Design & Analysis of Algorithms - Vol 2 | 17. Balanced Search Trees by Abraham | Learn Smarter
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17. Balanced Search Trees

This chapter discusses the concept of balanced search trees, focusing on different notions of balance and how to maintain it during insertion and deletion operations. It explains the significance of AVL trees, which are height-balanced trees that ensure the heights of left and right subtrees differ by at most one. Through analysis of tree operations, the importance of maintaining balance in search trees is emphasized to ensure efficient searching and operations.

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Sections

  • 17.1

    Balanced Search Trees

    This section introduces balanced search trees, emphasizing their need for efficiency in maintaining balance during various operations.

  • 17.1.1

    Operations On Search Trees

    This section discusses the operations on search trees, emphasizing the importance of maintaining balance for efficiency.

  • 17.1.2

    Notions Of Balance

    This section discusses the concept of balanced search trees, their operations, and the significance of maintaining balance in these structures.

  • 17.1.3

    Height-Balanced Trees

    This section discusses height-balanced trees, particularly AVL trees, emphasizing their structure and the importance of maintaining balance through operations like insertion and deletion.

  • 17.1.4

    Avl Trees

    This section introduces AVL trees, a type of self-balancing binary search tree that maintains balance through height constraints.

  • 17.1.5

    Slope And Rebalancing

    This section discusses the concept of slope in balanced search trees and the importance of rebalancing these trees after insertion and deletion operations.

  • 17.1.6

    Case Analysis For Rebalancing

    This section discusses the methods for maintaining balance in search trees during insertions and deletions to ensure efficient operations.

  • 17.2

    Rebalancing Process

    This section discusses the rebalancing process in balanced search trees, focusing on AVL trees and the importance of maintaining balance during insertions and deletions.

  • 17.2.1

    Single Rotation

    This section explains the concept of maintaining balance in search trees, specifically focusing on AVL trees and the mechanisms of rebalancing through rotations.

Class Notes

Memorization

What we have learnt

  • Balanced search trees maint...
  • AVL trees are characterized...
  • Rebalancing operations are ...

Final Test

Revision Tests