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





Solution

Using stack operations, insertion at front can be done directly by push operation.

So, AddFront takes:

$O(1)$

But insertion at rear needs moving elements because stack allows insertion only at top.

So, AddRear may require shifting $n$ elements.

Therefore, AddRear takes:

$O(n)$


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