GATE CS 2025 Set 1 — Question 21
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Databases → Indexing & File Organization → B & B+ Trees
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Question
Consider the following tree with 5 nodes, in which a node can store at most 3 key values. The value 23 is now inserted in the tree. Which of the following options(s) is/are CORRECT?
Correct answer
(B) At least one node will split and redistribute.; (D) The height of the tree will increase.
Solution
1.The current tree has a root with keys and four leaf nodes. The maximum number of keys per node is 3.
2.Inserting 23: The value 23 belongs in the rightmost leaf node .
3.Leaf Split: Adding 23 to causes an overflow. The node splits into two: and . The middle key (22) is promoted to the parent (root).
4.Root Split: The root now contains , which also overflows. It splits into two nodes (e.g., and ), and a key (e.g., 19) is promoted to a new root node.
5.Conclusion: At least one node splits (B is true), and the height of the tree increases from 2 to 3 (D is true). The number of nodes increases, so (C) is false.
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