Sounds trivial but I spent way too long on it because one of the test cases in the starter project is intentionally broken.
First, clarify the current rendering logic and identify where the path symbol overwrites S and E. Then, propose a priority-based rendering approach that ensures S and E are always drawn last or checked first, and discuss how to implement it cleanly.
Pro tip: Mention that you would add a unit test to prevent regression, showing you care about maintainability and not just a quick fix.
Examine the code to see the sequence in which cells are printed, and identify where the path symbol is written over S and E.
Establish that S and E have higher priority than the path symbol, and decide on a clear precedence order (e.g., S > E > path > wall).
Modify the display logic to check for S and E first, or render them last, ensuring they are never overwritten.
Run the maze printer with various mazes to confirm S and E are always visible, and add a regression test.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, explain that BFS runs forever when the visited set is missing or incorrectly updated, causing cycles to be re-explored indefinitely. Then, describe the fix: mark nodes as visited when enqueuing them, not when dequeuing, and ensure the visited set is checked before adding neighbors to the queue.
Pro tip: Mention that marking visited at enqueue time prevents duplicate entries in the queue, which is a common subtle bug that can also cause exponential memory usage even if the search terminates.
Recognize that infinite BFS typically means the algorithm is revisiting nodes, often due to a missing or ineffective visited set.
Explain how cycles in the maze graph cause BFS to loop if nodes are not marked as visited, leading to an infinite queue.
State that the visited set is either not used, or nodes are marked visited only when dequeued, allowing duplicates to be enqueued.
Mark nodes as visited immediately when they are enqueued, and check visited status before enqueuing neighbors.
Confirm the fix prevents infinite loops and discuss how enqueue-time marking also optimizes memory and time.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
The tricky part is deciding where to apply the constraint: on entry to the gate cell or on exit from it.
Clarify the exact movement rules for directional gates, then modify the neighbor-generation function to filter moves based on the gate's arrow. Keep the core BFS/DFS logic unchanged, and test with edge cases like gates at boundaries or conflicting directions.
Pro tip: Mention that you'd encapsulate the gate logic in a helper function to keep the main traversal clean and testable, and discuss how this change affects time/space complexity (still O(R*C) with constant extra work per cell).
Ask whether a gate cell allows only the indicated direction or also blocks entry from other directions. Confirm if gates can be at start/end and whether they override normal movement.
Locate the function that generates valid neighbors for a given cell. This is typically where you check boundaries and obstacles.
For each candidate neighbor, if the current cell is a gate, only allow the move if it matches the gate's direction. Alternatively, if the neighbor is a gate, ensure the move direction is allowed by that gate.
Consider gates at the maze edges, multiple gates, and gates that might create dead ends. Ensure the algorithm still terminates and finds a path if one exists.
Write unit tests for various gate configurations. Discuss time/space complexity: still O(R*C) since each cell is processed once, with O(1) extra check per neighbor.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This is the one that actually tests whether you understand BFS state space expansion.
Explain that the search state must be augmented to include the set of keys collected so far, since the same position can be reachable with different key sets. Use BFS where each state is (position, key_bitmask), and only allow transitions through doors if the corresponding key bit is set. Discuss how this affects visited tracking and state space size.
Pro tip: Mention that using a bitmask for keys is efficient and that the state space becomes O(R*C*2^K), which is manageable for small K. Also note that you can precompute which keys are reachable without doors to optimize, but the core idea is state augmentation.
The state should be (row, col, keys_bitmask), where keys_bitmask represents the set of keys collected. This captures all necessary information to determine valid moves.
Use a 3D visited array or a set of (row, col, keys_bitmask) to avoid revisiting the same state. A position alone is insufficient because different key sets enable different future paths.
When moving to a new cell, if it's a key, update the bitmask by setting the corresponding bit. If it's a door, only allow the move if the matching key bit is already set.
The state space is O(R*C*2^K) where K is the number of distinct keys. BFS time and space are proportional to this, which is feasible for small K (e.g., K ≤ 10).
Mention that you can precompute connected components of open areas and keys, or use bidirectional BFS, but the bitmask state is the fundamental change.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Reach territory, added recently from what I understand.
First, clarify the problem constraints and define the bomb's effect precisely. Then, design a helper to compute affected walls and integrate it into the search state, likely by tracking bomb usage and modifying the graph dynamically. Finally, discuss trade-offs between precomputation and on-the-fly updates, and analyze complexity.
Pro tip: Demonstrate awareness of state-space explosion: if the bomb can be used multiple times, the state must include remaining bombs or a bitmask of destroyed walls. Also, consider that destroying walls may create shortcuts, so the search must adapt.
Ask about bomb radius, whether it can be used once or multiple times, if walls are permanently destroyed, and if the bomb affects only walls or also other entities. Confirm the goal: shortest path? minimum bombs?
Given a bomb position, iterate over all walls within the radius (e.g., using Manhattan or Euclidean distance) and mark them as destroyed. Optimize by precomputing wall positions in a grid or using spatial indexing if needed.
Decide how to represent the modified maze in the search state. Options: include a bitmask of destroyed walls (if few), or recompute dynamically. Ensure the state captures enough to avoid revisiting equivalent configurations.
Use BFS for unweighted grids, Dijkstra/A* for weighted. Modify the algorithm to consider bomb usage as an action that transitions to a new state with updated walls. Handle visited states carefully to account for different wall configurations.
Discuss time/space complexity with and without bomb. Compare precomputing all possible bomb effects vs. on-the-fly computation. Mention potential optimizations like bidirectional search or heuristic guidance.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Clarify the problem constraints (grid size, energy costs, movement directions) and then model it as a shortest path problem on a weighted graph. Discuss Dijkstra's algorithm as the optimal solution for non-negative weights, and compare it with BFS or A* if heuristics apply.
Pro tip: Mention that if energy costs are uniform, BFS suffices, but for arbitrary non-negative costs, Dijkstra's is necessary; also note that if negative costs exist, Bellman-Ford would be required, though that's unlikely in this context.
Ask about grid dimensions, movement directions (4-way or 8-way), whether energy costs are non-negative, and if the start and exit are fixed. Confirm that the goal is to minimize total energy consumed.
Represent each cell as a node and possible moves as edges with weights equal to the energy cost of entering the destination cell. This transforms the problem into finding the shortest path from start to exit.
For non-negative weights, Dijkstra's algorithm is optimal. If all weights are equal, BFS is simpler and more efficient. If a heuristic like Manhattan distance is admissible, A* can speed up the search.
Dijkstra's with a priority queue runs in O(E log V) time, where E is edges and V is vertices. For a grid, this is O(N log N) where N is number of cells. Discuss space complexity and potential optimizations like early termination when the exit is reached.
Consider unreachable exit, negative costs (if allowed), and large grids. Walk through a small example to verify the approach and discuss potential pitfalls like integer overflow.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.