Page 66 - Data Structures Interactive Book

7.4.1 AVL Trees

An AVL tree is a self-balancing binary search tree. After each insertion or deletion, the

tree checks its balance factor (the difference in height between the left and right subtrees of

a node). If the balance factor exceeds 1 or -1, rotations are performed to restore balance. This

ensures that the height of the tree remains logarithmic, keeping operations efficient.

7.4.2 B-Trees

B-trees are multi-way search trees commonly used in databases and file systems.

Unlike binary trees, B-trees allow nodes to have multiple children, reducing the height of the

tree and minimizing disk access. This makes them ideal for applications where large amounts

of data must be stored and retrieved efficiently.

7.4.3 Heap Trees

A heap tree is a specialized binary tree used to implement priority queues. In a max-

heap, each parent node is greater than or equal to its children, while in a min-heap, each

parent is smaller. Heap trees support efficient insertion and deletion of the highest or lowest
priority element, making them essential in scheduling and resource allocation.

7.5 Applications of Trees

Trees are versatile and widely used in computer science and real-world systems.

• Hierarchical Data Representation: Trees naturally represent hierarchical structures

such as organizational charts, family trees, and classification systems.

• Expression Trees: In compilers, trees represent mathematical expressions, with

operators as internal nodes and operands as leaves. This allows systematic evaluation
of complex expressions.

• File System Organization: Operating systems use trees to represent directories and

files, enabling efficient navigation and management of storage.
These applications highlight the importance of trees as a fundamental tool for

organizing and processing data.

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