Priority Queue

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  Data Structures and Program Design Using Java

  A Self-Teaching Introduction

  • D. Malhotra, N. Malhotra(Authors)
  • 2020(Publication Date)
  • Mercury Learning and Information

    (Publisher)

  Descending Priority Queue: In this type of Priority Queue, elements can be inserted in any order. But at the time of deletion of elements from the queue, the largest element is searched and deleted first. For example: Operating systems, Routing.

   

  Frequently Asked Questions

  3. Define Priority Queue.

  Ans: A Priority Queue is a collection of elements such that each element has been assigned a priority and such that the order in which elements are deleted and processed comes from the following rules:

  (a) An element of higher priority is processed before any element of lower priority.

  (b) Two elements with same priority are processed according to the order in which they were added to the queue.

  The array elements in a Priority Queue can have the following structure:

  private class Node {

       int priority;

       int data;

       Node next;

       }

  5.5.2.1  Implementation of a Priority Queue

  A Priority Queue can be implemented in two ways:

  1. Array Representation of a Priority Queue
  2. Linked Representation of a Priority Queue

  Let us now discuss both these implementations in detail.

  1. Implementation of a Priority Queue using arrays

  While implementing a Priority Queue using arrays, the following points must be considered:

  • Maintain a separate queue for each level of priority or priority number.
  • Each queue will appear in its own circular array and must have its own pairs of nodes, that is, FRONT AND REAR.
  • If each queue is allocated the same amount of memory, then a 2D array can be used instead of a linear array.

  For example: FRONT [K] and REAR [K] are the nodes containing the front and rear values of row “K” of the queue, where K is the priority number. If we want to insert an element with priority K, then we will add the element at the REAR end of row K; K is the row as well as the priority number of that element. If we add F with priority number 4, then the queue will be given as shown in the following:

  Figure 5.15. Priority Queue after inserting a new element.

  2. Implementation of a Priority Queue using linked lists

  A Priority Queue can be implemented using a linked list. While implementing the Priority Queue using a linked list, every node will have three parts:

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  Data Structures and Program Design Using C++

  • D. Malhotra, N. Malhotra(Authors)
  • 2019(Publication Date)
  • Mercury Learning and Information

    (Publisher)

  Descending Priority Queue – In this type of Priority Queue, elements can be inserted in any order. But at the time of deletion of elements from the queue, the largest element is searched and deleted first. For example – Operating systems, Routing.

  Frequently Asked Questions Q. Define Priority Queue. Answer. A Priority Queue is a collection of elements such that each element has been assigned a priority and such that the order in which elements are deleted and processed comes from the following rules:

  a) An element of higher priority is processed before any element of lower priority.

  b) Two elements with same priority are processed according to the order in which they were added to the queue.

  The array elements in a Priority Queue can have the following structure: struct data { int item ; int priority ; int order ; } ;

  5.5.2.1Implementation of a Priority Queue

  A Priority Queue can be implemented in two ways:

  1. Array Representation of a Priority Queue

  2. Linked Representation of a Priority Queue

  Let us now discuss both these implementations in detail. 1. Implementation of a Priority Queue using arrays While implementing a Priority Queue using arrays, the following points must be considered: •Maintain a separate queue for each level of priority or priority number. •Each queue will appear in its own circular array and must have its own pairs of pointers, that is, FRONT AND REAR. •If each queue is allocated the same amount of memory, then a 2D array can be used instead of a linear array.

  For example – FRONT [K] and REAR [K] are the pointers containing the front and rear values of row “K” of the queue, where K is the priority number. If we want to insert an element with priority K, then we will add the element at the REAR end of row K; K is the row as well as the priority number of that element. If we add F with priority number 4, then the queue will be given as shown in the following:

  FRONT	REAR
  2	2
  1	3
  0	0
  5	1
  4	4

  FIGURE 5.15 Priority Queue after inserting a new element.

