Word Search II requires solving a word search puzzle by identifying all the words from a given list that can be formed on the board. The backtracking approach with pruning is crucial for efficiency, especially when handling large inputs. Focus on optimizing the backtracking by cutting off unnecessary branches to speed up the process and pass all test cases.
Problem Statement
In the Word Search II problem, you are given a 2D board of characters and a list of words. Your task is to return all the words from the list that can be formed by sequentially adjacent cells on the board. Adjacent cells can be horizontally or vertically neighboring, and each letter cell may only be used once per word.
To solve the problem, you need to efficiently search through the board using a backtracking approach. By starting from each letter and exploring all possible word paths, you must prune branches that do not lead to any valid words early on, optimizing your search to handle larger inputs.
Examples
Example 1
Input: board = [["o","a","a","n"],["e","t","a","e"],["i","h","k","r"],["i","f","l","v"]], words = ["oath","pea","eat","rain"]
Output: ["eat","oath"]
Example details omitted.
Example 2
Input: board = [["a","b"],["c","d"]], words = ["abcb"]
Output: []
Example details omitted.
Constraints
- m == board.length
- n == board[i].length
- 1 <= m, n <= 12
- board[i][j] is a lowercase English letter.
- 1 <= words.length <= 3 * 104
- 1 <= words[i].length <= 10
- words[i] consists of lowercase English letters.
- All the strings of words are unique.
Solution Approach
Backtracking Search with Trie
Use a Trie data structure to store all the words in the list, allowing for efficient prefix-based pruning during the search. Start at every board cell and explore potential words by backtracking, pruning whenever the current path does not lead to a valid word or prefix.
Pruning Unnecessary Searches
During the backtracking search, check if the current prefix matches any word in the Trie. If not, terminate the search early to avoid unnecessary exploration. This greatly speeds up the solution, especially when many words share prefixes.
Efficient Handling of Larger Inputs
Optimize the backtracking process by marking visited cells and cutting off branches as soon as possible. This allows the solution to scale with larger inputs, handling up to the problem's constraints of 30,000 words and board dimensions up to 12x12.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
The time complexity depends on the Trie structure and the backtracking search. In the worst case, all cells of the board are visited for each word. Space complexity is influenced by the Trie storage and recursion depth during backtracking.
What Interviewers Usually Probe
- The ability to optimize backtracking demonstrates an understanding of pruning and efficient search techniques.
- Effective use of the Trie structure is a key indicator of solving this problem efficiently.
- Understanding how to cut off unnecessary searches is critical for handling large test cases.
Common Pitfalls or Variants
Common pitfalls
- Not pruning the search early enough, leading to excessive recursion and time complexity.
- Forgetting to mark visited cells, which can cause revisiting and incorrect word formation.
- Using a brute-force approach without considering optimizations for large inputs.
Follow-up variants
- Word Search III with multiple boards and word lists.
- Word Search II on an NxM grid with varying path constraints.
- Multi-level Word Search where the words are split across different sections of the board.
How GhostInterview Helps
- GhostInterview assists in practicing the backtracking approach with pruning, helping you to optimize early termination during word search.
- Guidance on Trie usage allows you to efficiently implement the search and pruning steps, even for large test cases.
- With step-by-step feedback, GhostInterview helps you avoid common pitfalls like not marking visited cells or mismanaging recursion depth.
Topic Pages
Related GhostInterview Pages
- LeetCode Interview Copilot - Use GhostInterview as a live solver when you want direct help with LeetCode-style coding questions.
- Coding Interview Assistant - See how GhostInterview supports array, string, linked list, graph, and tree interview workflows.
- How GhostInterview Works - Review the screenshot, reasoning, and answer flow before using the solver in a live interview.
FAQ
How does backtracking apply to Word Search II?
Backtracking is used to explore all potential paths on the board, trying to form each word. Early pruning is essential to stop unnecessary searches.
What is the role of Trie in Word Search II?
A Trie helps efficiently search for word prefixes, enabling quick pruning of invalid paths during the backtracking process.
What optimization is key for large inputs in Word Search II?
Pruning early and marking visited cells effectively are critical optimizations to ensure the solution handles large boards and word lists efficiently.
How can I improve performance for Word Search II?
By using Trie and backtracking with pruning, you can minimize unnecessary explorations and optimize the search process.
What are common mistakes in solving Word Search II?
Failing to prune searches early, not managing recursion depth, or not marking visited cells are common issues that lead to inefficient or incorrect solutions.
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Given a string and dictionary, return all possible sentences by adding spaces where each word is in the dictionary.
Open problem page#79 Word SearchSolve Word Search with backtracking by exploring adjacent cells to match a target word in a grid.
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