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 10.1, Problem 3E
Program Plan Intro
To model the given queue operations on an initially empty queue Q stored in array Q[1..6] as per figure 10.2 of the textbook.
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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( )
Question A1
(a) Suppose that queue Q is initially empty. The following sequence of queue operations is
executed:
enqueue (5),
dequeue (),
enqueue (1),
enqueue (3),
isEmpty(),
dequeue (),
getRearElement(), dequeue(), enqueue (4).
enqueue (8),
getFrontElement(),
enqueue (6),
dequeue(),
enqueue (9),
enqueue (2),
enqueue (7),
(i) Write down the returned numbers (in order) of the above sequence of queue
operations.
(ii) Write down the values stored in the queue after all the above operations.
(b) Suppose that stack S initially had 5 elements. Then, it executed a total of:
25 push operations
R+5 peek operations
3 empty operations
R+1 stack_size operations
15 pop operations
The mentioned operations were NOT executed in order. After all the operations, it is
found that R of the above pop operations raised Empty error message that were caught and
ignored.
What is the size of S after all these operations? R is the last digit of your student ID. E.g.,
Student ID is 20123453A, then R= 3.
(c) Are…
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?
Chapter 10 Solutions
Introduction to Algorithms
Ch. 10.1 - Prob. 1ECh. 10.1 - Prob. 2ECh. 10.1 - Prob. 3ECh. 10.1 - Prob. 4ECh. 10.1 - Prob. 5ECh. 10.1 - Prob. 6ECh. 10.1 - Prob. 7ECh. 10.2 - Prob. 1ECh. 10.2 - Prob. 2ECh. 10.2 - Prob. 3E
Ch. 10.2 - Prob. 4ECh. 10.2 - Prob. 5ECh. 10.2 - Prob. 6ECh. 10.2 - Prob. 7ECh. 10.2 - Prob. 8ECh. 10.3 - Prob. 1ECh. 10.3 - Prob. 2ECh. 10.3 - Prob. 3ECh. 10.3 - Prob. 4ECh. 10.3 - Prob. 5ECh. 10.4 - Prob. 1ECh. 10.4 - Prob. 2ECh. 10.4 - Prob. 3ECh. 10.4 - Prob. 4ECh. 10.4 - Prob. 5ECh. 10.4 - Prob. 6ECh. 10 - Prob. 1PCh. 10 - Prob. 2PCh. 10 - Prob. 3P
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- 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?arrow_forwardConsider the current elements and its indexes in the queue of size 15: {index[00]=102, index[01]=165, index[02]=115, index[03]=384, index[04]=248, index[05]=111}, draw a table (like shown below) the sequence of elements using the operations listed from number 1 to 26 using the queue approach (A) - in shifting the elements one position forward every time an element is deleted. The following are the description of other operations to be used that would result in a QUEUE that contains the elements. IsTopValue – returns the value at the TOP of the queue. IsRearValue – returns the value at the REAR of the queue. IsTopIndex – returns the index of the value at the TOP of the queue. IsRearIndex – returns the index of the value at the REAR of the queue. IsIndexOf – returns the index of the specific value. IsValueOf – returns the value of the specific index. Insert (Q, 12) Dequeue (Q) Dequeue (Q) Insert (Q, 65) Insert (Q, 100) Insert (Q, 43) Dequeue (Q) IsTopValue (Q) Insert (Q, 61) Dequeue…arrow_forwardChoose two fundamental function signatures used in queue implementation, in which each node keeps an integer data. enqueue(int), dequeue(int, int) dequeue(int), remove (int) enqueue(int), dequeue(int) enqueue(int, int), dequeue(int) enqueue(int), dequeue( )arrow_forward
- Explain An Array-Based Queue (contd.)and write its Pseudo-Codearrow_forwardQ-2 Show the series of operations of operations and their effects on an initially empty Priority Queue. МЕТНODS RETURN VALUES PRIORITY QUEUES CONTENTS 1 insert(9,A) insert(7,B) 3 isEmpty() insert(5,C) 4 5 min() isEmpty() 7 insert(15,D) 8 removeMin() 9 removeMin() 10 min()arrow_forwardDevelop an Algorithm to implement an Enqueue operation in the linear Queue.arrow_forward
- Show the implementation of Linear Queue queue size =5 Enqueue(13) Enqueue(15) Enqueue(18) Enqueue(0) Enqueue(2) Enqueue(3) Dequeue() Enqueue(6) Peek() 1 A B I - E E hp 10 t9 144 inort sc & 67 Po• 8A 91 <- back Harrow_forwardUsing Java Design and implement a RandomQueue. This is an implementation of the Queue interface in which the remove() operation removes an element that is chosen uniformly at random among all the elements currently in the queue. (Think of a RandomQueue as a bag in which we can add elements or reach in and blindly remove some random element.) The add(x) and remove() operations in a RandomQueue should run in constant time per operation.arrow_forwardNote: Use enQueue() and deQueue() functions of queue only.arrow_forward
- 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.arrow_forwardillustrate the queue content after every operation in each of the following sequences. Determine the output of each sequence. assume a circular array representation. q2 = new (queue,4) enqueue(q2, 15) enqueue(q2, 28) print(dequeue(q2)) enqueue(q2, 31) print(peek(q2)) print(dequeue(q2)) print(dequeue(q2)) enqueue(q2, 47) print(peek(q2)) enqueue(q2, 54) print(dequeue(q2)) enqueue(q2, 66) clear(q2) enqueue(q2, 79) print(dequeue(q2))arrow_forwardDesign and implement a RandomQueue. This is an implementation of the Queue interface in which the remove() operation removes an element that is chosen uniformly at random among all the elements currently in the queue. (Think of a RandomQueue as a bag in which we can add elements or reach in and blindly remove some random element.) The add(x) and remove() operations in a RandomQueue should run in constant time per operation.arrow_forward
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