  2. Implementation of a Priority Queue using linked lists

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  Beginning Algorithms

  • Simon Harris, James Ross(Authors)
  • 2008(Publication Date)
  • Wrox

    (Publisher)

  172 Chapter 7 8 Priority Queues After studying a broad selection of sorting algorithms in the previous two chapters, you return to investigating data structures in this chapter. A Priority Queue is a special type of queue (see Chapter 4) that provides access to the largest element contained within it. This has many interest- ing applications, some of which you will see later in this book. We waited until we covered the sorting algorithms before discussing Priority Queues because the more complex Priority Queue implementations require you to understand the issues regarding sorting. As an example of when you might use a Priority Queue, imagine a role-playing game in which you are making your way through hostile territory, with threatening characters all around you. Some of these characters are more lethal than others. Being able to quickly identify the largest threat to your health would be a good survival strategy! Notice that it is not necessary to maintain the list of threatening characters in full sorted order. Given that you can have only one fight at a time, all you need to know at any one time is which threat is the largest. By the time you’ve dealt with the biggest one, others may have arrived on the scene, so the sort would have been of little use. This chapter covers the following topics: ❑ Understanding Priority Queues ❑ Creating an unordered list Priority Queue ❑ Creating a sorted list Priority Queue ❑ Understanding a heap and how it works ❑ Creating a heap-ordered list implementation of a Priority Queue ❑ Comparing the different Priority Queue implementations Understanding Priority Queues A Priority Queue is a queue that supports accessing items from the largest to the smallest.

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  Data Structures and Program Design Using Python

  A Self-Teaching Introduction

  • D. Malhotra, N. Malhotra, Dheeraj Malhotra, Neha Malhotra(Authors)
  • 2020(Publication Date)
  • Mercury Learning and Information

    (Publisher)

  Descending Priority Queue – In this type of Priority Queue, elements can be inserted in any order. But at the time of the deletion of elements from the queue, the largest element is searched and deleted first (for example – Operating systems, Routing).

  Frequently Asked Questions

  Q. Define Priority Queue.

  Answer:

  A Priority Queue is a collection of elements such that each element has been assigned a priority and such that the order in which elements are deleted and processed comes from the following rules:

  a.

  An element of higher priority is processed before any element of lower priority.

  b.

  Two elements with the same priority are processed according to the order in which they were added to the queue.

  The array elements in a Priority Queue can have the following structure:

  class ListNode :  def __init__( self, data ) : self.priority=priority self.data = data self.next = None

  5.5.2.1 Implementation of a Priority Queue

  A Priority Queue can be implemented in two ways:

  1. Array Representation of a Priority Queue

  2. Linked Representation of a Priority Queue

  Let us now discuss both these implementations in detail.

  1. Implementation of a Priority Queue using arrays

  While implementing a Priority Queue using arrays, the following points must be considered:

  • Maintain a separate queue for each level of priority or priority number.

  • Each queue will appear in its circular array and must have its pairs of nodes, that is, FRONT AND REAR.

  • If each queue is allocated the same amount of memory, then a 2D array can be used instead of a linear array.

  For Example

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  Big C++

  Late Objects

  • Cay S. Horstmann(Author)
  • 2017(Publication Date)
  • Wiley

    (Publisher)

  553 C H A P T E R 17 Priority QueueS AND HEAPS C H A P T E R G O A L S To become familiar with the Priority Queue data type To understand the implementation and efficiency of the heap data structure To use heaps for implementing Priority Queues and the heapsort algorithm C H A P T E R C O N T E N T S © tomazl/iStockphoto. 17.1 Priority QueueS 554 WE1 Simulating a Queue of Waiting Customers 557 17.2 HEAPS 557 17.3 THE HEAPSORT ALGORITHM 567 554 With a binary search tree, you can efficiently sort a set of elements. Sometimes, you don't need to sort the entire set, but you are just interested in the largest one; for example, the event with the highest priority in a set of events. In this chapter, you will study an ingenious tree structure, called a heap, that lets you efficiently find and remove the largest element. By repeatedly removing the maximum, you can sort a sequence. This is the basis of an efficient sorting algorithm called heapsort. 17.1 Priority Queues A Priority Queue is a container optimized for one special task; quickly locating the element with highest priority. Prioritization is a weaker condition than ordering. In a Priority Queue the order of the remaining elements is irrelevant, it is only the highest priority element that is important. Consider this example, where a Priority Queue contains strings denoting tasks: priority_queue tasks; tasks.push("2 - Shampoo carpets"); tasks.push("9 - Fix overflowing sink"); tasks.push("5 - Order cleaning supplies"); The strings are formatted so that they start with a priority number. When it comes time to do work, we will want to retrieve and remove the task with the top priority: string most_important = tasks.top(); // Returns "9 - Fix overflowing sink" tasks.pop(); The term Priority Queue is actually a misnomer, because the Priority Queue does not have the “first in/first out” behavior as a true queue does. In fact, the interface for the Priority Queue is more similar to a stack than to a queue.

