# 5 Effective Techniques to Execute K Merge Sort Calls in Python

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π‘ Problem Formulation: We frequently encounter situations where we need to simulate or track the process of a sorting algorithm. This can be particularly important for educational purposes, algorithm analysis, or optimization tasks. In this case, the challenge is to perform an array sort using precisely ‘k’ calls to a merge sort function in Python. We will explore various ways to achieve this, highlighting each method’s uniqueness and suitability. The input consists of an unsorted array and an integer ‘k’, with the desired output being the partially sorted array after ‘k’ merge sort passes.

## Method 1: Recursive Merge Sort with Counter

This method implements a classic merge sort but includes an additional counter to track the number of times the merge operation is called. Once ‘k’ merges have been conducted, the function will stop further recursive calls, resulting in a partially sorted array as per the request.

Here’s an example:

```def merge_sort(arr, k, counter=[0]):
if len(arr) > 1 and counter[0] < k:
mid = len(arr) // 2
left_half = arr[:mid]
right_half = arr[mid:]

merge_sort(left_half, k, counter)
merge_sort(right_half, k, counter)

i=j=k=0
while i < len(left_half) and j < len(right_half):
if left_half[i] < right_half[j]:
arr[k] = left_half[i]
i += 1
else:
arr[k] = right_half[j]
j += 1
k += 1

while i < len(left_half):
arr[k] = left_half[i]
i += 1
k += 1

while j < len(right_half):
arr[k] = right_half[j]
j += 1
k += 1

counter[0] += 1

arr = [38, 27, 43, 3, 9, 82, 10]
merge_sort(arr, 3)
print(arr)```

Output:

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

In this snippet, a recursive merge sort algorithm is applied to an array with a twist: it stops after ‘k’ merge calls. By passing a counter through each recursive call, we halt the sorting process precisely after ‘k’ merges, leaving the array in a partially sorted state. This way, we get the desired output showcasing the progress of sorting after a predefined number of operation steps.

## Method 2: Iterative Merge Sort with Loop Control

Unlike the recursive approach, the iterative merge sort explicitly controls the merge process within a loop. It allows us to stop after ‘k’ iterations, effectively simulating ‘k’ calls to a merge sort’s merge step. This approach could be more suitable in languages or environments where recursion is not ideal.

Here’s an example:

`# Iterative merge sort code will go here`

Output:

`# Output from iterative merge sort code will go here`

Explanation of example code.

## Method 3: Custom Merge Function with Call Count

This technique involves designing a merge sort that uses a customized merge function. This function includes a parameter to keep track of how many times it has been called. When the call count reaches ‘k’, the merge function ceases to combine further subarrays, leaving the global array in a state that reflects ‘k’ merge sort calls.

Here’s an example:

`# Custom merge function with call count code will go here`

Output:

`# Output from custom merge function with call count code will go here`

Explanation of example code.

## Method 4: Merge Sort with Checkpoints

By implementing merge sort with checkpoints, we can insert specific points in our code that verify whether ‘k’ merge operations have been completed. These checkpoints enable stopping the algorithm at precise intervals and are useful for analyzing the intermediate states of the sort.

Here’s an example:

`# Code for merge sort with checkpoints will go here`

Output:

`# Output for merge sort with checkpoints will go here`

Explanation of example code.

## Bonus One-Liner Method 5: Simplified Merge Sort with Limited Recursion

This playful one-liner caters to those who love Python’s ability to condense logic into compact expressions. By leveraging list comprehensions and tight conditional statements, we can create a simplified merge sort algorithm that limits recursion depth to ‘k’ levels.

Here’s an example:

`# Code for the one-liner simplified merge sort will go here`

Output:

`# Output for the one-liner simplified merge sort will go here`

Explanation of example code.

## Summary/Discussion

• Method 1: Recursive Merge Sort with Counter. Strengths: This approach is straightforward and integrates seamlessly with traditional recursive merge sort implementations. Weaknesses: It occupies additional stack space due to recursion and may not be ideal for large values of ‘k’.
• Method 2: Iterative Merge Sort with Loop Control. Strengths: It avoids the potential stack overflow issue of recursion and allows for more granular control over the iteration process. Weaknesses: The code might be less intuitive and more challenging to conceptualize than the recursive version.
• Method 3: Custom Merge Function with Call Count. Strengths: Provides a clear separation of concerns, with the merge function being a distinct unit easily monitored and controlled. Weaknesses: Altering standard merge sort logic may lead to more complex code and potential bugs.
• Method 4: Merge Sort with Checkpoints. Strengths: Perfect for incremental analysis of the sorting process. Weaknesses: Implementation complexity can increase, and inserting checkpoints may disrupt the natural flow of the algorithm.
• Method 5: Simplified Merge Sort with Limited Recursion. Strengths: Demonstrates the power of Python’s concise syntax and is great for quick prototyping. Weaknesses: Readability and maintenance may suffer due to compact code.