Data Structures: Priority Queues and Binary Heaps, Slides of Data Structures and Algorithms

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Chapter 6

Priority Queues

EE 232 Data Structures Session-05 , Spring-

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Motivations

 Printer Management

 Three jobs are sent to a printer

in the order A, B and C

• Job A --- print a pdf file
• Job B --- print a word document
• Job C --- print the data structure ppt slides

 One job might be particularly

important

 Desirable to allow that job to run

as soon as the printer is

available

front rear

A B^ C

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Motivations…

 Multitasking Operating System

 The scheduler of an operating system decides

which of the several processes to run

 One algorithm of the scheduler uses FCFS queue

• Jobs are initially placed at end of the queue
• The scheduler will repeatedly take the first job on the queue, run it until either it finishes or its time limit is up and place it at the end of the queue if it does not finish

 Interactive programs?

 Processes such as Internet explorer would work?

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Chapter 6: Priority Queues

6.1 Model

6.2 Simple Implementations

6.3 Binary Heap

6.4 Applications of Priority Queues

6.5 d - Heaps

6.6 Leftist Heaps

6.7 Skew Heaps

6.8 Binomial Queues

7/7/2012 Priorty Queues 6-

Chapter 6: Priority Queues

6.1 Model

6.2 Simple Implementations

6.3 Binary Heap

6.4 Applications of Priority Queues

6.5 d - Heaps

6.6 Leftist Heaps

6.7 Skew Heaps

6.8 Binomial Queues

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Model

 Priority queue is a data structure which allows at

least two operations

 Insert

 DeleteMin

• finds, returns and removes the minimum element in the priority queue

DeleteMin Priority Queue Insert

Basic model of a priority queue

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Simple Implementations

 Simple Linked List

 Insert

• at the front in O (1)

 DeleteMin

• traverse list in O ( N ) time

 Sorted Linked List

 Insert

• O ( N )

 DeleteMin

• O (1)

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Simple Implementations…

 Binary Search Tree

 Insert

• O (log N)

 DeleteMin

• O (log N)

 overkill to use BST

• no need for all the BST operations, pointers

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More tree terminology

 Degree of a node

 The degree of a

node n is the number

of its children

 Degree of a tree

 The degree of a tree

is the maximum

degree of any of its

nodes

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More tree terminology…

 A node n in a binary

tree is full if it has

degree two

 A full binary tree of

height h has leaves only

on level h and each of

its internal nodes is full

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Binary Heap

 Like binary search trees, heaps have two properties

 Structure property  Heap order property

 Structure Property

 A binary heap (or a heap) is a complete binary tree

 A complete binary tree of height h has between 2 h

and 2 h +1^ -1 nodes

 height of a complete binary tree is log N  which is O (log N )

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Binary Heap…

 *We are able to store a complete tree as an array

 Simply traverse the array in breadth-first order,

placing the entries into the array

*http://www.ece.uwaterloo.ca/~ece250/

For each depth, starting at zero: visit the nodes in the order from left to right

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Binary Heap…

 *To remove a node while keeping the structure, we

simply remove the last element in the array

*http://www.ece.uwaterloo.ca/~ece250/ docsity.com

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Binary Heap…

 For any element in array

position i

 The left child is in position 2i  The right child is in position 2i+  The parent is in position i/2

 No pointer storage

 Fast computation of 2i and

i/2 by bit shifting

i << 1 = 2i i >> 1 = i/2

A B C D E F G H I J

A

B C

D E F G

H I J