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  Hands-On Data Structures and Algorithms with Python

  • Dr. Basant Agarwal(Author)
  • 2022(Publication Date)
  • Packt Publishing

    (Publisher)

  The Priority Queue stores the data according to the priority associated with the data, so insertion of an element will be at a specific position in the Priority Queue. Priority Queues can be considered as modified queues that return the items in the order of highest priority instead of returning the items in the FIFO order. A Priority Queue can be implemented by modifying an enqueue position by inserting the item according to the priority. It is demonstrated in Figure 7.19, in which given the queue, a new item 5 is added to the queue at a specific index (here assuming that the data items having higher values have higher priority): Figure 7.19: A demonstration of a Priority Queue Let’s understand the Priority Queue with an example. When we receive data elements in an order, the elements are enqueued in the Priority Queue in the order of priority (assuming that the higher data value is of higher importance). Firstly, the Priority Queue is empty, so 3 is added initially in the queue; the next data element is 8, which will be enqueued at the start since it is greater than 3. Next, the data item is 2, then 6, and finally, 10, which are enqueued in the Priority Queue as per their priority, and when the dequeue operation is applied, the high priority item will be dequeued first. All the steps are represented in Figure 7.20 : Figure 7.20: A step-by-step procedure to create a Priority Queue Let us discuss the implementation of a Priority Queue in Python. We first define the node class

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  Objects, Abstraction, Data Structures and Design

  Using C++

  • Elliot B. Koffman, Paul A. T. Wolfgang(Authors)
  • 2012(Publication Date)
  • Wiley

    (Publisher)

  Therefore, a better way to implement a print queue would be to use a Priority Queue. A Priority Queue 8.5 Heaps and Priority Queues 489 is a data structure in which only the highest-priority item is accessible. During inser- tion, the position of an item in the queue is based on its priority relative to the pri- orities of other items in the queue. If a new item has higher priority than all items currently in the queue, it will be placed at the front of the queue and, therefore, will be removed before any of the other items inserted in the queue at an earlier time. This violates the FIFO property of an ordinary queue. E X A M P L E 8 . 7 Figure 8.34 sketches a print queue that at first (top of diagram) contains two docu- ments. We will assume that each document’s priority is inversely proportional to its page count (priority is 1/page_count). The middle queue shows the effect of insert- ing a document 3 pages long. The bottom queue shows the effect of inserting a sec- ond one-page document: It follows the earlier document with that page length. F I G U R E 8 . 3 4 Insertion into a Priority Queue 490 Chapter 8 Trees pages = 1 title = "web page 1" After inserting document with 3 pages After inserting document with 1 page pages = 4 title = "history paper" pages = 1 title = "web page 1" pages = 3 title = "Lab1" pages = 4 title = "history paper" pages = 1 title = "web page 1" pages = 1 title = "receipt" pages = 3 title = "Lab1" pages = 4 title = "history paper" The priority_queue Class C++ provides a priority_queue class that uses the same interface as the queue given in Chapter 6. The differences are in the specification for the top and pop functions. These are defined to return the largest item in the queue rather than the oldest item in the queue. Table 8.5 summarizes the functions of the priority_queue class.

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  eBook - ePub

  Quick Reference to Data Structures and Computer Algorithms, A

  An Insight on the Beauty of Blockchain

  • Divya Joseph, Raji Ramakrishnan Nair, Divya Joseph, Alen Joseph(Authors)
  • 2019(Publication Date)
  • BPB Publications

    (Publisher)

  Here we are taking array for implementing the dequeue. Similarly, as queue it has also 2 operations:

  1.	Add
  2.	Delete

  We maintain 2 pointers LEFT and RIGHT which indicate the left and right position of the dequeue.

  3.9 Priority Queue

  In Priority Queue every element of queue has some priority and based on that priority it will be processed. So, the element of more priority will be processed before the element which has less priority.

  Suppose 2 elements have same priority then in this case FIFO rule will follow, means the element which is at the first place in the queue will be processed first. In computer implementation, Priority Queue is used in the CPU scheduling algorithm, in which CPU has need to process those processes first which have more priority. In Priority Queue, an element can be inserted or deleted not only at the ends but at any position on the queue.

  Here, an element X of priority Pi may be deleted before an element which is at FRONT, similarly, insertion of an element is based on its priority, that is, instead of adding it after the REAR it may be inserted at an intermediate position dictated by its priority value.

