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My first instinct was plain BFS and I started coding it before realizing state is wrong if you don't track which keys you have.
Model the problem as a shortest path search in a state space where each state includes the current position and the set of keys collected. Use BFS to explore states in order of steps, since each move has unit cost. When encountering a door, only proceed if the corresponding key is in the collected set.
Pro tip: Mention that the state space can be reduced by only tracking keys that are actually present on the map, and that BFS guarantees the first time you reach the exit is the minimum steps. Also, note that revisiting cells is allowed but with different key sets, so visited states must include the key set.
Ask about grid size, number of keys, whether multiple keys of the same type exist, and if the exit is always reachable. Confirm that doors require the exact key and that keys are consumed or not.
Represent each state as (row, col, keys_bitmask) where keys_bitmask encodes which keys have been collected. Use a bitmask for efficiency if the number of key types is small.
Use a queue for BFS, starting from the initial state. For each state, explore four directions; if the next cell is a wall, skip; if it's a door, only proceed if the key is in the bitmask; if it's a key, update the bitmask. Mark visited states to avoid cycles.
When the exit cell is reached, return the current step count as the minimum. If the queue empties without reaching the exit, return -1 or indicate unreachable.
Discuss time complexity O(R*C*2^K) where K is number of key types, and space complexity similar. Mention potential optimizations like bidirectional BFS or A* if applicable.
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Pretty straightforward once you frame it as an unweighted graph over states.
Start by clarifying the problem context and why BFS is chosen over other algorithms like DFS or Dijkstra. Then explain the level-order traversal property of BFS and how it guarantees the shortest path in unweighted graphs, using a concrete example to illustrate.
Pro tip: Mention that BFS is optimal for unweighted graphs but not for weighted ones, and briefly note how you'd adapt if edge weights were introduced (e.g., Dijkstra). This shows you understand trade-offs and can anticipate follow-up questions.
Briefly summarize the problem, emphasizing that it involves finding the minimum number of steps or shortest path in an unweighted graph or grid.
State that BFS explores nodes in increasing order of distance from the source, making it ideal for finding shortest paths in unweighted graphs.
Explain how BFS processes nodes level by level, where each level corresponds to nodes at distance k from the source, ensuring the first time a target is reached, it's via the shortest path.
Mention that DFS might find a path but not necessarily the shortest, and Dijkstra's algorithm is overkill for unweighted graphs, though it generalizes BFS.
Summarize that because BFS visits nodes in non-decreasing order of distance, the first time the destination is dequeued, the path length is minimal.
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I listed a few: no keys exist at all (bitmask stays zero, doors just block you), exit is unreachable, multiple exits (return the min across all of them).
Systematically enumerate edge cases by category (input, boundary, structural, and performance) and explain how your solution handles each. Prioritize the most impactful edge cases for the problem and relate them to Pinterest's scale and data characteristics.
Pro tip: Tie edge cases to real-world scenarios at Pinterest, such as handling billions of pins or skewed user engagement, to show you think beyond correctness and consider production impact.
Restate the problem and ask clarifying questions about input size, data types, and expected behavior to identify potential edge cases.
Group edge cases into categories: empty/null inputs, boundary values, duplicates, ordering, and structural extremes (e.g., very large or small inputs).
Rank edge cases based on likelihood and severity, focusing on those that could cause failures or performance issues in production.
For each prioritized edge case, describe how your solution detects and handles it, including any trade-offs.
Mention how you would test these edge cases, such as unit tests or property-based testing, to ensure robustness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.