GATE CS 2024 Set 1 Q11 — File Organization and Indexing (B and B+ Trees)

In a $\text{B}^+$ tree of order $p$ (where $p$ is the maximum number of child pointers an internal node can have):

• Internal Nodes (excluding the root): Must have at least $\lceil p/2 \rceil$ child pointers. This ensures at least $50\%$ occupancy.
• Leaf Nodes: Must contain at least $\lceil (p-1)/2 \rceil$ keys, which also maintains approximately $50\%$ occupancy.
• Root Node: If the root is an internal node, it is only required to have at least $2$ child pointers. If the root is a leaf node, it can have as few as $0$ keys (when the tree is empty) or $1$ key.

Thus, the $50\%$ minimum occupancy requirement is relaxed only for the root node to allow the tree to grow from or shrink to a very small size without violating structural properties.

Therefore, the correct option is A.