#104 - Maximum Depth of Binary Tree

EasyBinary Tree - DFS

Given the root of a binary tree, return its maximum depth. A binary tree's maximum depth is the number of nodes along the longest path from the root node down to the farthest leaf node.

Input	Output
root = [3,9,20,null,null,15,7]	3
root = [1,null,2]	2

Solution Space

Try it

/**
 * Returns the maximum depth (height) of a binary tree.
 *
 * @param root Root of the binary tree
 * @returns Maximum depth (number of nodes on the longest root-to-leaf path)
 */
export function maxDepth(root: TreeNode | null): number {
  if (!root) return 0;
  return 1 + Math.max(maxDepth(root.left), maxDepth(root.right));
}

Approach: recursive DFS – base case returns 0 for null; each node adds 1 to the max of its children's depths.

Time: O(n) – visits every node exactly once.

Space: O(h) – call stack depth equals tree height; O(n) worst case for a skewed tree, O(log n) for balanced.

Alternative approaches:

Approach	Idea	Time	Space
Iterative BFS	Level-order traversal counting levels	O(n)	O(n) (queue width)

Why DFS recursion is preferred: one-liner logic, trivially correct, and O(h) space beats O(n) for balanced trees.

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