A completely filled binary tree with a height of 4 has ____ nodes.
A) 8
B) 12
C) 15
D) 16

Question

Quizplus · Accepted Answer

A completely filled binary tree (also known as a perfect binary tree) with height h has (2^(h+1)) - 1 nodes. For height 4, it has (2^(4+1)) - 1 = 31 nodes. However, if the question refers to a full binary tree with height 4 (where height is the number of edges on the longest path from the root to a leaf), it would have (2^(4+1)) - 1 = 31 nodes. If the height is defined as the number of levels (including the root level), then it would have (2^4) - 1 = 15 nodes.

A Completely Filled Binary Tree with a Height of 4