what is minimum number of key that can stored in B-tree?

Question

For a B-tree with height h and a minimum degree t, what is the minimum number of keys that can be stored in the B-tree? Show the process of reasoning. (Hint: A B-tree with only one root node is considered to have a height of 0. The definition of the minimum degree follows the textbook convention.

Summary

In this question, we have a  B-tree with height h and a minimum degree t, where we have the minimum number of key that can be stored in the B-tree. And also the process of reasoning.

Explanation

A Root node can have a minimum number of children is 2.

For all the child nodes, it is necessary to have at least t children. Suppose each child has a ‘t’ node, then a total number of nodes in the tree will be 2+(t-1) + …

Now, we can calculate the total minimum number of nodes in the tree of height h.
Min nodes = = .

As we see in the definition of B-tree. We already know that a node with a B number can have a B-1 key. So that each node will have t-1 keys and the root node have only 1 key.

Total number of minimum keys= minimum nodes*total keys
= * t-1
= keys.

Also read, For these situations, just design the h files you need to implement the classes you’d need.