Question:

Let H, I, L, and N 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 ?

GATE DA - 2024
GATE DA

Updated On: Jan 30, 2026

L ≤ I + 1
H + 1 ≤ N ≤ 2^H+1 − 1
H ≤ I ≤ 2^H - 1
H ≤ L ≤ 2^H-1

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The Correct Option is A, B, C

Solution and Explanation

The correct option is (A) : L ≤ I + 1, (B) : H + 1 ≤ N ≤ 2^H+1 − 1 and (C) : H ≤ I ≤ 2^H - 1.

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Let H, I, L, and N 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 ?

The Correct Option is A, B, C

Solution and Explanation

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Questions Asked in GATE DA exam

Let H, I, L, and N 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 ?