Consider the following $B^+$ tree with 5 nodes, in which a node can store at most 3 key values. The value 23 is now inserted in the $B^+$ tree. Which of the following options(s) is/are CORRECT?

Maximum Capacity per Node: Each node can hold at most $3$ keys (order of tree $p = 4$).

Current State:

• The root contains $3$ keys: $[6, 12, 19]$ (fully occupied).

• The rightmost leaf node contains $3$ keys: $[20, 21, 22]$ (fully occupied).

Insertion of $23$:

• The key $23$ must be inserted into the rightmost leaf node $[20, 21, 22]$.

• Inserting $23$ causes an overflow in this leaf node ($4$ keys: $[20, 21, 22, 23]$).

• The leaf node splits into two leaf nodes, and the median key is pushed up to the parent (root).

• Since the root node is already full ($[6, 12, 19]$), receiving another key causes the root node to overflow and split.

• Splitting the root creates a new root node at a new level above, thereby increasing the height of the tree.

Conclusion:

• Option (B) is correct: Nodes split during insertion.

• Option (D) is correct: The root node splits, increasing the tree height.

• Options (A) and (C) are incorrect because nodes split and new nodes are created.