Assess students' ability to analyze and compare QuickSort, MergeSort, and HeapSort across worst-case and average-case time complexity, auxiliary space requirements, in-place vs. out-of-place behavior, and algorithmic stability; include evaluating practical considerations such as recursion depth, constant factors, cache behavior, and input patterns that trigger worst-case behavior. Tasks should require deriving or justifying time/space bounds, explaining when stability is required and its implementation costs, and selecting or defending the best algorithm for concrete, real-world scenarios (e.g., memory-limited systems, stable-sorting needs, or large datasets). Emphasize analytical reasoning, short proofs or sketches, and applied examples.