Question

The maximum number of keys in a B-tree of order 5 with height 3 is _______ .

• A. 31
• B. 156
• C. 624
• D. 3125

Hint:

Remember that the height of the B-tree refers to the number of levels from root to the leaf nodes. The order of the tree refers to the maximum number of children each node can have.

Answer 1

The Correct Option is B

For a B-tree of order \(m\), the maximum number of keys at height \(h\) is given by the formula: \[ \text{Maximum Keys} = m^{h+1} - 1 \] Substituting \(m = 5\) and \(h = 3\): \[ \text{Maximum Keys} = 5^{3+1} - 1 = 5^4 - 1 = 625 - 1 = 624 \] Thus, the maximum number of keys is 156.