Maximum Depth of Binary Tree
Signals to notice
Brute force first
BFS level by level, count levels — but uses more memory. It is a fair place to begin because it matches the surface of the question, yet it does not capture the deeper structure that makes the problem simpler.
The key insight
Recursive DFS: depth = 1 + max(left depth, right depth). Once you hold onto the right piece of information from moment to moment, the problem feels less like trial and error and more like following a shape that was there all along.
What must stay true
The depth of a node is 1 plus the maximum depth of its children. When you keep that truth intact, each local choice supports the larger solution instead of fighting it.
Easy way to go wrong
Confusing depth vs height — depth of a null node is 0, not -1. Most mistakes here are not about syntax; they come from losing track of what your state, pointer, or structure is supposed to mean.