Clarify the problem constraints (grid size, movement allowed, wall representation) and then propose a graph traversal algorithm such as BFS or DFS to determine reachability. Explain the algorithm step-by-step, analyze time and space complexity, and discuss potential optimizations or edge cases.
Pro tip: Mention that BFS is generally preferred for reachability because it finds the shortest path if one exists, and it can be more memory-efficient than DFS in wide grids. Also, highlight that you can stop early once the goal is found.
Ask about grid dimensions, movement directions (4-way or 8-way), wall representation, and whether the start and goal are guaranteed to be valid cells. Confirm if diagonal moves are allowed and if there are any constraints on memory or time.
Select BFS for shortest path and optimal reachability, or DFS for simpler implementation if only reachability matters. Consider A* if heuristic is available and performance is critical.
Describe initializing a queue with the start cell, marking visited cells, and iteratively exploring neighbors until the goal is found or the queue is empty. Emphasize handling boundaries and walls.
State that time complexity is O(R*C) for BFS/DFS, where R and C are grid dimensions, and space complexity is O(R*C) in the worst case due to the queue/stack and visited set.
Mention edge cases like start equals goal, unreachable goal, or no walls. Suggest optimizations like bidirectional BFS or using a visited matrix to avoid revisiting cells.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
BFS naturally gives you this if you track depth.
Model the grid as an unweighted graph and use BFS to find the shortest path length from start to goal. If the grid has weighted cells, use Dijkstra's algorithm instead. Clearly state the assumptions about movement (4-directional vs 8-directional) and obstacles.
Pro tip: Mention that BFS is optimal for unweighted grids and that you can optimize space by using a 2D distance array or in-place marking. Also, discuss how to handle edge cases like start equals goal or no path exists.
Ask about movement rules (4 or 8 directions), whether cells have weights, and if diagonal moves are allowed. Confirm if the grid contains obstacles and if start/goal are guaranteed to be valid.
For unweighted grids, BFS is optimal. For weighted grids, use Dijkstra's algorithm. Mention that A* with Manhattan distance heuristic can be more efficient if the grid is large and obstacles are sparse.
Use a queue to explore level by level, tracking visited cells to avoid cycles. Maintain a distance array or store distance in the queue. Return the distance when the goal is reached.
Time complexity is O(R*C) for BFS, where R and C are grid dimensions. Space complexity is O(R*C) for the visited set and queue. For Dijkstra, it's O(R*C log(R*C)).
Test with start equal to goal, no path, single row/column, and large grids. Discuss how to reconstruct the path if needed, not just the length.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Clarify that the problem is to find the shortest path and reconstruct the sequence of nodes, not just the distance. Choose an algorithm like BFS for unweighted graphs or Dijkstra/A* for weighted graphs, and maintain a predecessor map to backtrack from the target to the source. After computing the shortest distances, reconstruct the path by following predecessors and then reverse it to get the correct order.
Pro tip: Mention that you can reconstruct the path without storing the entire path at each step by using a parent pointer array, which saves memory and is efficient. Also, discuss how to handle multiple shortest paths or tie-breaking if the problem requires a specific one.
Confirm whether the graph is weighted or unweighted, directed or undirected, and whether we need any shortest path or a specific one. Ask about edge cases like no path existing.
For unweighted graphs, BFS is optimal; for weighted graphs with non-negative weights, use Dijkstra; for negative weights, Bellman-Ford. Mention A* if heuristic is available.
During traversal, maintain a parent array or map that records the previous node for each visited node. This allows reconstructing the path later.
Starting from the target node, follow the parent pointers back to the source, collecting nodes. Reverse the collected list to get the path from source to target.
If no path exists, return empty or appropriate message. Analyze time and space complexity: O(V+E) for BFS, O(E log V) for Dijkstra, plus O(V) for path reconstruction.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
They went with weighted cells, so BFS is out and you need Dijkstra.
Clarify the problem variant and constraints first, then choose the appropriate shortest-path algorithm (e.g., Dijkstra for weighted costs, BFS for unweighted, multi-source BFS for multiple goals). Discuss trade-offs between algorithms and data structures, and outline how to adapt the solution for portals or all shortest paths.
Pro tip: Always discuss time and space complexity and consider edge cases like negative weights or unreachable goals; showing awareness of these demonstrates maturity and thoroughness.
Ask questions to understand the exact variant: are there portals, weighted edges, multiple goals, or need for all shortest paths? Confirm constraints like grid size, edge weights, and whether weights are non-negative.
Select the algorithm based on the variant: BFS for unweighted, Dijkstra for non-negative weighted, Bellman-Ford for negative weights, or multi-source BFS for multiple goals. For portals, model them as additional edges or nodes.
Decide on representations: adjacency list or grid with implicit edges, priority queue for Dijkstra, queue for BFS, and distance arrays. For all shortest paths, consider storing predecessors or using BFS/Dijkstra with path tracking.
Discuss time and space complexity of your approach, and compare with alternatives. Mention how portals or multiple goals affect complexity and how to optimize.
Consider unreachable goals, negative cycles, large grids, and portals creating cycles. Walk through a small example to validate the approach.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.