An AVL tree and a B-tree are both self-balancing tree data structures, but they have distinct differences in their structure, use cases, and balancing mechanisms. Here are the key differences:
Structure
Node Children:
AVL Tree: Each node in an AVL tree can have at most two children, making it a binary tree[2][3].
B-Tree: Nodes in a B-tree can have multiple children, with the number of children determined by the order of the tree. A B-tree of order $$m$$ can have at most $$m$$ children[1][4][6].
Balance Factor:
AVL Tree: Each node maintains a balance factor, which is the difference in heights between its left and right subtrees. The balance factor must be -1, 0, or +1 to ensure the tree remains balanced[2][5][8].
B-Tree: B-trees do not use a balance factor. Instead, they ensure that all leaf nodes are at the same level and that internal nodes are at least half full[4][6][13].
Balancing Mechanism
Rotations:
AVL Tree: Balancing is achieved through rotations (single and double rotations) whenever an insertion or deletion causes the tree to become unbalanced[2][5][12].
B-Tree: Balancing is achieved by splitting and merging nodes. When a node exceeds its maximum capacity, it is split, and the middle key is promoted to the parent node. Conversely, nodes are merged when they fall below their minimum capacity[4][6][13].
Use Cases
Memory Usage:
AVL Tree: Typically used for in-memory data structures where fast lookups, insertions, and deletions are required. They are efficient for applications where the data fits entirely in memory[1][2][8].
B-Tree: Designed for systems that read and write large blocks of data, such as databases and file systems. B-trees are optimized for minimizing disk I/O operations, making them suitable for large datasets stored on disk[1][4][6].
Performance
Height:
AVL Tree: The height of an AVL tree is $$O(\log n)$$, where $$n$$ is the number of nodes. This ensures that all operations (search, insert, delete) ...
