To implement the merge sort algorithm, you can follow these steps:

  1. Divide the unsorted list into two halves until you have sublists that contain only one element. This can be done recursively or iteratively.

  2. Sort each sublist individually. Again, this can be done recursively or iteratively.

  3. Merge the sorted sublists by comparing the elements of each sublist and placing them in the correct order. Start with the smallest elements of each sublist and continue merging until all elements are placed in the correct order.

  Here is an example of how you can implement merge sort algorithm in Python:

  python

  def merge_sort(arr):

   if len(arr) <= 1:

   return arr

   # Divide the list into halves

   mid = len(arr) // 2

   left_half = arr[:mid]

   right_half = arr[mid:]

   # Recursively sort each half

   left_half = merge_sort(left_half)

   right_half = merge_sort(right_half)

   # Merge the sorted halves

   return merge(left_half, right_half)

  def merge(left, right):

   result = []

   i = 0

   j = 0

   # Merge the two halves by comparing the elements

   while i < len(left) and j < len(right):

   if left[i] <= right[j]:

   result.append(left[i])

   i += 1

   else:

   result.append(right[j])

   j += 1

   # Add remaining elements from the left half

   while i < len(left):

   result.append(left[i])

   i += 1

   # Add remaining elements from the right half

   while j < len(right):

   result.append(right[j])

   j += 1

   return result

  This implementation divides the list into halves, recursively sorts the halves, and then merges them back together. It has a time complexity of O(n log n) in all cases.