Question

Arrange the following time complexities in increasing order.
(A). Bubble sort (worst case)
(B). Deleting head node in singly linked list
(C). Binary search
(D). Worst case of merge sort

• A. (A), (B), (C), (D)
• B. (B), (C), (D), (A)
• C. (B), (C), (A), (D)
• D. (C), (B), (D), (A)

Hint:

In general, the time complexity of sorting algorithms like merge sort and bubble sort is $O(n \log n)$ and $O(n^2)$ respectively.

Answer 1

The Correct Option is D

Step 1: Determine Time Complexities.
- Bubble Sort (Worst Case) (A): Time complexity is $O(n^2)$.
- Singly Linked List Head Deletion (B): Time complexity is $O(1)$.
- Binary Search (C): Time complexity is $O(\log n)$.
- Merge Sort (Worst Case) (D): Time complexity is $O(n \log n)$.

Step 2: Order by Time Complexity (Ascending).
The correct order from lowest to highest is: - (B) Deleting head node: $O(1)$ - (C) Binary search: $O(\log n)$ - (D) Merge sort: $O(n \log n)$ - (A) Bubble sort (worst case): $O(n^2)$

Step 3: Final Order.
The correct sequence is (B), (C), (D), (A).