Clarify the problem constraints (grid size, obstacles, start/exit representation) and then propose BFS as the optimal algorithm for unweighted shortest path. Walk through the BFS implementation, explaining how you track visited cells and distances, and analyze time and space complexity.
Pro tip: Mention that BFS is preferred over DFS because it guarantees the shortest path in unweighted graphs, and discuss potential optimizations like bidirectional BFS for large grids. Also, handle edge cases like start equals exit or no path exists.
Ask about grid dimensions, movement constraints, representation of start/exit, and whether obstacles are present. Confirm that the path length is the number of steps.
Explain that BFS is ideal for finding the shortest path in an unweighted grid. Mention that DFS would not guarantee the shortest path.
Describe using a queue to explore level by level, a visited set to avoid cycles, and tracking distance from start. Detail how to process neighbors in 4 directions.
State that time complexity is O(R*C) where R and C are grid dimensions, and space complexity is O(R*C) for the queue and visited set in the worst case.
Discuss cases like start equals exit (return 0), unreachable exit (return -1), and grids with no obstacles. Mention potential optimizations like bidirectional BFS.
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Model the maze as a graph where each state is (position, set of keys collected). Use BFS to find the shortest path, since all moves have equal cost. When encountering a door, only proceed if the corresponding key is in the set; when encountering a key, add it to the set.
Pro tip: Mention that the state space can be reduced by only tracking keys that are actually needed for doors on the path, but be prepared to discuss the trade-off between memory and simplicity. Also, note that BFS guarantees the shortest path in terms of steps, but if there are weighted moves, Dijkstra's algorithm would be needed.
Ask clarifying questions: Can multiple keys of the same type exist? Are keys reusable? Can doors be opened without keys? What are the grid dimensions? This ensures you understand constraints.
Represent each state as (row, col, keys_bitmask). Use a bitmask to efficiently track which keys have been collected, assuming a limited number of key types (e.g., up to 26).
Since each move costs 1, BFS explores states in order of increasing path length, guaranteeing the shortest path. Use a queue and a visited set to avoid revisiting states.
From a state, try all four directions. If the next cell is a wall, skip. If it's a door, check if the key is in the bitmask; if not, skip. If it's a key, update the bitmask. If it's the exit, return the distance.
Time complexity: O(R*C*2^K) where K is number of key types. Space: O(R*C*2^K). Discuss potential optimizations like pruning or A* if needed.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
I went straight to Dijkstra and the interviewer asked me to justify why not BFS.
Model the problem as a shortest path on a state graph where each state is (cell, energy), and use Dijkstra's algorithm with energy as part of the cost. Since energy can be refilled, the state space is finite if we cap energy at the maximum needed, and we can optimize by tracking the maximum energy achievable at each cell for a given cost.
Pro tip: Mention that you can reduce the state space by observing that you never need more energy than the maximum refill amount plus the distance to the exit, and that you can use a modified Dijkstra where you maximize energy for the same cost.
Ask about grid size, energy refill amounts, whether energy can exceed initial max, and if moves are 4-directional. Confirm that energy cannot go negative at any point.
Define state as (row, col, energy). Each move to an adjacent cell costs 1 energy, and landing on a refill cell adds its amount. The goal is to reach the exit with energy >= 0.
Use Dijkstra's algorithm where the cost is the number of moves (or total energy spent) and we track the maximum energy achievable for each cell at a given cost. Alternatively, use BFS with a priority queue on energy to avoid cycles.
Cap energy at a maximum value (e.g., max refill + grid size) to keep state space finite. Use a 2D array of best energy per cell to prune dominated states.
Time complexity O(R*C*E_max log(R*C*E_max)) where E_max is capped energy. Discuss trade-offs between BFS, Dijkstra, and A* if heuristic available.
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I knew this was TSP territory the second they said 'any order' and 'minimize total cost.' Held-Karp DP after precomputing pairwise BFS distances between all targets.
Recognize this as a variant of the Traveling Salesman Problem where you must visit K of N target cells (not all) and return to start, so the optimal strategy depends on K relative to N. Discuss both exact approaches (e.g., DP over subsets for small K) and heuristic/approximation approaches (e.g., greedy nearest neighbor, MST-based) for large K, and analyze trade-offs in time and solution quality.
Pro tip: Clarify constraints first (grid size, K, obstacles, movement rules) and state that if K is small, exact DP is feasible, but if K is large, you should discuss approximation algorithms and their guarantees—showing you understand practical engineering trade-offs.
Ask about grid dimensions, number of targets N, K value, movement allowed (4-directional vs 8-directional), obstacles, and whether targets can be revisited. This determines the appropriate algorithmic approach.
Represent the grid as a graph where nodes are start and target cells, and edge weights are shortest path distances (e.g., BFS for unweighted grid). This reduces the problem to finding a minimum-cost cycle visiting exactly K target nodes.
If K is small (≤ ~15), use dynamic programming over subsets (Held-Karp style) to find optimal tour. If K is large, use approximation algorithms like nearest neighbor, Christofides, or MST-based heuristics, and discuss their time complexity and approximation ratios.
Compare exact DP (O(2^K * K^2)) vs heuristics (O(K^2) or O(K^3)). Discuss memory usage, scalability, and whether optimality is required or a good-enough solution suffices.
Consider precomputing all-pairs shortest paths, pruning, or using A* for large grids. Handle cases like K=0, K=N, unreachable targets, and multiple optimal solutions.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Honestly the most interesting part of the whole thing.
Start by clearly defining the decision criteria for each algorithm based on graph properties (unweighted vs weighted, presence of heuristic) and performance trade-offs. Then, describe a modular code architecture where a common graph interface and traversal skeleton are reused, with algorithm-specific components plugged in. Emphasize how each algorithm builds upon the previous by generalizing the priority function and adding heuristics.
Pro tip: Mention that in practice, you'd often start with BFS for simplicity and only upgrade to Dijkstra or A* when performance requirements demand it, showing you balance engineering effort with optimization. Also, highlight that A* is essentially Dijkstra with a heuristic, so code reuse is natural.
Ask about graph size, edge weights, whether a heuristic is available, and if optimality is required. This determines which algorithm is suitable.
Explain when to use BFS (unweighted, shortest path in terms of edges), Dijkstra (weighted, non-negative, no heuristic), and A* (weighted with admissible heuristic for faster goal-directed search).
Propose a common graph representation (adjacency list) and a generic traversal function that takes a priority queue and a cost function. BFS uses a FIFO queue, Dijkstra uses a min-heap by distance, A* uses a min-heap by f-score.
Illustrate how BFS code can be refactored to Dijkstra by swapping the queue for a priority queue and adding distance tracking. Then, extend Dijkstra to A* by incorporating a heuristic in the priority calculation.
Mention time/space complexity, early termination, and practical considerations like using a visited set, handling negative weights, and heuristic admissibility.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.