Understanding the Problem
We are given three things: a startWord
, a targetWord
, and a list of allowed words called wordList
.
Our task is to transform startWord
into targetWord
, but under some important rules:
- We can only change one letter at a time.
- Each intermediate word formed during transformation must exist in the
wordList
.
- We are not just looking for one sequence, but all shortest sequences that complete the transformation.
This is like finding the shortest paths in a word graph, where each node is a word and edges connect words that differ by only one letter.
Step-by-Step Solution with Example
Step 1: Analyze the Example
Let’s take the example:
startWord = "hit"
targetWord = "cog"
wordList = ["hot", "dot", "dog", "lot", "log", "cog"]
We want to transform "hit" to "cog" using valid intermediate words. Valid paths include:
["hit", "hot", "dot", "dog", "cog"]
and
["hit", "hot", "lot", "log", "cog"]
. Both have 5 words and are the shortest.
Step 2: Use BFS to Find Levels
We perform Breadth-First Search (BFS) starting from startWord
. Why BFS?
- BFS explores all words level by level — this helps us find the shortest path(s).
- We build a graph (adjacency list) to remember how each word is connected and from which word it came.
- We also track the level (or step count) when we reach a word.
Step 3: Stop When Target is Reached
We stop BFS as soon as we reach the targetWord
. This ensures we do not explore longer paths than necessary. All words discovered at that level are part of the shortest sequence.
Step 4: Backtrack Using DFS
Once BFS is done, we now backtrack using Depth-First Search (DFS) from the targetWord
to startWord
, collecting all valid paths:
- We only move from a word to another word that is one level lower — this keeps the path short.
- Each path we build represents one valid shortest transformation sequence.
Step 5: Return the Results
All collected paths are stored and returned. Each path shows how we can go from startWord
to targetWord
using valid transformations.
Edge Cases
- Target word missing from the word list: If
targetWord
is not in the wordList
, no transformation is possible. We return an empty list.
- Start word not in list: That’s okay.
startWord
doesn’t have to be in wordList
.
- No path exists: BFS may complete without ever reaching
targetWord
. In this case, we also return an empty list.
- Words of different lengths: All words should be the same length for the one-letter transformation rule to make sense.
Finally
This problem is a combination of graph traversal and path reconstruction. We use BFS to determine the minimum number of steps and build the transformation graph, then DFS to collect all valid shortest paths. The use of two algorithms — BFS followed by DFS — ensures correctness and efficiency.
Understanding the reasoning behind each step — why BFS first, why we backtrack with DFS, and how we prune paths based on levels — helps make this problem clear and approachable even for beginners.
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