Question

What is maximum number of nodes in a binary tree of height 10?

Answer 1

Assuming (inductively) that for we have a minimum of N = 2 k + 1 nodes, if we add a node, it must branch from one of the leaves. But in order to maintain a full binary tree, we must add an additional node; that is, adding an additional levels requires at minimum two more nodes.

Answer 2

The maximum number of nodes in a binary tree of depth is 2 k − 1 , k ≥ 1 . The maximum number of nodes in a binary tree of depth is 2 k − 1 , k ≥ 1 .


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