How to Solve Word Search

Word Search requires exploring a grid to find if a word exists by traversing adjacent cells. Utilize backtracking with pruning to avoid unnecessary exploration of invalid paths.

Problem Statement

Given an m x n grid of characters and a string word, you need to determine if the word can be constructed from sequentially adjacent cells. These cells must be horizontally or vertically adjacent. The same cell may not be used more than once during the word construction.

The problem involves searching through the grid, applying backtracking to explore potential paths for forming the target word. Once a valid path is found, the search stops, returning true. If no valid path is found after checking all possibilities, return false.

Examples

Example 1

Input: board = [["A","B","C","E"],["S","F","C","S"],["A","D","E","E"]], word = "ABCCED"

Output: true

Example details omitted.

Example 2

Input: board = [["A","B","C","E"],["S","F","C","S"],["A","D","E","E"]], word = "SEE"

Output: true

Example details omitted.

Example 3

Input: board = [["A","B","C","E"],["S","F","C","S"],["A","D","E","E"]], word = "ABCB"

Output: false

Example details omitted.

Constraints

• m == board.length
• n = board[i].length
• 1 <= m, n <= 6
• 1 <= word.length <= 15
• board and word consists of only lowercase and uppercase English letters.

Solution Approach

Backtracking Search

The solution begins by iterating through each cell in the grid. From each starting cell, attempt to match the word by recursively exploring adjacent cells (up, down, left, right). Mark cells as visited during recursion to prevent revisiting. If a character matches and all characters of the word are found, return true. If no solution is found, backtrack to explore other possibilities.

Pruning Unnecessary Searches

Pruning is essential for optimizing performance. If a character doesn't match the target word at a certain cell, or if the number of remaining characters in the word is too large to fit within the grid boundaries, terminate the current recursive search. This reduces the number of paths explored, ensuring that only valid searches are pursued.

Edge Case Handling

Consider scenarios like when the word is larger than the grid or when the word can't be formed from any of the starting positions. Handle the cases where the word exists only if a precise sequence of adjacent cells is matched. Ensure that invalid paths (out of bounds or revisiting cells) are properly handled.

Complexity Analysis

The time complexity of this approach is O(m * n * 4^k), where m and n are the dimensions of the grid, and k is the length of the word. This is because each cell can potentially lead to 4 recursive calls, and the depth of recursion is limited by the word length. Space complexity is O(m * n) for the recursive call stack and visited cell tracking.

What Interviewers Usually Probe

• Do you know how to implement backtracking to solve problems like Word Search?
• Can you explain the role of pruning in reducing the complexity of backtracking?
• Will you consider edge cases like grid boundaries and revisited cells in your solution?

Common Pitfalls or Variants

Common pitfalls

• Forgetting to mark cells as visited during recursion, causing incorrect word matches.
• Not pruning invalid paths early enough, leading to unnecessary and time-consuming searches.
• Overlooking the case where the word exceeds the grid's size or cannot be constructed from adjacent cells.

Follow-up variants

• Can you solve Word Search for larger grids (e.g., 10x10)?
• How would you handle a grid containing multiple occurrences of the target word?
• What if the board was a 2D matrix containing numbers instead of letters?

How GhostInterview Helps

• Provides screenshots of the board and word input for easy visualization.
• Gives the answer path step-by-step with clear complexity explanations for interview clarity.
• Supports screen-sharing workflows to walk through recursive solutions and potential pitfalls in real-time.

Topic Pages

• Array
• String
• Backtracking
• Depth-First Search
• Matrix

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FAQ

What is the primary pattern used to solve the Word Search problem?

The primary pattern is backtracking search with pruning. By recursively exploring each cell and marking visited ones, unnecessary paths are eliminated.

How do you optimize the backtracking solution for Word Search?

Optimization comes from pruning invalid paths early, avoiding unnecessary recursion calls when a cell is out of bounds or the characters don’t match.

What are some common mistakes when solving Word Search using backtracking?

Common mistakes include failing to mark cells as visited or not handling edge cases like grid boundaries and revisiting cells.

Can the Word Search problem be solved iteratively?

While backtracking is the most natural solution for Word Search, it could be adapted to an iterative approach using a stack, but it would be less efficient.

What edge cases should be considered for Word Search?

Edge cases include when the word is longer than the grid, when no valid path exists, and when certain cells should not be revisited.