Design the object model and public API for a sparse matrix that stores only non-zero cells, supporting element access, row / column iteration, and basic arithmetic without ever materializing the dense grid.

Operating context. One process, in-memory. Logical dimensions can be enormous (say a million by a million) while non-zero density is tiny. A storage strategy — dictionary-of-keys, coordinate list, or compressed-sparse-row — is chosen per workload behind one interface. It backs graph adjacency and recommendation-feature matrices where most entries are zero.

Out of scope. Persistence or on-disk formats, distributed / blocked matrices, a dense-matrix fallback path, GPU or BLAS acceleration, and heavy factorizations such as LU or QR — keep to storage, access, transpose, add, and multiply.

What to produce. The class model (a SparseMatrix interface with pluggable storage backends), the public API (get, set, nonZeroCount, transpose, add, multiply, iterate non-zeros), the coordinate-to-storage mapping for the chosen backend, and how setting a cell to zero removes its entry rather than storing a zero — state the storage invariant explicitly.