Word Ladder
Recognize the pattern
Brute force idea
If you approach Word Ladder in the most literal way possible, you get this: DFS trying all possible one-letter changes — exponential. Explores deep paths when the shortest one might be shallow. 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 Word Ladder is this: BFS from the start word: each level represents one transformation step. Generate all valid one-letter changes, check against the word list. The first time you reach the end word is the shortest path. where M = word length, N = word list size. 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 Word Ladder is one steady idea: BFS guarantees the shortest path in an unweighted graph. Each word is a node; edges connect words differing by one letter. The first time BFS reaches the target is the minimum number of transformations. When you keep that truth intact, each local choice supports the larger solution instead of fighting it.
Watch out for
The trap in Word Ladder usually looks like this: Using DFS instead of BFS — DFS finds A path but not necessarily the shortest. Also, generating neighbors by trying all 26 letters at each position is often faster than comparing against every word in the list. When the code becomes mechanical before the idea is clear, small edge cases start breaking the whole story.