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4. Maximum Depth of Binary Tree

easyAsked at Byju's

Return the depth of a binary tree, measuring the longest root-to-leaf path.

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

Problem

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.

Constraints

  • 0 <= nodes <= 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-order traversal incrementing depth per level.

Time
O(n)
Space
O(n)
let q=[root],d=0;
while(q.length){
  const next=[];
  for(const n of q){ if(n.left)next.push(n.left); if(n.right)next.push(n.right); }
  q=next; d++;
}
return d;

Tradeoff:

2. Recursive DFS

Depth equals 1 plus the max depth of either subtree. Recursion mirrors the tree structure naturally.

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

Tradeoff:

Byju's-specific tips

Byju's interviewers value teaching clarity, so narrate the recursion as a lesson a K-12 student could follow before writing code.

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