Priority Queue

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• Advance Java with Data Structures and Beyond

24 pt

• Lecture 16
• Priority Queues-I

20 pt
20 pt
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Learn applications of Stacks and Queues
How to Implement Stack using Singly Linked List
What are Operations on Linked Queue
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Lecture Objectives

• By the end of this class, you will be able to

• Gain an understanding of the concept and
  importance of priority queues in data structures.
• Explore various methods and data structures for
  implementing priority queues.
• Introduce the concept of heaps and their role in
  priority queue implementations.
• Learn about complete binary trees and how they
  are used to implement priority queues efficiently.

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Priority queue and its characteristics
Heap and types of heap
Complete and full Binary Tree
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• Priority queue

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• A priority queue is an abstract data type that
  behaves similarly to the normal queue except that
  each element has some priority, i.e., the element
  with the highest priority would come first in a
  priority queue.

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Characteristics of a Priority Queue

• Every element in a priority queue has some
  priority associated with it.

• An element with a higher priority will be deleted
  before the deletion of the lesser priority.

• If two elements in a priority queue have the same
  priority, they will be arranged using the FIFO
  principle.

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Types of Priority Queue

• Ascending order priority queue
• In an ascending order priority queue, a lower
  priority number is given as a higher priority
  priority.

• Descending order priority queue
• In descending order priority queue, a higher
  priority number is given as a higher priority in
  a priority.

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Priority queue and its characteristics
Heap and types of heap
Complete and full Binary Tree
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• Heap

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Capturing and Non-capturing Groups

• A heap is a tree-based data structure that forms
  a complete binary tree and satisfies the heap
  property.
• If A is a parent node of B, then A is ordered
  concerning the node B for all nodes A and B in a
  heap.
• It means that the value of the parent node could
  be more than or equal to the value of the child
  node, or the value of the parent node could be
  less than or equal to the value of the child
  node.

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• Types of Heaps

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Max heap

• The max heap is a heap in which the value of the
  parent node is greater than the value of the
  child nodes.
• In Java, a max heap can be implemented using the
  PriorityQueue class from java.util package. The
  PriorityQueue class is a priority queue that
  provides a way to store elements in a queue-like
  data structure in which each element has a
  priority associated with it.
• Syntax PriorityQueue maxHeap new
  PriorityQueueltgt(Comparator.reverseOrder())

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Min heap

• The min heap is a heap in which the value of the
  parent node is less than the value of the child
  nodes.
• In Java, a min heap can be implemented using the
  PriorityQueue class from java.util package. The
  PriorityQueue class is a priority queue that
  provides a way to store elements in a queue-like
  data structure in which each element has a
  priority associated with it.
• Syntax PriorityQueueltIntegergt minHeap new
  PriorityQueueltIntegergt()

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Priority queue and its characteristics
Heap and types of heap
Complete and full Binary Tree
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• Priority Queue Operations

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Inserting the element in a priority queue (max
heap)

• If we insert an element in a priority queue, it
  will move to the empty slot by looking from top
  to bottom and left to right.
• If the element is not in a correct place then it
  is compared with the parent node if it is found
  out of order, elements are swapped. This process
  continues until the element is placed in the
  correct position.

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2. Removing the minimum element from

the priority queue

• As we know in a max heap, the maximum element is
  the root node. When we remove the root node, it
  creates an empty slot.
• The last inserted element will be added to this
  empty slot. Then, this element is compared with
  the child nodes, i.e., left-child and
  right-child, and swapped with the smaller of the
  two. It keeps moving down the tree until the heap
  property is restored.

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• Complete Binary Tree

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Complete Binary Tree

• A complete binary tree is a binary tree in which
  all the levels are completely filled except
  possibly the lowest one, which is filled from the
  left.
• A complete binary tree is just like a full binary
  tree, but with two major differences
• All the leaf elements must lean towards the left.
• The last leaf element might not have a right
  sibling i.e. a complete binary tree doesn't have
  to be a full binary tree.

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Terminology of Complete Binary Tree

• Root Node in which no edge is coming from the
  parent. For example, node A

• Child The node having some incoming edge is
  called the child. For example, nodes B, and F
  are the child of A and C respectively.

• Sibling Nodes having the same parent are
  siblings. For example, D and E are siblings as
  they have the same parent B.

• Degree of a node Number of children of a
  particular parent. For example- The degree of A
  is 2 and the Degree of C is 1. The degree of D is
  0.

• Internal/External nodes Leaf nodes are external
  nodes and non leaf nodes are internal nodes.

• Level Count nodes in a path to reach a
  destination node. For example, the level of node
  D is 2 as nodes A and B form the path.

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Properties of Complete Binary Tree

• A complete binary tree is said to be a proper
  binary tree where all leaves have the same depth.

• In a complete binary tree, the number of nodes at
  depth d is 2d.

• In a complete binary tree with n nodes, the
  height of the tree is log(n1).

• All the levels except the last level are full.

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Creation of Complete Binary Tree

• Algorithm
• For the creation of a Complete Binary Tree, we
  require a queue data structure to keep track of
  the inserted nodes.
• Step 1 Initialize the root with a new node when
  the tree is empty.
• Step 2 If the tree is not empty then get the
  front element .If the front element does not have
  a left child, then set the left child to a new
  node .If the right child is not present, then set
  the right child as a new node
• Step 3 If the node has both children, then pop
  it from the queue.
• Step 4 Enqueue the new data.

A complete Binary Tree can be represented
using an array. If the parent is index i the left
child is at 2i1 and the right child is at 2i2.
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Full Binary Tree

• A full binary tree can be defined as a binary
  tree in which all the nodes have 0 or two
  children. In other words, the full binary tree
  can be defined as a binary tree in which all the
  nodes have two children except the leaf nodes.
• A full binary tree is a binary tree in which all
  of the nodes have either 0 or 2 offspring. In
  other terms, a full binary tree is a binary tree
  in which all nodes, except the leaf nodes, have
  two offspring.

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Priority queue and its characteristics
Heap and types of heap
Complete and Full Binary Tree
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