I started with the brute force scan, which is just iterating every cell, grouping by block index (row/3, col/3), tracking the min per block, then comparing across blocks.
First, clarify the problem constraints and edge cases, then propose a straightforward O(m*n) scan that computes the minimum of each 3x3 block and tracks the global minimum. After establishing correctness, discuss potential pruning optimizations such as early termination or skipping blocks whose partial minimum already exceeds the current global minimum.
Pro tip: Emphasize that the O(m*n) solution is optimal in the worst case because every cell must be examined at least once, but mention that pruning can improve average-case performance when the global minimum is found early.
Ask about grid dimensions (m, n), whether they are multiples of 3, and how to handle incomplete blocks. Confirm the return format: just the minimum value or also coordinates.
Iterate over each 3x3 block (non-overlapping), compute its minimum by scanning its 9 cells, and keep track of the global minimum and its block coordinates.
Explain that the algorithm visits each cell exactly once, so time is O(m*n) and space is O(1) beyond input storage. This is optimal since every cell must be read.
Propose early termination: if during a block scan the running minimum is already greater than or equal to the current global minimum, skip the rest of that block. Also consider processing blocks in an order likely to find a small minimum early.
Address grids not divisible by 3 (ignore leftover rows/columns or define partial blocks). Summarize that the simple scan is optimal, and pruning can help in practice.
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