Design & Analysis of Algorithms - Vol 2 | 18. AVL Tree Rotations by Abraham | Learn Smarter
K12 Students

Academics

AI-Powered learning for Grades 8–12, aligned with major Indian and international curricula.

Professionals

Professional Courses

Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.

Games

Interactive Games

Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.

Typing
Memory
Math
English Adventures
Knowledge
18. AVL Tree Rotations

The chapter explains the mechanics of balancing binary search trees, particularly focusing on rotations to maintain height balance. It elucidates the conditions under which left and right rotations should be executed in response to imbalances in the tree structure. By optimizing these operations, the approach ensures logarithmic time complexity for various operations including insertion, deletion, and searching.

Enroll to start learning

You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.

Sections

  • 18

    Avl Tree Rotations

    This section discusses AVL tree rotations used for maintaining balance within height-balanced binary search trees.

    Learning Practice

  • 18.1

    Case When Slope Is -1

    This section discusses the implications of a slope of -1 in tree rebalancing, particularly how it affects the structure and balance of a binary search tree.

    Learning Practice

  • 18.2

    Rebalancing After Insertions

    This section discusses how to rebalance height-balanced binary search trees after insertion operations, focusing on left and right rotations based on slope conditions.

    Learning Practice

  • 18.3

    Handling Nodes With Height +2

    This section discusses how to rebalance binary trees when a certain node height exceeds 2, using rotations to ensure balance.

    Learning Practice

  • 18.4

    Handling Nodes With Height -2

    This section discusses the process of handling tree balance specifically when a node has a height of -2, detailing the necessary rotations to maintain an AVL tree's balance.

    Learning Practice

  • 18.5

    Rotation Operations

    This section covers the principles and procedures for performing rotation operations in height-balanced binary search trees, focusing on maintaining the balance through specific rotation techniques.

    Learning Practice

  • 18.6

    Rebalancing During Deletions

    This section discusses the rebalancing process for binary search trees (BST) during deletion, emphasizing the importance of maintaining balance for height efficiency.

    Learning Practice

  • 18.7

    Efficient Height Management

    This section explores the mechanisms of height management in binary search trees, particularly how to maintain balance using rotations to ensure efficient operations.

    Learning Practice

  • 18.8

    Summary Of Avl Tree Operations

    This section covers the balancing operations of AVL trees, primarily focusing on rotations used to maintain tree balance during insertion and deletion.

    Learning Practice

References

ch40 part b.pdf

Class Notes

Memorization

What we have learnt

  • Balancing trees using rotat...
  • Height balance conditions a...
  • Using height information st...

Final Test

Revision Tests