GATE | GATE-CS-2015 (Set 1) | Question 65

The height of a tree is the length of the longest root-to-leaf path in it. The maximum and minimum number of nodes in a binary tree of height 5 are
(A) 63 and 6, respectively
(B) 64 and 5, respectively
(C) 32 and 6, respectively
(D) 31 and 5, respectively


Answer: (A)

Explanation:

Number of nodes is maximum for a perfect binary tree.
A perfect binary tree of height h has 2h+1 - 1 nodes

Number of nodes is minimum for a skewed binary tree.
A perfect binary tree of height h has h+1 nodes.

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