6. Suppose a circular queue of capacity (n – 1)elements is implemented with an array of nelements. Assume that the insertion anddeletion operation are carried out usingREAR and FRONT as array index variables,respectively. Initially, REAR = FRONT = 0.The conditions to detect queue full andqueue empty are:Full: (REAR+1) mod n ==empty: (FRONT+1) mod n == REARFRONT,Full: (REAR+1) mod n == FRONT,empty: REAR == FRONTFull: (FRONT+1) mod n == REAR,empty: REAR == FRONTFull: REAR == FRONT, empty:(REAR+1) mod n == FRONT

IMP Point About Queue: We use a circular array as a circular queue because We delete from the rear…

Suppose a circular queue of capacity (n – 1) elements is implemented with an array of n elements. Assume that the insertion and deletion operation are carried out using REAR and FRONT as array index variables,

Suppose a circular queue of capacity (n – 1) elements is implemented with an array of n elements. Assume that the insertion and deletion operation are carried out using REAR and FRONT as array index variables,

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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4) Given that a queue is being represented by the following circular representation in an array (front is currently 4 and back is currently 7): array component: 0 1 2 4 5 6 7 8 | | | | 37 | 41 | 12 | 34 | | a) Show what this representation would like after the following sequence of operations are performed: deq(q, i); deq(q, j); enq(q, 81); enq(q, 72); enq(q, 38); deq(q, k); (indicate the current position of front and back for each operation) b) What is an advantage of this implementation of a queue? c) What is a disadvantage of this implementation of a queue?
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.
Use a triply linked structure as opposed to an array for implementing a priority queue using a heapordered binary tree. Each node will require three links: two to move up the tree and one to move down it. Even if the maximum size of the priority queue is unknown at the outset, your solution should nonetheless provide logarithmic running times for each operation.
Starting with an empty Circul Queue, what will be the state of Circular Queue, front, rare, size and number of elements after each of the following operations performed in the order ( i ) enque(A) (ii) enque (B) (iii) enque (C) (iv) dequeue( ) (v) dequeue( ) (vi) enque(D) (vii) enque(E ) (viii) dequeue( )
Problem 1: Consider an array-based queue implementation. Suppose we wish to use an extra bitin queue records to indicate whether a queue is empty.1. Modify the declarations and operations for a circular queue to accommodate this feature.2. Would you expect the change to be worthwhile?Problem 2: Consider an array-based queue implementation. A variant of the circular queuerecords the position of the front element and the length of the queue.1. Is it necessary in this implementation to limit the length of a queue to maxlength - 1?2. Write the five queue operations for this implementation.3. Compare this implementation with the circular queue implementation discussed in class.Problem 3: A dequeue (double-ended queue) is a list from which elements can be inserted ordeleted at either end.1. Develop an array-based implementation for dequeue.2. Develop a pointer-based implementation for dequeue.
Indicate the Big-O rate of growth of run-time for: a) Insertion into a queue that is implemented using and ordinary array with the front of the queue always maintained in component zero of the array. b) Deletion from a queue that is implemented using an ordinary component zero of the array. c) Deletion from a queue using a circular array implementation.
The Min-priority Queue is an abstract data type (ADT) for maintaining a collection of elements,each with an associated value called a key. The ADT supports the following operations:• INSERT(Q,x): insert the element x into the queue Q.• MIN(Q): returns the element of Q with the smallest key.• EXTRACT-MIN (Q): removes and returns the element of Q with the smallest key.Implement in Java the Min-priority Queue ADT defined above using a) an array based binary heap b) a binary search tree. Observe that the ADT implementation operations should be in the form q.insert(x),q.min(), etc. Explain in the report your implementation, noting the running time (using bigOh notation) of each operation in both implementations. c) What are the worst-case running times of the three ADT operations when theunderlying BST is self-balancing? Briefly explain your answer. d) Implement an extension of BST that allows MIN and EXTRACT-MIN operations in O(1). Briefly describe your implementation in the report. Hint:…
Suppose an initially empty queue, Q, has performed a total of 68 enqueue() operations, 20 peek() operations, and 13 dequeue() operations, 5 of which returned null to indicate an empty queue. What is the current size of Q?
Implement 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 traverse down the tree and one to traverse up the tree. Even if no maximum priority-queue size is known ahead of time, your implementation should guarantee logarithmic running time per operation.
Consider the Double ended output restricted Queue implemented as a circular array based queue at the right. How will it look like after following operations have been performed on it in the given order: EnqueueFront(5) EnqueueFront(8) Dequeue() EnqueueRear(6) Dequeue() EnqueueRear(9)
Suppose there are two singly linked lists both of which intersect at some point and become a single linked list. The head or start pointers of both the lists are known, but the intersecting node is unknown. Also, the number of nodes in each of the list before they intersect are unknown and both the list may have it different. List1 may have n nodes before it reaches intersection point and List2 might have m nodes before it reaches intersection point where m and n may be m = n, m > n or m < n. Give an algorithm for finding the merging point. Hints: A brute force approach would be to compare every pointer in one list with every pointer in another list. But in this case the complexity would be O(mn)
A double linked list may be implemented in a workspace array by utilising only one index next. That is, we do not need to retain a distinct field back in the workspace array nodes to detect the backward linkages. The goal is to add a member workspace[current] into workspace[current] rather than the index of the next element on the list. The difference is the index of the next item less the index of the entry preceding current. We must additionally keep two pointers to subsequent nodes in the list, the current index and the prior index of the node right before current in the linked list.To find the next entry of the list, we calculate workspace[current].difference + previous; Similarly, to find the entry preceding previous, we calculate current − workspace[previous].difference;