What are B-trees? Explain with example.

B-trees are a type of self-balancing search tree that efficiently maintains sorted data and allows operations such as searches, sequential access, insertions, and deletions in logarithmic time. They are widely used in databases and file systems to store large amounts of data due to their efficient handling of read and write operations.

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### Definition of B-tree

A B-tree is a generalization of a binary search tree where nodes can have more than two children. It is defined by the following properties:

1. Order (m): A B-tree of order \( m \) allows a maximum of \( m-1 \) keys and \( m \) child pointers in a node.
2. Root Node: The root node must have at least one key unless the tree is empty.
3. Internal Nodes: All internal nodes (except the root) must have at least \( \lceil m/2 \rceil - 1 \) keys and at most \( m-1 \) keys.
4. Leaf Nodes: All leaf nodes are at the same level, ensuring a balanced tree structure.
5. Sorted Keys: Keys within a node are stored in sorted order, and subtrees are structured based on the values of keys.
6. Search Property: A key \( k \) in a node has the property that all keys in the left child subtree are less than \( k \), and all keys in the right child subtree are greater than \( k \).

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### Structure of a Node in a B-tree

Each node in a B-tree contains:
- An array of keys: \( [k_1, k_2, \ldots, k_t] \), where \( t \) is the number of keys in the node.
- An array of child pointers: \( [C_0, C_1, \ldots, ___ ______ __________ _____ ___ _______ ______ ___ ___ ____ _______ ___.
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