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Why LeetCode 127 is actually a graph problem wearing a fake moustache. LeetCode 127 (Word Ladder) is the reason I have trust issues. It sits there, looking innocent. It’s tagged as "Hard," but you read the description and think, "Oh, come on. I just need to change 'HIT' to 'COG' by changing one letter at a time? This is basically Scrabble. I got this." So you start coding. You are confident. You type loud. You are the main character. You write a recursive solution (DFS) to find the path. You hit "Run." Time Limit Exceeded. Okay, fine. You realize it's a "Shortest Path" problem. You switch to BFS (Breadth-First Search). You check every word in the list against your current word to find neighbors. Time Limit Exceeded. Now you’re sweating. The interviewer is staring. You realize this isn't a string problem. This is a math problem. Here is the hard truth about Word Ladder that most tutorials glaze over: The size of the dictionary (N) is the trap. If you try to find neighbors by iterating through the word list (for w in wordList), you are doing O(N⋅L) work for every single node. If N is 5000, you are toast. In my new video, I break down the solution that actually passes: The Alphabet Mutation Trick. Instead of looking at the dictionary, look at the word itself. Don't ask: "Is 'HOT' in the list? Is 'DOT' in the list?" Instead, force the mutation: Take 'HIT'. Change 'H' to 'a'...'z'. Change 'I' to 'a'...'z'. Check if that new string exists in your Set. Why? Because checking 26×Length combinations is mathematically way faster than iterating through a 5000-word dictionary. I also cover a crucial optimization in the code that saves you from maintaining a massive visited array: "Destructive Visits." As soon as we find a word in the Set, we add it to our Queue and immediately delete it from the Set. If it's gone, we can't visit it again. No cycles. No separate memory allocation for visited. Clean. Ruthless. Efficient. If your brain feels like it's melting, don't worry. I spent the last few days creating a video that visualizes this exact logic. I break down: Why DFS fails (and the "Toddler looking for shoes" analogy). Why we use a Queue and level_size loop to track distance. The exact Python implementation using deque and Set lookups. Stop trying to brute force your way through string problems. Sometimes you just need to mutate the alphabet. Link to the full breakdown is in the comments below! 👇 #leetcode #softwareengineering #codinglife #python #algorithms #graphs #developerhumor #techcareers