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

Question

Quizplus · Accepted Answer

A completely filled binary tree is a tree where every level is completely filled with nodes, except the last level which can either be completely filled or partially filled. 
For a binary tree with a height of 4, the number of nodes can be calculated as follows: 
- Level 0 (root): 1 node 
- Level 1: 2 nodes 
- Level 2: 4 nodes 
- Level 3: 8 nodes 
- Level 4: 16 nodes (if completely filled)

Therefore, the total number of nodes in a completely filled binary tree with a height of 4 is 1+2+4+8+16 = 31. However, since the question specifies a completely filled binary tree, the last level must be completely filled, which means there are only 15 nodes in total. The correct answer is therefore D)15.

A Completely Filled Binary Tree with a Height of 4