What are the differences between B trees and B+ trees?

In a b-tree you can store both keys and data in the internal and leaf nodes, but in a b+ tree you have to store the data in the leaf nodes only.

Is there any advantage of doing the above in a b+ tree?

Why not use b-trees instead of b+ trees everywhere, as intuitively they seem much faster?

I mean, why do you need to replicate the key (data) in a b+ tree?

The image below helps show the differences between B+ trees and B trees.

Advantages of B+ trees:

• Because B+ trees don't have data associated with interior nodes, more keys can fit on a page of memory. Therefore, it will require fewer cache misses in order to access data that is on a leaf node.
• The leaf nodes of B+ trees are linked, so doing a full scan of all objects in a tree requires just one linear pass through all the leaf nodes. A B tree, on the other hand, would require a traversal of every level in the tree. This full-tree traversal will likely involve more cache misses than the linear traversal of B+ leaves.

Advantage of B trees:

• Because B trees contain data with each key, frequently accessed nodes can lie closer to the root, and therefore can be accessed more quickly.

The principal advantage of B+ trees over B trees is they allow you to pack in more pointers to other nodes by removing pointers to data, thus increasing the fanout and potentially decreasing the depth of the tree.

The disadvantage is that there are no early outs when you might have found a match in an internal node. But since both data structures have huge fanouts, the vast majority of your matches will be on leaf nodes anyway, making on average the B+ tree more efficient.

B+Trees are much easier and higher performing to do a full scan, as in look at every piece of data that the tree indexes, since the terminal nodes form a linked list. To do a full scan with a B-Tree you need to do a full tree traversal to find all the data.

B-Trees on the other hand can be faster when you do a seek (looking for a specific piece of data by key) especially when the tree resides in RAM or other non-block storage. Since you can elevate commonly used nodes in the tree there are less comparisons required to get to the data.

1. In a B tree search keys and data are stored in internal or leaf nodes. But in a B+-tree data is stored only in leaf nodes.
2. Full scan of a B+ tree is very easy because all data are found in leaf nodes. Full scan of a B tree requires a full traversal.
3. In a B tree, data may be found in leaf nodes or internal nodes. Deletion of internal nodes is very complicated. In a B+ tree, data is only found in leaf nodes. Deletion of leaf nodes is easy.
4. Insertion in B tree is more complicated than B+ tree.
5. B+ trees store redundant search keys but B tree has no redundant value.
6. In a B+ tree, leaf node data is ordered as a sequential linked list but in a B tree the leaf node cannot be stored using a linked list. Many database systems' implementations prefer the structural simplicity of a B+ tree.