← Pure Storage Interview Insights
Started at the brute force O(n^4) and worked down from there.
Clarify the problem: determine if the grid is a binary matrix where 1s represent possible square corners, or if all cells are valid. Then, for each possible top-left corner and size, check if all four corners are 1s (or if all cells are valid). Optimize by precomputing prefix sums or using dynamic programming to count squares efficiently.
Pro tip: Mention that the brute-force approach is O(n^3) or O(n^4), but you can optimize to O(n^2) using dynamic programming or prefix sums, showing you consider scalability. Also, discuss trade-offs between time and space complexity.
Ask whether the grid is binary (1s and 0s) and whether squares must have all four corners as 1s or all cells as 1s. Confirm if squares can be of any size and orientation (only axis-aligned).
Explain that you can iterate over all possible top-left corners and sizes, and for each, check if the square is valid. Analyze time complexity: O(n^3) for checking all cells or O(n^4) if checking each cell individually.
Propose using prefix sums to check if a square is all 1s in O(1) time, reducing overall complexity to O(n^3). Alternatively, use dynamic programming to count squares with all 1s in O(n^2) time.
Consider empty grid, non-square grids, and large inputs. Discuss memory usage and whether the grid can be modified in-place.
Restate the chosen approach, its complexity, and why it's optimal for the given constraints. Mention potential follow-up optimizations if needed.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.