Design and Implement a Lazy Array with Testable Laziness

Problem: Implement a Lazy Array and Explain How to Test Its Laziness Implement a lazily-evaluated array/sequence LazyArray. Requirements LazyArray should be defined by a generator/computation function for element values, instead of computing all elements eagerly. An element is computed only when it is accessed (e.g., by index) or when a materialization is triggered. Decide whether to cache computed elements (if not specified, explain your choice and implement accordingly). Interface (you may adjust as long as it is consistent) __len__(): return the length. get(i) / __getitem__(i): return the i-th element. materialize(): return a normal Python list (or equivalent), computing all elements. Discussion How would you test that the implementation is truly lazy? Provide actionable testing ideas (e.g., using a side-effectful function to verify “not computed until accessed”, and to verify caching behavior). Constraints n up to 1e5. Access should be as close to amortized O(1) as possible (if cached). Example (illustrative) Input: n=5, f(i)=i*i Operation: get(3) Output: 9 Example Input n=5, f(i)=i*i; ops: get(3) Output 9