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Model the grid as a graph where each open cell is a node connected to its four neighbors. Use BFS from the start cell to find the shortest path to the target, tracking the number of moves. If the target is never reached, return -1.
Pro tip: Clarify edge cases upfront: what if start or target is blocked? What if they are the same cell? Handling these gracefully shows attention to detail. Also, mention that BFS is optimal for unweighted grids, but if the grid is huge, consider bidirectional BFS to reduce search space.
Confirm grid dimensions, movement rules (4-directional), and what constitutes a valid move. Ask about edge cases like blocked start/target or same start and target.
Recognize that this is a shortest path problem on an unweighted graph, so BFS is ideal. Mention that DFS would not guarantee shortest path.
Initialize a queue with the start cell and a visited set or distance matrix. Process cells level by level, exploring neighbors in all four directions.
Increment distance as you move to the next level. Return the distance when the target is reached; if the queue empties, return -1.
State time and space complexity: O(m*n) for both. Discuss potential optimizations like bidirectional BFS or early exit if target is found.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clearly defining the recursive DFS with backtracking and memoization: a function that explores all valid moves from the current cell, marks the cell as visited, recurses, then unmarks it. Use memoization to cache results for each cell to avoid redundant computations. Then compare with BFS, focusing on tradeoffs in time/space complexity, optimality, and practical use cases.
Pro tip: Emphasize that memoization in DFS is only valid if the problem has optimal substructure and overlapping subproblems; otherwise, it can lead to incorrect results. Also, mention that BFS is generally preferred for shortest path in unweighted grids, while DFS with memoization is better for counting paths or when memory is constrained.
Describe the recursive function that takes the current position and explores all valid neighboring cells, using a visited set to avoid cycles. After exploring, backtrack by unmarking the cell.
Add a memo table (e.g., 2D array) to store results for each cell, such as the number of paths from that cell to the target. Before recursing, check if the result is already computed; if so, return it.
State that with memoization, each cell is computed once, leading to O(m*n) time and space. Without memoization, it's exponential. Compare with BFS which is also O(m*n) time but uses O(m*n) space for the queue.
Discuss that BFS guarantees shortest path in unweighted graphs and is iterative (no recursion depth issues), while DFS with memoization can be more memory-efficient for certain problems (e.g., counting paths) and avoids storing all frontier nodes.
Summarize when to choose each: BFS for shortest path, DFS with memoization for counting paths or when the search space is deep and narrow, and mention that both can be adapted for weighted graphs with modifications.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.