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Took me a minute to even understand what 'cut' meant here.
Treat this as a 2D bin packing problem with exact square placements. Use backtracking with pruning: sort squares in descending order, try placing each square at the first available cell, and backtrack if placement fails. Optimize with memoization or bitmask for small grids, and discuss heuristics for larger inputs.
Pro tip: Mention that the problem is NP-hard in general, so for large grids you'd use heuristics or note that exact solutions are only feasible for small inputs. This shows awareness of computational limits and practical engineering trade-offs.
Ask about grid size limits, number of squares, and whether squares can be rotated (they can't, since they're squares). Confirm that squares must align with integer grid lines and cannot overlap.
Propose backtracking with pruning: sort squares descending by size, maintain a grid occupancy matrix, and recursively place each square at the first empty cell. For small grids, use bitmask DP; for larger, discuss heuristics like greedy with backtracking.
Describe the recursive function: find the first empty cell, try placing the current square if it fits, mark cells as occupied, recurse to the next square, and unmark on backtrack. Prune if remaining area is insufficient or if a square cannot fit anywhere.
State that worst-case time is exponential, but pruning and sorting reduce practical runtime. Mention memoization of grid states (e.g., using bitmask for small grids) and symmetry breaking to avoid redundant states.
Test with empty list, squares larger than grid, total area exceeding grid, and cases where squares fit perfectly. Also consider grids with dimensions smaller than some squares.
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