**Introduction**

The tree is one of the most commonly used data structures in computer science. As a result, numerous alternative variants have been created. We'll get a deeper understanding of the so-called B-trees in this blog. To accomplish so, we must first comprehend its various components and structure. Following that, we'll look at their various operations, such as searching, insertion, and deletion. Finally, we'll go over the advantages and disadvantages of using B-trees for data storage.

A B-tree of order m, according to Knuth's definition, is a tree that satisfies the following properties:

- A maximum of m children can be found in each node.
- Except for root, every non-leaf node has at least m/2 child nodes.
- There are at least two children if the root is not a leaf node.
- There are k-1 keys in a non-leaf node with k children.
- All of the leaves are on the same level and are devoid of any information.

The keys of each internal node serve as separation values, dividing its subtrees. For example, if an internal node has three subtrees, it must have two keys: a1 and a2. All values in the leftmost subtree will be less than a1, all values in the middle subtree will be between a1 and a2, and all values in the rightmost subtree will be greater than a2. Internal nodes

source: cpp.edu

Must Recommended Topic, __Generalization in DBMS__ and __Recursive Relationship in DBMS____.__

## Searching an element

The generalized form of searching for an element in a Binary Search Tree is searching for an element in a B-tree. The steps below are followed.

- Starting with the root node, compare k to the node's first key. Return the node and the index if k is the node's first key.
- Return NULL if k.leaf = true (i.e. not found).
- If k is the root node's initial key, recursively search the left child of this key.
- Compare k to the node's next key if the current node contains more than one key and k is greater than the first key. If k is the following key, look for the key's left child (i.e., k lies between the first and the second keys). Otherwise, look for the key's right child.
- Repeat steps 1â€“4 until you reach the leaf.

Example:

source: iq.opengenus.org