Sparse Matrix Class (Store / Print / Add / Multiply)

After a ~15-minute resume shallow-dive, the MLE phone screen turns into an object-design coding task: build a class that stores a sparse matrix compactly and supports printing it back as a dense grid, matrix addition, and matrix multiplication. Requirements Design a class to store a sparse matrix (most entries are zero) in a compact representation. Support: Storage — hold non-zero entries without materializing the full dense grid. Print — render the matrix back as a normal dense 2-D grid (zeros filled in). Addition — add two sparse matrices, returning a new sparse matrix. Multiplication — multiply two sparse matrices. Notes The expected representation is a dictionary keyed by (row, col) -> value, storing only non-zero cells, with the matrix dimensions tracked separately so print can fill in zeros. Addition iterates the union of populated keys. Multiplication is where candidates stumble under time pressure: group the left matrix's entries by their column index k and the right matrix's by their row index k, then only multiply the overlapping non-zero k indices instead of looping the dense shapes. The MLE screen front-loads a ~15-minute resume shallow-dive before the coding starts — have a crisp project summary ready so it doesn't eat coding time. Preparation Implement the dict-of-(row, col) class with add and multiply once end-to-end; the shared-inner-index k multiplication is the part to rehearse. Pre-draft the print method that reconstructs the dense grid so you don't burn live time on it.