Logic Clarification for sorting an array of array in python based off the value of a number using merge sort?

I want to sort an array of array with merge sort based off the last number in each internal array from highest value to lowest value:

arraySample=[['a', 'new', 3], ['a', 'new', 3],  ['b', 'new', 1], ['c', 'old', 2], ['c', 'old', 2], ['d', 'new', 1],['a', 'new', 3],['e', 'old', 3],['e', 'old', 3],['e', 'old', 3]]

In addition , I want to make sure that it is also sorted in a way such that the elements with the same name should still be ordered together .

I.e the 3 elements of 'a' should be ordered together , followed by the 3 elements of 'e' etc..

For now here is the code I have and at the bottom is the output:

Merge

def merge(arr1, arr2, index):
    arr3 = []
    sizeA = len(arr1)
    sizeB = len(arr2)

    indexa = indexb = 0

    while indexa < sizeA and indexb < sizeB:
        if arr1[indexa][index] >= arr2[indexb][index]:
            arr3.append(arr1[indexa])
            indexa += 1
        else:
            arr3.append(arr2[indexb])
            indexb += 1

    arr3.extend(arr1[indexa:sizeA])
    arr3.extend(arr2[indexb:sizeB])
    return arr3

Merge Sort

def mergesort(array, index=-1):
    size = len(array)

    if size == 1:
        return array

    midindex = size // 2
    firsthalf = array[0:midindex]
    secondhalf = array[midindex:size]

    firsthalf = mergesort(firsthalf, index)
    secondhalf = mergesort(secondhalf, index)
    array = merge(firsthalf, secondhalf, index)

    return array
mergesort(arraySample)
for i in arraySample:
    print(str(i)+"\n")

Output

['a', 'new', 3]

['a', 'new', 3]

['b', 'new', 1]

['c', 'old', 2]

['c', 'old', 2]

['d', 'new', 1]

['a', 'new', 3]

['e', 'old', 3]

['e', 'old', 3]

['e', 'old', 3]

However the expected output is:

['a', 'new', 3]

['a', 'new', 3]

['a', 'old', 3]

['e', 'old', 3]

['e', 'new', 3]

['e', 'old', 3] 

['c', 'old', 2]

['c', 'old', 2]

['b', 'new', 1]

['d', 'new', 1]

May I know how could improve or change the code to solve this issue? I am a beginner to Data Structures and Algorithms but I am trying to learn. Please note that I am trying to avoid the usage of external methods and libraries as well as in-built methods. Thank you !

Your code currently uses index to determine how items should be ordered, and you use -1 (the default) for it. But as you want to add the first member (name) into the order logic, you need to pass along more information. It could be a second index (which would be 0), but maybe it is better to pass a key function as argument. Then let that function return a value (a tuple) that determines the order of the given element.

Note that the sorted list is returned by your mergesort function, so the main code should capture that returned list.

Here is your code updated with that idea:

def merge(arr1, arr2, key):  # takes a key argument
    arr3 = []
    sizeA = len(arr1)
    sizeB = len(arr2)

    indexa = indexb = 0

    while indexa < sizeA and indexb < sizeB:
        if key(arr1[indexa]) < key(arr2[indexb]):  # call key to determine order
            arr3.append(arr1[indexa])
            indexa += 1
        else:
            arr3.append(arr2[indexb])
            indexb += 1

    arr3.extend(arr1[indexa:])
    arr3.extend(arr2[indexb:])
    return arr3

def mergesort(array, key):
    size = len(array)

    if size == 1:
        return array

    midindex = size // 2
    firsthalf = array[0:midindex]
    secondhalf = array[midindex:size]

    firsthalf = mergesort(firsthalf, key)
    secondhalf = mergesort(secondhalf, key)
    array = merge(firsthalf, secondhalf, key)

    return array

arraySample=[['a', 'new', 3], ['e', 'old', 3],['a', 'new', 3],  ['b', 'new', 1], ['c', 'old', 2], ['c', 'old', 2], ['d', 'new', 1],['a', 'new', 3],['e', 'old', 3],['e', 'old', 3]]

# Pass a key function:
#    descending by member 2: `-a[2]`
#    ascending by member 0: `a[0]`

result = mergesort(arraySample, lambda a: (-a[2], a[0]))

for elem in result:
    print(elem)