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12. Maximum Depth of Binary Tree

easyAsked at Coursera

Find the maximum depth of a binary tree, a foundational tree-traversal problem Coursera uses to test recursive thinking for hierarchical course-content structures.

By Alex Chen, Founder, InterviewChamp.AI · Last verified

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.

Constraints

  • Number of nodes is in the range [0, 10^4]
  • -100 <= Node.val <= 100

Examples

Example 1

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

Example 2

Input
root = [1,null,2]
Output
2

Approaches

1. Brute force (BFS level count)

Use a queue to traverse level by level, incrementing depth each level.

Time
O(n)
Space
O(n)
function maxDepth(root) {
  if (!root) return 0;
  const queue = [root]; let depth = 0;
  while (queue.length) {
    depth++;
    for (let i = queue.length; i > 0; i--) {
      const n = queue.shift();
      if (n.left) queue.push(n.left);
      if (n.right) queue.push(n.right);
    }
  }
  return depth;
}

Tradeoff:

2. DFS recursion

Recursively compute depth of left and right subtrees, returning 1 + max of the two. Elegant and O(n) time with O(h) stack space.

Time
O(n)
Space
O(h)
function maxDepth(root) {
  if (!root) return 0;
  return 1 + Math.max(maxDepth(root.left), maxDepth(root.right));
}

Tradeoff:

Coursera-specific tips

Coursera interviews emphasize algorithms for educational platforms, content recommendation systems, and scalable delivery pipelines. Medium-difficulty graph and DP problems are typical.

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