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Went with DFS plus backtracking which is the right call.
Use depth-first search (DFS) with backtracking to explore all possible paths from each cell that matches the first character of the word. At each step, check if the current cell matches the next character, mark it as visited, and recursively explore its four neighbors. If any path forms the word, return true; otherwise, backtrack and continue.
Pro tip: Mention that you can optimize space by temporarily modifying the grid to mark visited cells (e.g., replacing with a special character) instead of using a separate visited matrix, and restore it during backtracking. This shows attention to memory efficiency and in-place modification skills.
Confirm the problem constraints: grid dimensions, character set, whether the word can be empty, and if diagonal moves are allowed. Also discuss edge cases like empty grid or word longer than total cells.
Select DFS with backtracking as the primary approach. Explain why BFS is less suitable due to the need to track visited cells per path, which is naturally handled by DFS recursion.
Define a recursive function that takes the current cell coordinates and the index in the word. Base case: if index equals word length, return true. Check bounds, character match, and visited status before recursing.
Mark the current cell as visited before exploring neighbors. After exploring, unmark it (backtrack) to allow other paths to use it. Discuss using a separate boolean matrix or in-place modification.
Iterate over all cells as starting points. If any DFS returns true, return true. Discuss pruning: if the remaining word length exceeds available unvisited cells, return false early.
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