My first instinct was plain BFS and I coded half of it before realizing the state space is wrong.
Model the problem as a shortest path search on an expanded state space where each state includes the current position and the set of keys collected. Use BFS to explore states in increasing order of steps, since each move costs 1. Return the minimum steps when reaching the exit with any key set.
Pro tip: Before coding, clarify constraints (grid size, number of keys) to choose the right state representation—bitmask for keys is efficient for up to ~10 keys. Also, mention that BFS guarantees the shortest path because all edges have equal weight.
Ask about grid dimensions, number of keys, and whether multiple keys of the same type exist. This determines the state space size and representation.
Represent each state as (row, col, keys_bitmask). Use a bitmask to track collected keys efficiently, enabling constant-time key checks and updates.
Use a queue to perform BFS from the start state. For each state, explore four directions; if a door is encountered, only proceed if the corresponding key bit is set.
Maintain a visited set to avoid revisiting states. When the exit cell is reached, return the current step count as the minimum.
Discuss time and space complexity: O(R*C*2^K) where K is number of keys. Mention potential optimizations like early exit or bidirectional BFS if needed.
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The brute force is obvious and I wrote it first, which I think was the right call to show I understood the problem.
Clarify the problem constraints and tie-breaking rules, then propose a trie built on reversed words to efficiently find the longest common suffix for each query. Discuss complexity, trade-offs, and how you would benchmark the solution against a brute-force baseline.
Pro tip: Mention that you would preprocess the word list into a trie and store the best candidate at each node based on the tiebreakers, so each query is answered in O(L) time where L is the query length. Also, highlight that benchmarking should include realistic data distributions and measure both time and memory.
Ask about input sizes, expected query patterns, and the exact tie-breaking rules (longest suffix, then shortest word length, then smallest index).
Propose building a trie from the reversed words, where each node stores the best word (according to tiebreakers) that passes through it.
For each query, traverse the trie from the reversed query characters, keeping track of the deepest node that has a stored word, and return that word.
Explain that preprocessing takes O(N * L) time and O(N * L) space, and each query takes O(L) time, which is optimal for this problem.
Describe how to benchmark against brute force using large random datasets, measure time and memory, and discuss potential optimizations like memory pooling or compression.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.