2. An ordered stack is a data structure that stores a sequence of items and supports the following operations. • OrderedPush(x): removes all items smaller than x from the beginning of the sequence and then adds x to the beginning of the sequence. • Pop: deletes and returns the first item in the sequence (or Null if the sequence is empty). Suppose we implement an ordered stack with a simple linked list, using the obvious OrderedPush and Pop algorithms. Prove that if we start with an empty data structure, the amortized cost of each OrderedPush or Pop operation is O(1).

2. An ordered stack is a data structure that stores a sequence of items and supports the following operations. • OrderedPush(x): removes all items smaller than x from the beginning of the sequence and then adds x to the beginning of the sequence. • Pop: deletes and returns the first item in the sequence (or Null if the sequence is empty). Suppose we implement an ordered stack with a simple linked list, using the obvious OrderedPush and Pop algorithms. Prove that if we start with an empty data structure, the amortized cost of each OrderedPush or Pop operation is O(1).

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter18: Stacks And Queues

Section: Chapter Questions

Problem 21SA

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