Start by clarifying the problem constraints (grid size, word length, case sensitivity) and then propose a brute-force approach that checks each cell as a starting point and each of the 8 directions, moving step by step. Then analyze the time complexity as O(R*C*8*L) and space as O(1) (or O(L) if recursive), and discuss optimizations like early termination, pruning, and avoiding redundant checks by not re-scanning the same path from different starting points.
Pro tip: Mention that you can precompute the first and last characters of the word and only start from cells matching the first character, and also check if the last character matches before traversing the full path to prune early. This shows attention to constant-factor optimizations that matter in production systems.
Ask about grid dimensions, word length, whether the word can be empty, and if the grid can contain non-uppercase characters. This ensures you handle all cases correctly.
For each cell, try all 8 directions, and for each direction, check if the word matches by moving step by step. This is straightforward and easy to implement.
Time: O(R*C*8*L) where R,C are grid dimensions and L is word length. Space: O(1) iterative, O(L) recursive due to call stack. Discuss how this scales.
Prune by checking first and last characters, stop early if out of bounds or mismatch, and avoid re-checking the same path from different starting points by only starting from cells that match the first character.
Mention if the grid is large and many queries are expected, pre-processing (e.g., building a trie or suffix automaton) might be beneficial, but for a single query, brute-force is optimal.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This is where I spent most of my time and honestly where things got messy.
Start by clarifying the problem: given a grid of characters and a target word, determine if the word can be formed by a path of orthogonal moves without revisiting cells. Then describe a backtracking DFS that explores all possible starting cells and paths, with pruning and memoization where possible. Finally, analyze time and space complexity, contrast with the fixed-direction version, and address edge cases and scalability.
Pro tip: Emphasize that the worst-case complexity is exponential, but in practice, pruning (e.g., early termination, frequency checks) and memoization on (cell, index) states can drastically reduce the search space. Also, mention that for very large grids or long words, you might need to consider bidirectional search or A* with heuristics.
Restate the problem: find a simple path (no repeated cells) in a grid where consecutive cells are orthogonal neighbors and the characters spell the target word. Ask about grid size, word length, and whether multiple paths are allowed.
Use DFS with backtracking: for each cell matching the first character, recursively explore all four directions, marking cells as visited and unmarking on backtrack. Prune by checking if remaining characters can possibly be formed (e.g., character frequency).
Time: O(N * M * 4^L) worst-case, where N*M is grid size and L is word length, but often much less due to pruning. Space: O(L) for recursion stack and visited set. Contrast with fixed-direction version which is O(N*M*L) if direction is fixed.
Empty word: return true. Single character: check if it exists in grid. Repeated letters: ensure visited set prevents reuse. Large grids: discuss optimizations like memoization, bidirectional search, or limiting search to cells with matching characters.
Mention that while backtracking is straightforward, it may be slow for large inputs. Suggest optimizations: pre-check character counts, use bitsets for visited, or employ heuristic search (A*) if applicable.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.