ISRO | ISRO CS 2009 | Question 30

Last Updated : 05 Jun, 2018

Consider a binary tree with n nodes, where each node can have at most two children. The height of the tree is defined as the maximum number of edges between the root node and any leaf node. Which of the following statements is true regarding the height h of this binary tree?

(A)

The height of the tree is always equal to n-1.

(B)

The height of the tree can be greater than or equal to n-1.

(C)

The height of the tree is always equal to logâ‚‚(n).

(D)

The height of the tree can be greater than or equal to logâ‚‚(n).

Explanation:

In a binary tree, the height h represents the longest path from the root node to any leaf node. This path can consist of n-1 edges in the worst case, where each node has exactly one child except for the leaf nodes. However, it’s also possible for a binary tree to have a height less than n-1, depending on its structure.

Consider a binary tree where each parent node has only one child (left or right) while the other child is null. In this case, the height of the tree will be less than n-1. On the other hand, a balanced binary tree, such as a complete binary tree, can have a height equal to n-1 when it contains the maximum number of nodes.

Therefore, option b) is correct, as the height of a binary tree can be greater than or equal to n-1, depending on its structure and the arrangement of nodes.

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