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GATE DA 2024 Q52: Bounds on height, nodes and leaves of a binary tree

Question

Let HH, II, LL, and NN represent height, number of internal nodes, number of leaf nodes, and the total number of nodes respectively in a rooted binary tree.

Which of the following statements is/are always TRUE?

Try it: multiple select: one or more correct options

Select one or more options
Select all correct options. No negative marking, no partial marks.
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Answer: A, B, C (official GATE 2024 final answer key)

Concept used: Counting nodes level by level: level kk has at most 2k2^k nodes, and a path of length HH needs HH internal nodes.

First step: Test the extremes: a path (one node per level) and a complete tree. A path has L=1<HL = 1 < H, which rules out D.

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Source: official GATE 2024 DA question paper and final answer key, organised by IISc Bangalore. Question paper · Answer key

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