GATE CS 2015 Set 1 — Question 15
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Programming & Data Structures → Trees → Binary Tree Properties
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Question
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
Correct answer
(A) 63 and 6, respectively
Solution
The question defines height as the length of the longest root-to-leaf path, which implies the number of edges on the path.For a binary tree of height :Maximum number of nodes:
This occurs in a full/complete binary tree.Minimum number of nodes:
This occurs in a skewed binary tree (essentially a linked list structure).Thus, the maximum and minimum number of nodes are 63 and 6 respectively.
This occurs in a full/complete binary tree.Minimum number of nodes:
This occurs in a skewed binary tree (essentially a linked list structure).Thus, the maximum and minimum number of nodes are 63 and 6 respectively.
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