Introduction to Algorithms
Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 17.2, Problem 1E
Program Plan Intro

To show that the cost of n stack operations including copying the stack is O(n) by assigning the suitable amortized costs to the various stack operations.

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S1 and S2 are two sorted stacks of n and m numbers, with the top elements of each stack pointing to the smallest number in their list. To ensure that all of the components in stacks S1 and S2 are available in MERGE in decreasing order, with the largest element at the top, create a stack MERGE that combines the items in stacks S1 and S2.Remember that there are (n + m) components in the stack MERGE.
multiple choice: consider an array based implementation of a stack and its push operation. Beginning with an array of length 1 = (2^0), consider where the array’s length will be doubled whenever an insertion(via the push operation) is attempted when the array is full. What is the amortized complexity of performing a sequence of n push operations. a) Θ(log n) b) Θ(n) c) Θ(n^2) d) Θ(1)
a. Propose a data structure that supports the stack push and pop operations and a third operation FindMin, which returns the smallest element in the data structure, all in O(1) worst case time.   b. Prove that if we add the fourth operation DeleteMin which finds and removes the smallest element, then at least one of the operations must take Ω(log n) time.
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