The height of a rooted tree is the maximum height of any leaf. The length of the unique path from a leaf of the tree to the root is, by definition, the height of that leaf. A rooted tree in which each non-leaf vertex has at most two children is called a binary tree. If each non-leaf vertex has exactly two children, the tree is called a full binary tree. Consider the following statements. Which of the following is true?
The maximum possible height of a FULL binary tree with $L$ leaves is $L-1.$
See this comment:
https://gateoverflow.in/375244/Go-classes-2023-discrete-mathematics-test-5-question-23?show=376981#c376981
Knowing the number of leaves does not bound the height of a tree — it can be arbitrarily large. So a binary tree with $35$ leaves and height $100$ is possible.
Elaborating option (C)
@Deepak Poonia sir maximum leaves will be when the tree is a complete binary tree. So for a height of 100 maximum leaves will be $2^{100} $. So 35 leaves are possible and the number of leaves is possible from 1 till $2^{100} $ for height 100.
Option B is false bcz just consider left skewed tree with 5 nodes. The height of the tree will be 4 and the number of leaves will be 1. So, we can clearly see that the number of leaves does not bound the height of the binary tree.
That’s right @samarpita.
64.3k questions
77.9k answers
244k comments
80.0k users
