Merge Sort II

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

Problem Highlights

• 💡 Difficulty: Medium
• ⏰ Time to complete: 20 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: How should merge() handle arrays of different lengths?
  • A: merge() should be able to merge two sublists of different lengths seamlessly, adding remaining elements from the longer sublist once comparisons are complete.

HAPPY CASE
Input: left = [1,3,5], right = [2,4,6]
Output: [1,2,3,4,5,6]
Explanation: The sublists are merged into a single sorted list.

EDGE CASE
Input: left = [1,2,3], right = []
Output: [1,2,3]
Explanation: Since one of the sublists is empty, the merge simply returns the non-empty sublist.

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 foundational component of the merge sort algorithm:

• Understanding how to merge two sorted lists is essential for implementing the full merge sort algorithm.

3: P-lan

Plan the solution with appropriate visualizations and pseudocode.

General Idea: Develop a function merge() that combines two sorted sublists into one sorted list.

1) Initialize an empty list `result`.
2) Use two pointers to track the current index of each sublist (`i` for `left`, `j` for `right`).
3) Compare elements from both sublists and append the smaller one to `result`.
4) If one sublist is exhausted, append the remainder of the other sublist to `result`.
5) Return the `result` list.

⚠️ Common Mistakes

• Not handling the remaining elements in one of the sublists after the main comparisons are done.
• Failing to maintain the order when merging, leading to an incorrectly sorted result.

4: I-mplement

Implement the code to solve the algorithm.

def merge(left, right):
    i, j = 0, 0
    result = []
    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
    result.extend(left[i:])  # Append remaining elements from left if any
    result.extend(right[j:])  # Append remaining elements from right if any
    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 the function with inputs [1,3,5] and [2,4,6] to ensure it merges correctly to [1,2,3,4,5,6].
• Check with one empty input [1,2,3] and [] to confirm it returns [1,2,3].

6: E-valuate

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

• Time Complexity: O(n + m) where n and m are the lengths of the two sublists, since every element in each list is processed once.
• Space Complexity: O(n + m) for the space needed to hold the result list.