Fancy Stack
In this chapter, we discuss the complexity of various operations of a stack which supports a multipop operation.
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We are all aware of the push and pop operations offered by a stack data structure. Both push and pop are trivial and take O(1) or constant time. Now imagine the stack also offers a multipop operation, which allows us to pop k elements at once, assuming the stack holds atleast k elements. If we conduct n operations on the stack, what is the average time complexity of each of the n operations?
Naive Analysis
Consider a sequence of n pop, push, and multipop operations. The maximum number of elements that can accumulate in the stack is also n since the sequence can consist of all push operations. In the worst case, the multipop operation would take O(n) time to pop all the n elements of a stack. So, in general, the time complexity for execution of n operations in the worst case will be:
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