Algorithm Complexity Analysis

To find algorithms with the same order of complexity, we need to determine the time complexity for each given operation:

• A. Deletion from Queue: For standard queue implementations (like linked lists or circular arrays), removing an element from the front takes constant time. Complexity: $O(1)$.
• B. Worst case Search in Binary Search Tree (BST): In the worst case, a BST can become unbalanced, resembling a linked list. Searching requires traversing the height of the tree. Complexity: $O(n)$, where $n$ is the number of nodes.
• C. Insertion in Stack: For standard stack implementations (like linked lists or arrays), adding an element to the top takes constant time. Complexity: $O(1)$.
• D. Quick Sort worst Case: The worst-case scenario for Quick Sort occurs with consistently poor pivot choices, leading to skewed partitions. Complexity: $O(n^2)$, where $n$ is the number of elements.

Comparing Complexities

Comparing the determined complexities:

• Deletion from Queue: $O(1)$
• Worst case Search in BST: $O(n)$
• Insertion in Stack: $O(1)$
• Quick Sort worst Case: $O(n^2)$

Algorithms A (Deletion from Queue) and C (Insertion in Stack) both have a time complexity of $O(1)$, meaning they have the same order of complexity.