Longest Word in Dictionary
Recognize the pattern
Brute force idea
If you approach Longest Word in Dictionary in the most literal way possible, you get this: Sort words, for each word check if all prefixes exist — with hash set. Works but doesn't exploit the structure. 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 real unlock in Longest Word in Dictionary comes when you notice this: Build a trie from all words. DFS the trie: only follow branches where isEnd is true at each step (each prefix must be a complete word). The deepest valid path is the longest word. Instead of recomputing the world every time, you preserve just enough context to let the next decision become obvious.
Key invariant
The compass for Longest Word in Dictionary is this: A word is 'buildable' if every prefix of it is also in the dictionary. In the trie, this means every node along the path must be marked as a word end. As long as that statement keeps holding, you can trust the steps built on top of it.
Watch out for
The trap in Longest Word in Dictionary usually looks like this: Not handling ties — when multiple words have the same length, return the lexicographically smallest. DFS with alphabetical child ordering naturally handles this. When the code becomes mechanical before the idea is clear, small edge cases start breaking the whole story.