Height and Depth of a binary Tree

What is Height in a Binary Tree?

Let’s take a binary tree:

Think of height like climbing up. The higher we go, the greater the height.

• If we stand on the ground, our height is 0.
• In the same way, in a binary tree, the height of a leaf node is 0.
• We measure height from bottom to top by taking the longest path.

📌 Definition: The height of a binary tree is the number of edges on the longest path from the root to a leaf node.

👉 In the first image, the height of the tree is 3 because the longest path from root to a leaf has 3 edges.

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What is Depth in a Binary Tree?

Depth tells us how deep a node is in the tree.

Let’s think of a pond:

• The more we dive under the water, the deeper we go.
• Similarly, in a tree, the depth of the root node is 0.
• As we move downward, the depth increases.

📌 Definition: The depth of a node is the number of edges from the root to that node.

👉 In the first image, the maximum depth is 3, which means the deepest node is 3 edges away from the root.

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Another Example

In this tree:

• The height is 4 (longest path from root to leaf has 4 edges).
• The maximum depth is also 4 (deepest node is 4 edges away from the root).