# Difference between B-tree and Binary Tree

## What is B-TREE?

The nodes of B-tree are sorted during in-order traversal, and it is called self-balancing tree. A node in a B-tree can have more than two offspring, in contrast to binary trees. The height of a B-tree equals logM N, where N is the number of nodes and M is the order of the tree. And with each update, the height is automatically adjusted.

With the lowest value on the left and the highest on the right, data is sorted in a specific sequence in the B-tree. Compared to a binary tree, a B-tree requires more work to enter data or keys.

The B-Tree must meet the following requirements:

• The B-tree's leaf nodes must all be at the same height.
• There shouldn't be any empty sub-trees above the B-leaf tree's nodes.
• The height of the B-tree should be as low as possible.

• It preserves keys arranged for sequential traversal.
• It uses hierarchical indexing to minimize disk reads.
• Uses partially complete blocks to speed up inserts and deletes.
• Recursive algorithm to keep indexes balanced.

## What is Binary Tree?

The unique variety of a general tree is a binary tree. In a binary tree, a node can only have a maximum of two nodes, unlike a B-tree. There is a restriction on a node's degree in a binary tree since nodes in a binary tree can only have two child nodes (or degree two). A binary tree's root node is its highest node, and it has two primary subtrees: a left subtree and a right subtree. The binary tree can be empty, unlike the normal tree. Binary trees can also be sorted via in-order traversal, much like B trees can. However, it can also be ordered by post-order and preorder. Data insertion in a binary tree is less difficult than a B-tree.

• An ideal way to take advantage of the hierarchical nature of data storage
• reflect the structural relationships that exist in a given dataset
• Make inserts and deletes faster than linked lists and arrays.
• A flexible way to store and move data.
• Used to store as many nodes as possible.
• Faster than linked lists and slower than arrays when accessing elements.

## Differences between a B-tree and a Binary tree

• In a B-tree, a node can have at most 'M' (where 'M' is the order in the tree) a number of child nodes. In a binary tree, a node can have at most two child nodes or subtrees.
• B-trees are called permuted trees because the nodes are permuted sequentially as they are traversed. A binary tree is not a sorted tree. You can sort in order, preorder, or post-order traversal.
• The height of a B-tree is log(M*N), where 'M' is the order of the tree and N is the number of nodes. The height of a binary tree is log2(N), where N is the number of nodes.
• A B-Tree is executed when the data is loaded to disk. Unlike B-trees, binary trees are executed as data is loaded into RAM (faster memory).
• A B-Tree is a self-balancing tree. The height of the tree is automatically adjusted with each update. A binary tree is not a self-balancing tree.
• Inserting data or keys into a B-tree is more complicated than a binary tree. In binary trees, data insertion is less complicated than in B-trees.
• B-Trees are used in DBMS (e.g. indexing code). Binary trees are used in things like Huffman coding and code optimization.
• A B-tree is called a permuted tree because its nodes are permuted in traversal order. Therefore, a binary tree can be sorted in post-order, pre-order, or horizontal order, but it is not a sorted tree.

## Conclusion

B-trees are widely used instead of binary trees and binary search trees. The main reason for this is the memory hierarchy where CPUs are connected to caches using high-bandwidth channels and CPUs are connected to disks via low-bandwidth channels. A binary tree is used when storing records in RAM (small and fast) and B-tree is used when storing records on disk (large and slow). Using a B-tree instead of binary tree results in a higher branching factor and a lower tree height, resulting in significantly faster access times.