Which of the following is true about the height of a binary tree with n nodes?

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Question: Which of the following is true about the height of a binary tree with n nodes?

Options:

Correct Answer: Height <= n

Solution:

The height of a binary tree with n nodes can be at most n in the case of a skewed tree, hence Height <= n.

Which of the following is true about the height of a binary tree with n nodes?

Which of the following is true about the height of a binary tree with n nodes?

Step 1: Understand what a binary tree is. A binary tree is a structure where each node has at most two children.
Step 2: Know what 'height' means. The height of a tree is the number of edges on the longest path from the root to a leaf.
Step 3: Consider the case of a skewed tree. A skewed tree is one where all nodes are either to the left or to the right, forming a straight line.
Step 4: In a skewed tree with n nodes, the height is n - 1 because there are n nodes but only n - 1 edges connecting them.
Step 5: Therefore, the maximum height of a binary tree with n nodes is n - 1, which means the height can be at most n.
Step 6: Conclude that the height of a binary tree with n nodes is less than or equal to n.

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