Word Ladder

Word Ladder

What is this problem about?

The "Word Ladder" problem is a classic sequence transformation challenge. You are given a beginWord, an endWord, and a wordList. You need to find the length of the shortest transformation sequence from the start word to the end word, where only one letter can be changed at a time, and every intermediate word must exist in the provided word list. If no such path exists, you return 0.

Why is this asked in interviews?

This is a quintessential Graph Traversal problem asked by top companies like Amazon, Microsoft, and Google. It tests your ability to model a problem where nodes are words and edges are single-character differences. Finding the "shortest" path in an unweighted graph is a prime candidate for Breadth-First Search (BFS), and this problem evaluates if you can implement BFS efficiently.

Algorithmic pattern used

The primary pattern is Breadth-First Search (BFS).

1. Use a Queue to store the current word and the current step count.
2. Use a Set for the word list to allow O(1) lookups.
3. For each word, generate all possible one-letter variations (by changing each character from 'a' to 'z').
4. If a variation exists in the word list, add it to the queue and remove it from the list (to prevent cycles).

Example explanation

Start: hit, End: cog, List: ["hot", "dot", "dog", "lot", "log", "cog"].

1. hit -> hot (1 change, level 2)
2. hot -> dot, lot (level 3)
3. dot -> dog; lot -> log (level 4)
4. dog -> cog; log -> cog (level 5) Shortest path length: 5.

Common mistakes candidates make

• Using DFS: Attempting to find the shortest path with Depth-First Search is highly inefficient and may lead to a Time Limit Exceeded error.
• Redundant Processing: Comparing the current word with every word in the dictionary (O(N)) instead of generating 26 variations for each character (O(26*L)), which is usually much faster.
• Off-by-one: Forgetting that the path length includes both the start and the end words.

Interview preparation tip

Master the "Level-order BFS" pattern. For Word Ladder, keeping track of the "level" (distance) is crucial. Also, consider Bidirectional BFS for an extra optimization that can significantly speed up the search in large word lists.