1. Introduction

Merge Sort is a divide-and-conquer algorithm that works by recursively breaking down a list into two halves until each sublist contains a single element, and then merging those sublists in a manner that results into a sorted list.

2. Implementation Steps

1. Divide the unsorted list inton sublists, each containing one element (a list of one element is considered sorted).

2. Repeatedly merge sublists to produce new sorted sublists until there is only one sublist remaining.

3. Implementation in Python

def merge_sort(arr):    # Base condition to exit the recursive call    if len(arr) <= 1:        return arr    # Split the list in half    mid = len(arr) // 2    left_half = arr[:mid]    right_half = arr[mid:]    # Recursively sort both halves    left_half = merge_sort(left_half)    right_half = merge_sort(right_half)    # Merge the sorted halves    merged = []    i = 0    j = 0    while i < len(left_half) and j < len(right_half):        if left_half[i] < right_half[j]:            merged.append(left_half[i])            i += 1        else:            merged.append(right_half[j])            j += 1    while i < len(left_half):        merged.append(left_half[i])        i += 1    while j < len(right_half):        merged.append(right_half[j])        j += 1    return mergedarr = [38, 27, 43, 3, 9, 82, 10]sorted_arr = merge_sort(arr)print(sorted_arr)

Output:

[3, 9, 10, 27, 38, 43, 82]

Explanation:

1. The functionmerge_sort starts by checking if the length ofarr is less than or equal to 1. If it is, the list is already sorted, and we return it as-is.

2. We then split the list into two halves using the middle index. These halves areleft_half andright_half.

3. We recursively sort both halves by callingmerge_sort on them.

4. Once both halves are sorted, we merge them together in sorted order. We use two pointersi andj to track our position in theleft_half andright_half, respectively.

5. We compare the current elements ofleft_half andright_half, append the smaller element to themerged list, and move the pointer of that half forward.

6. After one of the halves is exhausted, we append the remaining elements of the other half tomerged.

7. Finally, the merged sorted list is returned.

Related Algorithms in Python