Data Structures and Algorithms in Python | 36. Priority queues and heaps - Part B by Abraham | Learn Smarter
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36. Priority queues and heaps - Part B

Heaps serve as a tree-based implementation of priority queues, enabling efficient operations such as insert and delete max in logarithmic time. The chapter explores various functionalities of heaps, including building techniques and sorting methods. By utilizing a bottom-up approach, heaps can be constructed in linear time, and the chapter also distinguishes between max heaps and min heaps, highlighting their applications in sorting and data prioritization.

Sections

  • 36.1

    Insert Operation

    This section outlines the insert operation in a binary heap, detailing its time complexity and how it effectively maintains the heap properties.

    Learning Practice

  • 36.1.1

    Complexity Of Insert

    This section discusses the time complexity associated with inserting nodes in a heap and the delete max operation.

    Learning Practice

  • 36.2

    Delete Max Operation

    The Delete Max operation in heaps efficiently removes the maximum value from the root, maintaining the heap property while ensuring logarithmic time complexity.

    Learning Practice

  • 36.2.1

    Restoring The Heap Property

    This section explores the operations involved in restoring the heap property through insertions and deletions in a heap data structure, highlighting the efficiency of these operations.

    Learning Practice

  • 36.2.2

    Behavior Of Delete Max

    The Delete Max operation efficiently removes the maximum element from a heap while maintaining the heap property.

    Learning Practice

  • 36.3

    Array Representation Of Heaps

    This section covers the operations on heaps, specifically insertion and deletion, and highlights the array representation of heaps.

    Learning Practice

  • 36.3.1

    Index Calculations

    This section discusses the insert and delete max operations in heaps, illustrating how these operations relate to the tree's height and how index calculations simplify manipulation.

    Learning Practice

  • 36.4

    Building A Heap

    This section explains the process and efficiency of heap operations, including insertion and deletion of nodes, and outlines two methods for building heaps.

    Learning Practice

  • 36.4.1

    Naive Heap Construction

    This section discusses the naive construction of heaps, focusing on operations such as insertion and deletion, and how these operations relate to the heap structure.

    Learning Practice

  • 36.4.2

    Efficient Heap Construction

    This section discusses efficient heap operations, particularly the complexities of insertion and deletion in heaps, and introduces methods for constructing heaps efficiently.

    Learning Practice

  • 36.4.2.1

    Bottom-Up Heapifying

    The section covers the concepts of insert and delete operations in a heap, focusing on the efficiency of these operations and the bottom-up method for heap construction.

    Learning Practice

  • 36.5

    Heap Applications

    This section covers the operations of inserting and deleting elements in heaps, emphasizing their time complexities and representations.

    Learning Practice

  • 36.5.1

    Heap Sort

    Heap Sort is an efficient sorting algorithm that leverages a binary tree structure called a heap to manage nodes.

    Learning Practice

  • 36.6

    Final Summary

    This section summarizes the concepts of heaps, including their operations like insert and delete max, their time complexities, and the distinction between max-heaps and min-heaps.

    Learning Practice

  • 36.6.1

    Properties Of Heaps

    This section discusses the operations on heaps, focusing on insertion and deletion of maximum elements, while showcasing their efficiency and structural properties.

    Learning Practice

  • 36.6.2

    Min-Heaps

    This section covers the structure and operations of Min-Heaps, emphasizing insertion, deletion, and efficient heap construction.

    Learning Practice

References

Chapter 36 part-B.pdf

Class Notes

Memorization

What we have learnt

  • Heaps can implement priorit...
  • Building a heap can be done...
  • Max heaps and min heaps dif...

Final Test

Revision Tests