Data Structure and Algorithm [Assignment 2] Sunday, May 01, 2022, 11:59pm Question 1: We are given a Queue data structure that supports standard operations like enqueue() and dequeue(). We need to implement a Stack data structure using only instances of Queue and queue operations allowed on the instances.

Data Structure and Algorithm [Assignment 2] Sunday, May 01, 2022, 11:59pm Question 1: We are given a Queue data structure that supports standard operations like enqueue() and dequeue(). We need to implement a Stack data structure using only instances of Queue and queue operations allowed on the instances.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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10.12 It is possible for one linear structure to be more general than another.(a) Can a Queue be implemented using a Stack? What is the level of complexity of each Queue operation? (b) Can a Stack be implemented using a Queue? What are the various Stack techniques' complexities? 10.13 Explain how we could efficiently build a Queue as a pair of Stacks, known as a "stack pair." (Hint: Consider one of the stacks to be the head of the queue and the other to be the tail.)
Construct a priority queue using a heapordered binary tree, but instead of an array, use a triply linked structure. Each node will require three links: two to go down the tree and one to traverse up the tree. Even if no maximum priority-queue size is specified ahead of time, your solution should ensure logarithmic running time per operation.
X) and POP(S, Y), where S is supposedly a stack and X is the element to be insertedinto S and Y the element deleted from S, are worked upon by the queues that operatetogether as a stack. Assume that the ADT operations of ENQUEUE, DEQUEUE andEMPTYQUEUE are only available for the queues.Demonstrate the working of your method on a list {a, b, c}, which is to beoperated upon as a stack by the queues Q1 and Q2.
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).
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Problem 3: Almost a priority queue. Design a data structure that supports the followingoperations for almost a priority queue:(i) FindSecondSmallest() which returns the second smallest item in the data structure.(ii) Insert(x) which inserts item x to the data structure.(iii) DeleteSecondSmallest() which removes the second smallest item from the datastructure.Your data structure should implement the operation FindSecondSmallest() in O(1), andthe other two operations in O(log n), where n is the number of elements in the datastructure.
12.22 Demonstrate how, in an in-order traversal, the associated stack can beremoved and replaced with a single reference. (Hint: We only need to know thetop of the stack, and the elements below the stack top are determined by thestack top.)12.23 Which other traversals can be rewritten by replacing their Linear structure with a single reference? How does this change impact the complexity ofeach of the iterations?
10.12 There is a possibility that one linear structure is more universal than another.(a) Can a Stack be used to implement a Queue? What is the degree of difficulty of each Queue operation? (b) Can a Queue be used to implement a Stack? What are the complexity of the various Stack techniques? 10.13 Describe how we may efficiently construct a Queue as a pair of Stacks, referred to as a "stack pair." (Hint: Think of one stack as the head of the queue and the other as the tail.) 10.12 There is a possibility that one linear structure is more universal than another.(a) Can a Stack be used to implement a Queue? What is the degree of difficulty of each Queue operation? (b) Can a Queue be used to implement a Stack? What are the complexity of the various Stack techniques? 10.13 Describe how we may efficiently construct a Queue as a pair of Stacks, referred to as a "stack pair." (Hint: Think of one stack as the head of the queue and the other as the tail.) 10.12 There is a possibility that…
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A priority queue is implemented as a linked list, sorted from largest to smallest element. a. How would the definition of PQType change? b. Write the Enqueue operation, using this implementation. c. Write the Dequeue operation, using this implementation. d. Compare the Enqueue and Dequeue operations to those for the heap implementation, in terms of Big-O notation.
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