Valid Parentheses
Recognize the pattern
Brute force idea
The naive version of Valid Parentheses sounds like this: Generate all possible bracket matchings and validate — exponential. That direct path helps you understand the question, but it tends to treat every possibility as brand new instead of learning from earlier steps.
Better approach
The deeper shift in Valid Parentheses is this: Use a stack: push opening brackets, pop and match when you see a closing one. 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 Valid Parentheses is one steady idea: The stack always contains unmatched opening brackets in the order they appeared. When you keep that truth intact, each local choice supports the larger solution instead of fighting it.
Watch out for
One easy way to drift off course in Valid Parentheses is this: Forgetting to check that the stack is empty at the end — leftover openers mean invalid. The fix is usually to return to the meaning of each move, not just the steps themselves.