GATE | GATE CS 1997 | Question 60

A size-balanced binary tree is a binary tree in which for every node, the difference between the number of nodes in the left and right subtree is at most 1. The distance of a node from the root is the length of the path from the root to the node. The height of a binary tree is the maximum distance of a leaf node from the root.

a. Prove, by using induction on h, that a size-balance binary tree of height h contains at least 2h nodes.
b. In a size-balanced binary tree of height h≤1, how many nodes are at distance h−1 from the root? Write only the answer without any explanations.



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