Word Search II
Given a 2D board and a list of words, find all words on the board. The search must be optimized using a Trie and Backtracking.
Why Interviewers Ask This
Stripe values engineers who can balance algorithmic rigor with practical system performance. This question tests your ability to optimize brute-force search using a Trie for prefix pruning, demonstrating deep understanding of space-time trade-offs. It evaluates whether you can handle complex backtracking without hitting Time Limit Exceeded errors, a critical skill for high-throughput payment systems.
How to Answer This Question
1. Clarify constraints: Ask about board dimensions and word list size to determine if a simple DFS is viable or if optimization is mandatory.
2. Propose the Trie structure: Explain that inserting all words into a Trie allows early termination during traversal when a path no longer matches any word prefix.
3. Define the backtracking logic: Describe iterating through every cell, initiating a DFS, marking visited cells to prevent cycles, and backtracking by unmarking them.
4. Discuss optimization details: Mention removing found words from the Trie to avoid re-scanning and handling duplicate word detection efficiently.
5. Analyze complexity: Calculate time complexity as O(M*N*4^L) where L is max word length, noting how the Trie reduces the effective branching factor significantly compared to checking each word individually.
Key Points to Cover
- Explicitly mentioning the Trie data structure for prefix-based pruning
- Demonstrating clear backtracking mechanics including state restoration
- Discussing the removal of found words to optimize subsequent searches
- Providing accurate time and space complexity analysis
- Connecting the algorithm's efficiency to real-world system constraints
Sample Answer
To solve this efficiently, I would first build a Trie from the given list of words. This allows us to check prefixes in constant time relative to the depth of the node. If we start a search from a specific cell on the board and the path formed doesn't exist in the Trie, we immediately prune that branch, saving significant computation compared to checking every word against every path.
I would then iterate through every cell in the grid. For each unvisited cell, I'd initiate a Depth-First Search. During the DFS, I traverse adjacent cells (up, down, left, right), appending characters to form a string. Before proceeding deeper, I check if the current string exists as a prefix in our Trie. If it does not, we return immediately. If we reach a node marked as an end-of-word, we add that word to our results set and remove it from the Trie to prevent duplicates and unnecessary future checks.
After exploring all paths from a cell, I must backtrack by resetting the visited status so other paths can reuse it. Finally, I would analyze the complexity: while worst-case is exponential, the Trie pruning makes this feasible for typical inputs. At Stripe, where latency matters, this approach ensures we don't waste resources scanning irrelevant paths, directly addressing their need for scalable, efficient backend logic.
Common Mistakes to Avoid
- Failing to use a Trie and instead checking every word against every path, causing TLE
- Forgetting to mark cells as visited during recursion, leading to infinite loops
- Not backtracking (unmarking cells) after returning from a recursive call
- Ignoring duplicate word handling, which can cause incorrect result sets
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