Fancy Stack
Explore how to analyze the average time complexity of a stack that supports push, pop, and multipop operations using amortized analysis methods. Understand why naive worst-case analysis may give overly pessimistic results and learn the aggregate and accounting methods for more accurate complexity assessment. This lesson equips you to reason about the efficiency of stack operations beyond simple constant time assumptions.
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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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