A 2-3 tree of height h always has at least ______ nodes.
A)h²
B)h² - 2
C)2h
D)2h - 1

Question

Quizplus · Accepted Answer

A 2-3 tree is a balanced tree where each node can have either two or three children. The minimum height of a 2-3 tree is log3(n+1) - 1 where n is the number of nodes in the tree. So, for a height of h, the minimum number of nodes will be 2^(h+1)/3 - 1. Therefore, the best choice for the minimum number of nodes for a 2-3 tree of height h is 2h - 1 (Option D).

A 2-3 Tree of Height H Always Has at Least