Maximum Depth of Binary Tree

The problem

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

The depth of any tree is one plus the larger depth of its two subtrees. You do not need to trace or compare whole paths down to individual leaves; depth is an inductive quantity synthesized entirely at the return step of each subproblem.

Full solution

Postorder bottom-up recursion: depth is synthesized at the return step from the two subtrees, no queue or explicit stack needed.

class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right


def max_depth(root: TreeNode | None) -> int:
    if root is None:
        return 0
    # depth of a tree = 1 + the larger depth of its two subtrees
    return 1 + max(max_depth(root.left), max_depth(root.right))

class TreeNode {
  constructor(val = 0, left = null, right = null) {
    this.val = val;
    this.left = left;
    this.right = right;
  }
}

function maxDepth(root) {
  if (root === null) return 0;
  // depth of a tree = 1 + the larger depth of its two subtrees
  return 1 + Math.max(maxDepth(root.left), maxDepth(root.right));
}

The theory behind it

Binary Trees — the ground this problem stands on. All Binary Trees problems

What Binary Trees is

A binary tree is a branching data structure that starts at a single top node called the root, like an upside-down family tree. Every node holds a piece of data and can branch out to at most two children below it, known as the left child and the right child. Because there is no ordering rule about which values go left or right, finding a specific item can require checking every single node in the entire tree.

When to reach for it

Reach for binary trees when problems present hierarchical data with left and right child pointers. Questions asking for tree height, maximum depth, path sums from root to leaf, diameter, lowest common ancestor, or checking whether two trees are mirror reflections of each other all signal binary tree traversals. Any problem asking to inspect or reconstruct a tree layer by layer or path by path belongs here.

How the pattern works

Think recursively by focusing on what a single node must do. If the current node is null, return the base answer immediately. Otherwise, ask the left child for its result, ask the right child for its result, and combine both answers with the current node value before returning up to the parent. For horizontal scans, use a queue to read nodes layer by layer, measuring the queue length at the start of each layer to group nodes by depth.

What each operation costs

Which roles need this problem

Binary Trees is a core topic for these 4 roles — if you're targeting one of them, this problem is early in your path, not optional.

Secondary for 5 more roles, including Full-Stack Developer, Android Developer, iOS Developer.