Implement Merge Sort

Question

Implement the Merge Sort algorithm to sort a given array of integers.

Codemia · Accepted Answer

To implement Merge Sort, we will use the divide-and-conquer strategy. The array will be divided into two halves, sorted recursively, and then merged back together. This approach ensures that the sorting is done in a systematic way, leading to an efficient algorithm.

Here is a Python implementation of the Merge Sort algorithm:

```python
def merge_sort(arr):
    if len(arr) > 1:
        mid = len(arr) // 2  # Finding the mid of the array
        left_half = arr[:mid]  # Dividing the elements into 2 halves
        right_half = arr[mid:]

merge_sort(left_half)  # Sorting the first half
        merge_sort(right_half)  # Sorting the second half

i = j = k = 0

# Copy data to temp arrays L[] and R[]
        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

# Checking if any element was left
        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

return arr
```

The time complexity of Merge Sort is O(n log n) in all cases (best, average, and worst) due to the consistent division of the array and merging process. The space complexity is O(n) because of the temporary arrays used for merging.

It is important to handle edge cases in our implementation. If the input array is empty or contains only one element, the function should return the array as is, since it is already sorted. This can be easily managed with a base case in the recursive function.

While Merge Sort is efficient for large datasets, it can be optimized for smaller arrays by switching to a simpler sorting algorithm like Insertion Sort. Additionally, for linked lists, a modified version of Merge Sort can be used that avoids the need for extra space.

Implement Merge Sort

J.P. Morgan

What the Interviewer Expects

Key Topics to Cover

How to Approach This

Possible Follow-up Questions

Sharpen Your Skills on Codemia

Sample Answer

Approach

Algorithm

Submit Your Answer

J.P. Morgan Software Engineer II Interview Guide

Related Questions

Binary Search on graph

Count kth largest element in array

Find connected components in string

Merge Three Sorted strings

Binary Search on string