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

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.

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  1. 18
    Avl Tree Rotations

    This section discusses AVL tree rotations used for maintaining balance...

  2. 18.1
    Case When Slope Is -1

    This section discusses the implications of a slope of -1 in tree...

  3. 18.2
    Rebalancing After Insertions

    This section discusses how to rebalance height-balanced binary search trees...

  4. 18.3
    Handling Nodes With Height +2

    This section discusses how to rebalance binary trees when a certain node...

  5. 18.4
    Handling Nodes With Height -2

    This section discusses the process of handling tree balance specifically...

  6. 18.5
    Rotation Operations

    This section covers the principles and procedures for performing rotation...

  7. 18.6
    Rebalancing During Deletions

    This section discusses the rebalancing process for binary search trees (BST)...

  8. 18.7
    Efficient Height Management

    This section explores the mechanisms of height management in binary search...

  9. 18.8
    Summary Of Avl Tree Operations

    This section covers the balancing operations of AVL trees, primarily...

What we have learnt

  • Balancing trees using rotations preserves the height balance of binary search trees.
  • Height balance conditions are determined by comparing the heights of subtrees.
  • Using height information stored in tree nodes allows for efficient balancing without full tree traversal.

Key Concepts

-- HeightBalanced Tree
A binary tree where the height of the two child subtrees of any node differ by no more than one.
-- Rotations
Local operations performed on a tree to change its structure while maintaining the binary search property.
-- Complexity
The performance measure, indicating that all operations related to a height-balanced tree can be performed in logarithmic time relative to the number of nodes.

Additional Learning Materials

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