the correct line is for k in range(p, r + 1):.

You can represent "infinity" in you problem by using the maximum element of A in the range [p, r] plus one. That will make the job done.

You not need to return the array A because all changes are being done through its reference.

Also, q = (p + (r - 1)) // 2 isn't wrong (because p < r) but correct equation is q = (p + r) // 2 as the interval you want middle integer value of two numbers.