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

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

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  1. 17.1
    Balanced Search Trees

    This section introduces balanced search trees, emphasizing their need for...

  2. 17.1.1
    Operations On Search Trees

    This section discusses the operations on search trees, emphasizing the...

  3. 17.1.2
    Notions Of Balance

    This section discusses the concept of balanced search trees, their...

  4. 17.1.3
    Height-Balanced Trees

    This section discusses height-balanced trees, particularly AVL trees,...

  5. 17.1.4

    This section introduces AVL trees, a type of self-balancing binary search...

  6. 17.1.5
    Slope And Rebalancing

    This section discusses the concept of slope in balanced search trees and the...

  7. 17.1.6
    Case Analysis For Rebalancing

    This section discusses the methods for maintaining balance in search trees...

  8. 17.2
    Rebalancing Process

    This section discusses the rebalancing process in balanced search trees,...

  9. 17.2.1
    Single Rotation

    This section explains the concept of maintaining balance in search trees,...

What we have learnt

  • Balanced search trees maintain efficient operations such as search, insert, and delete.
  • AVL trees are characterized by a height balance condition that keeps the difference in heights of subtrees at most one.
  • Rebalancing operations are crucial after insertions or deletions to maintain the height balance of a tree.

Key Concepts

-- Balanced Search Tree
A data structure that maintains balance during insertions and deletions, ensuring operations remain efficient.
-- AVL Tree
A type of balanced search tree that maintains a height balance condition, where the heights of the left and right subtrees differ by at most one.
-- Height of a Tree
The number of nodes along the longest path from the root to a leaf node, influencing the tree's efficiency.
-- Slope
The difference in height between the left and right subtrees, which can indicate whether a tree is balanced.

Additional Learning Materials

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