Clarify the movement constraints (e.g., right/down only vs. all four directions) and whether costs are non-negative, as this determines the algorithm. For right/down only, use dynamic programming with a 2D table; for all directions with non-negative costs, use Dijkstra's algorithm. Discuss time and space complexity and possible optimizations.
Pro tip: At Amazon, emphasize scalability and real-world constraints: mention that if the matrix is huge, you can optimize space to O(n) using a 1D DP array, and discuss how the solution would change if costs could be negative (requiring Bellman-Ford).
Ask about allowed moves (right/down only or all four directions), cost values (non-negative?), and matrix size. This determines the algorithm choice.
If only right/down moves, use dynamic programming; if all directions with non-negative costs, use Dijkstra's algorithm. Explain why the chosen algorithm is optimal.
For DP, define dp[i][j] as min cost to reach (i,j) and recurrence dp[i][j] = cost[i][j] + min(dp[i-1][j], dp[i][j-1]). For Dijkstra, define state as (cost, row, col) and use a priority queue.
Write pseudocode, handle base cases, and analyze time and space complexity. Mention possible optimizations like space reduction for DP.
Walk through a small example, test edge cases (1x1 matrix, single row/column), and discuss how the solution scales.
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