I went straight to dynamic programming but kept second-guessing whether the problem allowed revisiting cells.
Start by clarifying the problem constraints (e.g., maze size, obstacles, movement directions) and then explain a dynamic programming approach where dp[i][j] represents the number of unique paths to cell (i,j). Discuss how to handle obstacles and optimize space, and mention alternative approaches like BFS/DFS with memoization.
Pro tip: As a PM, emphasize the importance of understanding the problem's real-world constraints and trade-offs (e.g., time vs. space complexity) before diving into the algorithm. Show that you can translate technical solutions into product decisions.
Ask questions to understand the maze representation, allowed moves (e.g., right/down only or all four directions), obstacles, and constraints. Confirm whether paths are unique by cell sequence or by direction sequence.
Decide between dynamic programming (for grid with only right/down moves) or graph traversal (BFS/DFS with memoization) for more complex mazes. Explain why the chosen approach is suitable.
For DP, define dp[i][j] as the number of paths to cell (i,j). Derive the recurrence: dp[i][j] = dp[i-1][j] + dp[i][j-1] if no obstacle, else 0. Initialize base cases.
State time and space complexity (e.g., O(m*n) time and space for DP). Discuss potential optimizations like using a 1D array to reduce space to O(n).
Mention edge cases (e.g., no path, start/end blocked) and how to handle them. If time permits, discuss extensions like weighted paths or multiple destinations.
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