Consider the following tree diagrams: Which of these trees is considered to be balanced?
A) I
B) I and II
C) II and III
D) I and III

Question

Consider the following tree diagrams:  Which of these trees is considered to be balanced?
A) I 
B) I and II 
C) II and III 
D) I and III

Quizplus · Accepted Answer

A balanced tree is a tree in which the difference in height between the left and right subtrees of any node is no more than 1. In diagram I, the height difference between the left and right subtrees of the root node is 2, making it unbalanced. In diagram III, the height difference between the left and right subtrees of the node with label 4 is also 2, making it unbalanced. However, in diagram II, all nodes have a height difference of at most 1, making it a balanced tree. Therefore, the correct answer is B, which includes the balanced tree II along with unbalanced trees I and III.

Consider the Following Tree Diagrams: Which of These Trees