What is the difference between a B-tree and a binary search tree?

The main difference between a B-tree and a binary search tree lies in their structure and the way they organize and store data.

1. Structure:
- A binary search tree is a binary tree where each node can have at most two children: a left child and a right child. The left child contains smaller values, and the right child contains larger values.
- A B-tree is a balanced tree that can have multiple children per node. The number of children in a B-tree can vary within a certain range, typically denoted by a parameter called the "order" of the B-tree.

2. Balancing:
- Binary search trees are not inherently balanced, meaning that their structure can become skewed and lead to inefficient search and insertion operations. In the worst case, a binary search tree can degenerate into a linked list, resulting in O(n) time complexity for search and insertion.
- B-trees, on the other hand, are self-balancing trees. They maintain a balance by ensuring that all leaf nodes are at the same level. This balancing property allows B-trees to provide efficient search, insertion, and deletion operations with a time complexity of O(log n).

3. Usage:
- Binary search trees are commonly used when the data is dynamic and frequently changing, as they provide efficient average-case performance for search, insertion, and deletion operations. They are suitable for small to medium-sized datasets.
- B-trees are typically used in scenarios where the data is stored on disk or in a database, where efficient disk access is crucial. B-trees can handle large datasets and provide efficient operations even when the data is stored on secondary storage devices.

In summary, the main differences between a B-tree and a binary search tree are their structure, balancing properties, and usage scenarios. B-trees are self-balancing and suitable for large datasets stored on disk, while binary search trees are simpler and more suitable for smaller dynamic datasets.