  Note: Priority Queue doesn’t strictly follow first-in -first-out (FIFO) principle which is the basic principle of a queue.

  Two operations going on: Insertion and Deletion. There are various ways of implementing the structure of a Priority Queue. These are as follows:

  (i)	Using a simple /circular array
  (ii)	Multi-queue implementations
  (iii)	Using a double linked list, and
  (iv)	Using heap tree

  Linked –list representation of a Priority Queue

  This representation assumes the node structure as the following:

  LLINK and RLINK are two usual link fields DATA is to store the actual content and PRIORITY is to store the priority value of the item. FRONT and REAR are 2 pointers pointing the first and last node in the queue, respectively. Here all the nodes are in sorted order according to the priority values of the items in the nodes. Following is an instance of Priority Queue:

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  A Textbook of Data Structures and Algorithms, Volume 1

  Mastering Linear Data Structures

  • G. A. Vijayalakshmi Pai(Author)
  • 2022(Publication Date)
  • Wiley-ISTE

    (Publisher)

  Additionally, A, B and C login at times 0, 1 and 2, respectively. Figure 5.12 illustrates the simulation of the job scheduler for priority-based job requests. Figure 5.13 shows a snapshot of the Priority Queue at times 4, 8 and (J 6 (6)) (J 3 (2)) Time 5 Time 10 Time 14 B C (J 2 (3)) (J 6 (6)) C A (J 4 (1)) (J 2 (3)) A B Job Queue Queues 123 12. Observe that the processor while scheduling jobs and executing them falls into idle modes during time periods 7–9 and 15–17. Figure 5.12. Simulation of the time-sharing system for priority-based jobs Figure 5.13. Snapshots of the Priority Queue at times 4, 8 and 12 B 3 (2) O 2 (3) O 1 (2) R 2 (1) R 1 (4) At time 4 R O B At time 8 R O B At time 12 R O B B: Batch Processing Queue R: Real Time Queue O: On-line Priority Queue 124 A Textbook of Data Structures and Algorithms 1 Summary – A queue data structure is a linear list in which all insertions are made at the rear end of the list and deletions are made at the front end of the list. – A queue follows the principle of FIFO or FCFS and is commonly implemented using arrays. It therefore calls for the testing of QUEUE_FULL/QUEUE_EMPTY conditions during insert/delete operations, respectively. – A linear queue suffers from the drawback of QUEUE_FULL condition invocation even when the queue in not physically full to its capacity. This limitation is over come to an extent in a circular queue. – Priority Queue is a queue structure in which elements are inserted or deleted from a queue based on some property known as priority. – A deque is a double ended queue with insertions and deletions done at either ends or may be appropriately restricted at one of the two ends. – Job scheduling in time-sharing system environments is an application of queues and Priority Queues. ADT for queues Data objects: A finite set of elements of the same type.

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  Data Structures and Algorithms in Java

  • Michael T. Goodrich, Roberto Tamassia, Michael H. Goldwasser(Authors)
  • 2014(Publication Date)
  • Wiley

    (Publisher)

  . . . . . . . 392 9.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395 360 Chapter 9. Priority Queues 9.1 The Priority Queue Abstract Data Type 9.1.1 Priorities In Chapter 6, we introduced the queue ADT as a collection of objects that are added and removed according to the first-in, first-out (FIFO) principle. A com- pany’s customer call center embodies such a model in which waiting customers are told “calls will be answered in the order that they were received.” In that setting, a new call is added to the back of the queue, and each time a customer service rep- resentative becomes available, he or she is connected with the call that is removed from the front of the call queue. In practice, there are many applications in which a queue-like structure is used to manage objects that must be processed in some way, but for which the first-in, first-out policy does not suffice. Consider, for example, an air-traffic control center that has to decide which flight to clear for landing from among many approaching the airport. This choice may be influenced by factors such as each plane’s distance from the runway, time spent waiting in a holding pattern, or amount of remaining fuel. It is unlikely that the landing decisions are based purely on a FIFO policy. There are other situations in which a “first come, first serve” policy might seem reasonable, yet for which other priorities come into play. To use another airline analogy, suppose a certain flight is fully booked an hour prior to departure. Be- cause of the possibility of cancellations, the airline maintains a queue of standby passengers hoping to get a seat. Although the priority of a standby passenger is influenced by the check-in time of that passenger, other considerations include the fare paid and frequent-flyer status. So it may be that an available seat is given to a passenger who has arrived later than another, if such a passenger is assigned a better priority by the airline agent.

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