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Merge Sort I
Unit 7 Session 2 (Click for link to problem statements)
- 💡 Difficulty: Medium
- ⏰ Time to complete: 25 mins
- 🛠️ Topics: Divide and Conquer, Recursion, Sorting Algorithms
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.
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.
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.
- 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.
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
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.
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.