Define B-tree of order m? When is it preferred to use B-trees?

1.	Define B-tree of order m? When is it preferred to use B-trees?
Answer» A B-Tree of order M is either the empty tree or it is an M-way search tree T with the following properties: (i) The root of T has at least two subtrees and at most M subtrees. (ii) All internal nodes of T (other than its root) have between [M / 2] and M subtrees. (iii) All external nodes of T are at the same level. Just as AVL trees are balanced binary search trees, B-trees are balanced M-way search trees. By imposing a balance condition, the shape of an AVL tree is constrained in a way which guarantees that the search, insertion, and withdrawal operations are all O(log n), where n is the number of items in the tree. The shapes of B-Trees are constrained for the same reasons and with the same effect.

Answer»

A B-Tree of order M is either the empty tree or it is an M-way search tree T with the following properties:

(i) The root of T has at least two subtrees and at most M subtrees.

(ii) All internal nodes of T (other than its root) have between [M / 2] and M subtrees.

(iii) All external nodes of T are at the same level.

Just as AVL trees are balanced binary search trees, B-trees are balanced M-way search trees. By imposing a balance condition, the shape of an AVL tree is constrained in a way which guarantees that the search, insertion, and withdrawal operations are all O(log n), where n is the number of items in the tree. The shapes of B-Trees are constrained for the same reasons and with the same effect.

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