Implement a Lazy Array (Deferred Evaluation)

Implement a Lazy Array (deferred-evaluation array) that computes elements only when they are accessed. Requirements: Design a data structure representing an array of length n, where elements are not computed at initialization time but only upon access. Provide APIs (names may vary, semantics must match): get(i): return the value at index i (0-indexed). The first access triggers computation. (Optional) set(i, value_or_fn): set a concrete value or a function that can produce the value. (Optional) initialize from a generator function f(i) such that element i is computed by calling f(i). Explain/implement: How laziness is guaranteed (unaccessed indices are never computed). Whether repeated get calls recompute or cache results. Describe how you would test laziness (e.g., counters/logging/mocks to prove unaccessed elements are never evaluated). Suggested scale: n up to 1e5. Provide at least 5 test cases covering: Unaccessed elements must not be computed Repeated access to the same index Boundary indices Large-scale access Mixed set/get (if supported) Example Input n=5, gen(i)=i*i; do not call get Output gen is never invoked (evaluation count = 0)