If a binary tree has 'n' nodes, what is the maximum height of the tree?

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Question: If a binary tree has \'n\' nodes, what is the maximum height of the tree?

Options:

Correct Answer: n

Solution:

The maximum height of a binary tree occurs when the tree is skewed (like a linked list), resulting in a height of n.

If a binary tree has 'n' nodes, what is the maximum height of the tree?

If a binary tree has 'n' nodes, what is the maximum height of the tree?

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 that the height of a tree is the number of edges on the longest path from the root to a leaf.
Step 3: Realize that the maximum height occurs when the tree is skewed, meaning all nodes are in a straight line (like a linked list).
Step 4: In a skewed binary tree with 'n' nodes, there will be 'n-1' edges from the root to the last node, making the height equal to 'n'.
Step 5: Conclude that the maximum height of a binary tree with 'n' nodes is 'n'.

Binary Tree Height – The height of a binary tree is defined as the number of edges on the longest path from the root to a leaf node.
Skewed Trees – A skewed binary tree is one where all nodes have only one child, leading to a maximum height equal to the number of nodes.