Maximum Depth of Binary Tree
Recognize the pattern
Brute force idea
If you approach Maximum Depth of Binary Tree in the most literal way possible, you get this: 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.
Better approach
The deeper shift in Maximum Depth of Binary Tree is this: 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.
Key invariant
At the center of Maximum Depth of Binary Tree is one steady idea: 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.
Watch out for
A common way to get lost in Maximum Depth of Binary Tree is this: 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.