What is the maximum number of keys that a B+ -tree of order 3 and of height 3 have?

A B+ tree of order 'm' and height 'h' can have a maximum of mh keys.

Here's how we calculate it:

1. The root of a B+ tree of order 'm' can have a maximum of m-1 keys.

2. Each internal node (excluding the root) can have a maximum of m keys.

3. The number of internal nodes at each level increases exponentially with the height of the tree. Specifically, there can be up to m^(h-1) internal nodes at height 'h'.

4. Therefore, the total number of keys in a B+ tree of order 'm' and height 'h' is (m-1) + m*(m^(h-1) - 1).

For a B+ tree of order 3 and height 3, this formula gives us:

(3-1) + 3*(3^(3-1) - 1) = 2 + 3*(9 - 1) = 2 + 3*8 = 2 + 24 = 26.

So, a B+ tree of order 3 and height 3 can have a maximum of 26 keys.