A double-ended queue (dequeue) supports adding and removing items from both the ends of the queue. The operations supported by dequeue are AddFront(adding item to the front of the queue), AddRear(adding item to the rear of the queue), RemoveFront (removing item from the front of the queue), and RemoveRear (removing item from the rear of the queue). You are given only stacks to implement this data structure. You can implement only push and pop operations. What’s the time complexity of performing AddFront() and AddRear(), assuming m is the size of the stack and n is the number of elements?

Correct option is B

For a deque implemented using two stacks, the AddFront() operation takes constant time O(1) as it directly pushes the element onto a stack. However, AddRear() involves transferring elements between stacks to maintain the correct order, resulting in a time complexity of O(n) in the worst case, where n is the number of elements in the deque.
Information Booster
1. Understanding Deque Operations:
· AddFront(): Adding an element to the front involves a simple push operation on the first stack. This operation is efficient and takes O(1) time.
· AddRear(): To add an element to the rear, elements need to be transferred between the two stacks to maintain the deque order. This transfer involves n pop and push operations, resulting in O(n) time complexity.
2. Steps for AddRear():
· Transfer all elements from Stack 1 to Stack 2 (requires n operations).
· Push the new element onto Stack 1.
· Transfer all elements back to Stack 1 from Stack 2 (requires n operations again in the worst case).
3. Explanation of Complexities:
· O(1) for AddFront() since it directly pushes the element onto Stack 1 without needing element transfers.
· O(n) for AddRear() due to the reordering process.
4. Other Operations:
· RemoveFront(): Similar to AddFront(), it involves operations only on Stack 1, taking O(1).
· RemoveRear(): Similar to AddRear(), it involves transferring elements between stacks, taking O(n).
Additional Knowledge
· Stacks in Deque Implementation: Two stacks simulate a deque by dividing responsibilities (Stack 1 for the front, Stack 2 for the rear).
· The efficiency of deque operations using stacks depends on minimizing element transfers.
· Real-world scenarios often optimize deque implementations to avoid excessive O(n) operations.