Model the maze as a graph and use BFS to find the shortest path because all edges have equal weight. Start from the start cell, explore level by level, and return the distance when the target is reached; if the queue empties, return -1.
Pro tip: Clarify edge cases upfront (e.g., start == target, out-of-bounds, or blocked start/target) and mention that BFS guarantees the shortest path in unweighted grids. Also, discuss space complexity and potential optimizations like bidirectional BFS for large mazes.
Confirm grid dimensions, movement rules, and what to return if start or target is invalid or blocked. Discuss edge cases like start equals target.
Explain that BFS is optimal for unweighted shortest path problems. Mention that DFS would not guarantee the shortest path.
Initialize a queue with the start cell and a visited set. While the queue is not empty, dequeue a cell, check if it's the target, and enqueue all valid unvisited neighbors with distance+1.
State time and space complexity O(rows * cols). Mention potential optimizations like bidirectional BFS or early termination when target is found.
Walk through a small example to verify correctness, including a case where the target is unreachable.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Tripped up slightly on the path reconstruction.
Use BFS to find the shortest path length, but during traversal, store the predecessor of each visited cell. After reaching the target, backtrack from the target to the start using the predecessor map to reconstruct the path.
Pro tip: Clarify early whether the maze allows diagonal moves and whether the path should be returned as a list of coordinates or directions. Also, mention that BFS guarantees the shortest path in unweighted grids, so no need for Dijkstra.
Ask about movement rules (4-directional vs 8-directional), start/end points, and expected output format for the path.
Explain that BFS is optimal for unweighted shortest path. Use a queue for BFS and a separate structure (e.g., dictionary or 2D array) to record each cell's predecessor.
During BFS, when exploring neighbors, if a neighbor is unvisited, mark it visited, set its predecessor to the current cell, and enqueue it.
Once the target is reached, start from the target and follow predecessors back to the start, then reverse the sequence to get the path from start to end.
Discuss cases like no path, start equals end, and analyze time/space complexity (O(R*C) for both).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Model the maze as a graph and use BFS to find the shortest distance from start to all reachable cells. Then, process cells in increasing order of distance, computing the number of shortest paths to each cell by summing the counts from its predecessors that are one step closer. Apply modulo 1,000,000,007 at each addition to prevent overflow.
Pro tip: Clarify the maze representation (e.g., grid with obstacles, 4-directional movement) and whether 'distinct' paths are defined by different sequences of moves. Also, mention that if the graph is unweighted, BFS is optimal; if weighted, Dijkstra's algorithm is needed.
Ask about the maze structure (grid size, obstacles, movement directions) and confirm that 'shortest paths' means minimum number of steps. Ensure modulo is applied to the final count.
Represent each cell as a node and edges between adjacent passable cells. This abstraction helps in applying standard graph algorithms.
Run BFS from the start to compute the shortest distance to every reachable cell. If the target is unreachable, return 0.
Initialize path count to 1 at start. Process cells in increasing distance order; for each neighbor with distance one greater, add the current cell's path count to the neighbor's count modulo 1e9+7.
After processing all cells, the path count at the target is the answer. If target was unreachable, it remains 0.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
3D BFS with state (row, col, walls_remaining).
Model the problem as a shortest path search on an expanded state space where each state is (row, col, walls_broken). Use BFS since each move costs 1, and track the minimum steps to reach the target with at most k walls broken. Discuss trade-offs between BFS and other approaches like Dijkstra or A* if costs vary.
Pro tip: Clarify early whether 'breaking a wall' means moving onto a wall cell or destroying it permanently; this affects state definition and visited tracking. Also mention that BFS on the expanded graph is optimal because all edges have unit weight, but if k is large, consider bidirectional BFS or A* with a heuristic to reduce search space.
Ask about grid size, movement directions (4 or 8), whether start/target can be walls, and if breaking a wall consumes a step. Confirm that k is an integer and walls are impassable unless broken.
State = (r, c, w) where w is walls broken so far (0 ≤ w ≤ k). From a cell, move to adjacent non-wall cells with same w, or to wall cells with w+1 if w < k. Each transition costs 1 step.
Use BFS because all edges have unit weight. Maintain a 3D visited array or a 2D array storing min walls broken to reach each cell, to avoid revisiting states with more walls broken.
Use a queue for BFS, track steps as level order. Early exit when target is reached. Discuss optimizations like bidirectional BFS or A* if k is large, and memory trade-offs of 3D visited vs. 2D with min walls.
Time: O(m*n*k) since each cell can be visited with up to k walls broken. Space: O(m*n*k) for visited. Handle cases where target is unreachable even with k walls, or k ≥ number of walls.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Model the problem as a shortest path search where the state includes the current cell and the number of bombs remaining. Use BFS with state (row, col, bombs_left), and when moving to an adjacent cell, if it's a wall, you can either detonate a bomb (if bombs_left > 0) to clear a cross shape, or go around. Precompute the effect of detonating a bomb at each cell to quickly check if a wall is destroyed.
Pro tip: Clarify with the interviewer whether bomb detonation is instantaneous and whether the cross destruction is permanent, and discuss the trade-off between BFS with state and A* with a heuristic like Manhattan distance to handle larger grids efficiently.
Ask about grid size, bomb count, whether walls are permanently destroyed, and if detonation counts as a step. Confirm movement rules (4-directional?) and if start/target can be walls.
State is (r, c, bombs_left). From a cell, you can move to adjacent non-wall cells (cost 1). If adjacent cell is a wall and bombs_left > 0, you can detonate a bomb (cost 1) to clear a cross shape, then move into that cell (cost 1) or stay? Clarify if detonation and move are separate steps.
For each cell, precompute the set of walls destroyed if a bomb is detonated there. This allows O(1) lookup during BFS to check if a wall is cleared.
Use BFS to find the shortest path from start to target, exploring states in order of steps. Use a visited set to avoid revisiting states. If bombs_left is part of state, the state space is O(R*C*(b+1)).
Time complexity O(R*C*(b+1)) for BFS, plus precomputation O(R*C*(R+C)). Discuss potential optimizations like A* with Manhattan distance, or bidirectional BFS if b is small.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.