Merge Sort I

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Unit 7 Session 2 (Click for link to problem statements)

Problem Highlights

• 💡 Difficulty: Medium
• ⏰ Time to complete: 25 mins
• 🛠️ Topics: Divide and Conquer, Recursion, Sorting Algorithms

1: U-nderstand

Understand what the interviewer is asking for by using test cases and questions about the problem.

• Established a set (2-3) of test cases to verify their own solution later.
• Established a set (1-2) of edge cases to verify their solution handles complexities.
• Have fully understood the problem and have no clarifying questions.
• Have you verified any Time/Space Constraints for this problem?

• Q: What is the behavior of the merge sort algorithm when dealing with duplicate values?
  • A: Merge sort should handle duplicates without any issues, as it will retain their order relative to each other, ensuring stability.

HAPPY CASE
Input: [5,3,8,6,2,7,1,4]
Output: [1,2,3,4,5,6,7,8]
Explanation: The list is sorted in ascending order.

EDGE CASE
Input: [1,1,1,1]
Output: [1,1,1,1]
Explanation: The merge sort should handle arrays of identical elements without changing their order.

2: M-atch

Match what this problem looks like to known categories of problems, e.g. Linked List or Dynamic Programming, and strategies or patterns in those categories.

This problem is a classic example of the divide and conquer technique:

• Using recursion to divide the problem into smaller parts, sort each part, and then merge them back together.

3: P-lan

Plan the solution with appropriate visualizations and pseudocode.

General Idea: Implement the merge sort algorithm, which involves recursively splitting the list into halves until the sublists are trivially sorted (one element), then merge these sorted lists back into a complete sorted list.

1) If the list length is 0 or 1, it is already sorted, so return it.
2) Split the list into two halves.
3) Recursively apply merge sort to both halves.
4) Merge the two sorted halves into a single sorted list using the merge function.
5) Return the merged and sorted list.

⚠️ Common Mistakes

• Not correctly merging the two halves can lead to unsorted segments or missing elements.
• Failing to handle edge cases like empty lists or lists with one element.

4: I-mplement

Implement the code to solve the algorithm.

def merge_sort(lst):
    if len(lst) <= 1:
        return arr
    
    mid = len(arr) // 2
    left_half = arr[:mid]
    right_half = arr[mid:]
    
    # Recursive calls to merge_sort for sorting the left and right halves
    left_half = merge_sort(left_half)
    right_half = merge_sort(right_half)
    
    return merge(left_half, right_half)
    
def merge(left, right):
    result = [] 
    i = j = 0  
    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
    while i < len(left):
        result.append(left[i])
        i += 1
    while j < len(right):
        result.append(right[j])
        j += 1
    
    return result

5: R-eview

Review the code by running specific example(s) and recording values (watchlist) of your code's variables along the way.

• Test with input [5,3,8,6,2,7,1,4] to ensure it sorts correctly to [1,2,3,4,5,6,7,8].
• Check with an array of identical elements [1,1,1,1] to confirm correct handling.

6: E-valuate

Evaluate the performance of your algorithm and state any strong/weak or future potential work.

• Time Complexity: O(n log n) which is typical for merge sort due to the log-linear complexity of dividing and merging.
• Space Complexity: O(n) due to the space required for storing the temporary subarrays during the merge process.