DSA interview question

Binary Tree Basics: Size, Height and Leaf Count

Easy · Data structures · Topics: tree, theory

The problem

A new engineer on a team that works with hierarchies (org charts, folder trees, decision trees) is asked to write the three most basic tree measurements. Size is the number of nodes. Height is the number of nodes on the longest root-to-leaf path (0 for an empty tree). Leaves is the number of nodes with no children. Each one follows the same recursive shape: the answer for a tree is built from the answers for its two subtrees, and the empty tree is the base case. That's the core idea behind almost every binary tree problem.

Example: [1, 2, 3, 4, 5, null, 6] → size 6, height 3, leaves 3.

Function signature

int size(TreeNode* root);
int height(TreeNode* root);   // nodes on the longest root-to-leaf path; 0 for an empty tree
int leaves(TreeNode* root);

Test cases

Input (level order)	Output	Explanation
`[1, 2, 3, 4, 5, null, 6]`	`size=6 height=3 leaves=3`	Leaves 4, 5, 6
`[1, 2, 3]`	`size=3 height=2 leaves=2`
`[1, 2, null, 3, null, 4]`	`size=4 height=4 leaves=1`	A left chain
`[1]`	`size=1 height=1 leaves=1`	The root is a leaf
`[]`	`size=0 height=0 leaves=0`

(Confirm: height is counted in nodes, not edges; the input uses LeetCode's level-order format.)

How interviewers phrase it

"Explain binary tree terminology (root, leaf, height, depth, size) and compute the size, height and number of leaves of a binary tree."

Clarifying questions to ask

Is height counted in nodes or edges? (Nodes here; the edge count is one less for a non-empty tree.)
Is an empty tree allowed? (Yes: all three are 0.)
Recursive or iterative?

Follow-ups to expect

"What's the recursive pattern?"
"Depth vs height?"
"What are full, complete and perfect trees?"
"Iterative versions?"
"Complexity?"

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