# Solution Alignment The prompt asks for an implementation-level answer. The safest way to present it is to define the state, maintain clear invariants, then walk through complexity and tests. ## Problem Restatement Define a minimal Iterator interface (e.g., hasNext(), next()) for integers without using IDE-generated scaffolding. Implement two iterator classes in Java: ( 1) FlattenIterator that iterates through a list of lists of integers, skipping empty lists; ( 2) FilterIterator that wraps any Integer iterator and yields only elements satisfying a provided predicate. Both must be robust to edge cases (empty input, single element, repeated hasNext() calls), throw appropriate exceptions when next() is invalid, and operate in O( 1) amortized time per element with O( 1) or O(depth) extra space as appropriate. Provide brief unit tests demonstrating correctness and discuss time/space complexity. ## Recommended Approach Start with a brute-force baseline to confirm correctness, then identify the repeated work or ordering property that enables a better data structure such as a hash map, heap, stack, queue, two pointers, prefix sums, BFS/DFS, or dynamic programming. Write the implementation around a small invariant and test that invariant directly. ## Correctness The implementation should maintain an invariant after each loop or operation that directly matches the problem statement. At termination, that invariant implies the returned value has considered every valid candidate exactly once, or has preserved the required data-structure state after every API call. ## Complexity State the baseline complexity and the optimized complexity. For most interview constraints, justify why the optimized approach meets the expected input size. ## Edge Cases and Tests Empty and singleton inputs, duplicates, ties, invalid inputs, boundary values, and tests that exercise the main invariant.