Height of Binary Tree in DSA C++ - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the height of a binary tree?

The height of a binary tree is the number of edges on the longest path from the root node to a leaf node. It measures how tall the tree is.

beginner

How do you calculate the height of an empty binary tree?

The height of an empty binary tree is defined as -1 because there are no nodes and no edges.

beginner

What is the height of a binary tree with only one node (the root)?

The height is 0 because there are no edges from the root to any leaf (the root itself is a leaf).

intermediate

Explain the recursive approach to find the height of a binary tree.

To find the height, recursively find the height of the left subtree and the right subtree, then take the maximum of these two heights and add 1 for the current node.

intermediate

Why do we add 1 when calculating the height recursively?

We add 1 to count the current node itself, moving one level down the tree.

What is the height of a binary tree with only the root node?

A 0

B 1

C -1

D 2

A tree with only root has height 0 because there are no edges.

What is the height of an empty binary tree?

A 1

B 0

C -1

D Undefined

By definition, an empty tree has height -1.

Which of these best describes how to find the height of a binary tree?

A Find the longest path from root to leaf in edges

B Count the number of leaf nodes

C Count the number of nodes

D Find the shortest path from root to leaf

Height is the longest path from root to leaf measured in edges.

In the recursive height calculation, what do you do after finding left and right subtree heights?

A Add them

B Ignore them

C Take the minimum

D Take the maximum and add 1

We take the maximum height of the two subtrees and add 1 for the current node.

If a binary tree has height 3, how many edges are there on the longest path from root to leaf?

A 2

B 3

C 4

D 5

Height counts edges, so height 3 means 3 edges on the longest path.

Describe how to find the height of a binary tree using recursion.

Think about how you break down the problem into smaller parts.

Explain why the height of an empty binary tree is defined as -1.

Consider what height means and how it relates to edges.