Top Merge Sort Interview Questions and Answers

Merge sort is a popular divide-and-conquer sorting algorithm that has numerous advantages, making it a common topic in technical interviews. In this article, we’ll explore some of the most frequently asked merge sort interview questions and provide detailed explanations to help you ace your next coding interview.

1. What is Merge Sort?

Merge sort is a efficient sorting algorithm that follows the divide-and-conquer approach. It works by recursively dividing the input array into two halves until each subarray contains only one element. Then, it merges these subarrays in a sorted manner to produce the final sorted array.

The algorithm can be broken down into three steps:

Divide: Divide the unsorted array into two halves recursively until each subarray contains only one element.
Conquer: Sort each subarray by treating it as an array of size one (already sorted).
Combine: Merge the sorted subarrays back together to form a single sorted array.

2. Is Merge Sort an In-Place Algorithm?

No, merge sort is not an in-place algorithm. During the “merge” step, an additional array is required to store the merged elements from the sorted subarrays. This extra space requirement makes merge sort not an in-place algorithm.

3. Is Merge Sort a Stable Sorting Algorithm?

Yes, merge sort is a stable sorting algorithm. A stable sorting algorithm maintains the relative order of equal elements in the input array. In other words, if two elements have the same value, their order in the sorted output will be the same as in the input array.

4. What is the Time Complexity of Merge Sort?

The time complexity of merge sort is O(n log n) in all cases (best, average, and worst), where n is the number of elements in the input array. This is because the algorithm divides the input array in half at every level of recursion, resulting in log n levels, and merges the subarrays in linear time, O(n).

5. What is the Space Complexity of Merge Sort?

The space complexity of merge sort is O(n), where n is the number of elements in the input array. This is because the algorithm requires an additional array of the same size as the input array to store the merged elements during the “combine” step.

6. When is Merge Sort Preferred Over Other Sorting Algorithms?

Merge sort is preferred in the following scenarios:

When the input data is large and can fit in memory, as merge sort has a time complexity of O(n log n) in all cases.
When the input data needs to be sorted stably, as merge sort is a stable sorting algorithm.
When the input data is stored in external storage (e.g., hard disk), as merge sort can be easily adapted for external sorting.

7. How Can Merge Sort Be Optimized?

One way to optimize merge sort is by using insertion sort for small subarrays. When the subarray size falls below a certain threshold (typically around 10-15 elements), insertion sort can be used instead of recursively dividing and merging. This hybrid approach combines the advantages of both algorithms and can improve performance for certain input distributions.

8. Can Merge Sort Be Used for Linked Lists?

Yes, merge sort can be adapted to work with linked lists. However, since linked lists do not allow random access, the algorithm needs to be modified slightly. Instead of dividing the list into halves, we use a slow and fast pointer technique to find the middle of the list. Then, we recursively sort the two halves and merge them back together.

9. What is the Worst-Case Scenario for Merge Sort?

The worst-case scenario for merge sort occurs when the input array is already sorted in reverse order. In this case, the algorithm still needs to perform the full divide-and-conquer process, resulting in the maximum number of comparisons and merge operations.

10. How Does Merge Sort Handle Duplicate Elements?

Merge sort can handle duplicate elements naturally, as it is a stable sorting algorithm. During the merge step, if two elements are equal, the algorithm preserves their relative order from the input array in the sorted output.

These are just a few examples of the types of questions you might encounter in a merge sort interview. By understanding the algorithm’s fundamentals, time and space complexities, advantages, and disadvantages, you’ll be well-prepared to tackle any merge sort-related questions that come your way.

Algorithms: Merge Sort

FAQ

How do you explain merge sort in an interview?

Merge sort is defined as a sorting algorithm that works by dividing an array into smaller subarrays, sorting each subarray, and then merging the sorted subarrays back together to form the final sorted array.

How do you solve merge sort questions?

If we observe from the above visualization, divide and conquer idea of merge sort will go like this: Divide: We divide the problem of size n into two equal sub-problems of size n/2 by calculating the mid-index. Subproblem 1: Sorting array A[] from l to mid. Subproblem 2: Sorting array A[] from mid + 1 to r.

What is the best scenario for merge sort?

with the best-case happening when the largest element of one sorted sub-list is smaller than the first element of its opposing sub-list, for every merge step that occurs. Only one element from the opposing list is compared, which reduces the number of comparisons in each merge step to N/2.

What makes merge sort faster?

Merge sort is faster in this situation because it reads the data sequentially. Data insertion in any part of the linked list is also very efficient if we are given the reference to the previous node so that the merge operation can be implemented in-place.