Lecture 114:-In-Place Merge Sort

In-place merge sort is a variant of the merge sort algorithm that aims to use a minimal amount of additional memory space. While the standard merge sort typically requires additional space proportional to the size of the input array, in-place merge sort attempts to sort the array using only a constant amount of extra space.

The main challenge with achieving an in-place merge is that the standard merge step involves copying elements from two separate subarrays into a temporary buffer, and then merging them back into the original array. To perform an in-place merge, you need to find a way to merge the subarrays directly within the original array, without using additional memory.

One common technique used to achieve in-place merging is the "Two-Pointers" approach. Here's a general outline of the in-place merge sort algorithm using this approach:

Divide: Divide the array into two halves.

Recursively Sort: Recursively sort the two halves using in-place merge sort.

Merge In-Place: Implement an in-place merge step to merge the two sorted halves back into the original array.

Here's a simplified version of the in-place merge function:

pythonCopy code

def merge(arr, left, mid, right): left_end = mid right_start = mid + 1 while left <= left_end and right_start <= right: if arr[left] <= arr[right_start]: left += 1 else: temp = arr[right_start] index = right_start while index != left: arr[index] = arr[index - 1] index -= 1 arr[left] = temp left += 1 left_end += 1 right_start += 1 def in_place_merge_sort(arr, left, right): if left < right: mid = (left + right) // 2 in_place_merge_sort(arr, left, mid) in_place_merge_sort(arr, mid + 1, right) merge(arr, left, mid, right) # Example usage arr = [8, 4, 2, 1, 6, 3, 7, 5] in_place_merge_sort(arr, 0, len(arr) - 1) print(arr) # Output: [1, 2, 3, 4, 5, 6, 7, 8]

In this example, the merge function is modified to perform an in-place merge of two subarrays within the original array. The in_place_merge_sort function sorts the array using the in-place merge approach.

It's important to note that achieving a fully in-place merge sort that uses no additional memory at all can be quite complex and may involve more intricate techniques. The version presented here is a simplified illustration of the concept.