Took me a minute to even remember how quad trees work.
Clarify the quad tree definition: each node represents a submatrix and is a leaf if all values are identical, otherwise it has four children. Then use a recursive divide-and-conquer approach: check if the current submatrix is uniform; if so, create a leaf node; otherwise, split into four quadrants and recurse. Optimize by using prefix sums for O(1) uniformity checks.
Pro tip: Mention that this is similar to image compression and that the recursion depth is O(log n), so stack overflow is rarely an issue. Also, discuss how to handle non-square matrices by padding or defining quadrants appropriately.
Ask about matrix dimensions, value types, and whether the matrix is square. Confirm the quad tree node structure (e.g., val, isLeaf, topLeft, topRight, bottomLeft, bottomRight).
Write a function that takes the top-left coordinate and size of the current submatrix. It checks if all values are the same; if yes, returns a leaf node; otherwise, splits into four quadrants and recurses.
Use a 2D prefix sum to check if a submatrix is uniform in O(1) time, reducing overall complexity from O(n^2 log n) to O(n^2).
If the submatrix size is 1, return a leaf node. Ensure recursion terminates and correctly combines child nodes.
Discuss time and space complexity. Walk through a small example to verify correctness, and consider edge cases like empty matrix or all identical values.
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