Evaluate learners' ability to analyze and compare time and space trade-offs among quicksort, mergesort, heapsort, and insertion sort, including best/average/worst-case time complexities, auxiliary space requirements, in-place vs stable behavior, and practical performance on varied inputs (random, nearly sorted, reverse-sorted, small N). Require justification for algorithm choice in given scenarios and brief explanations or examples illustrating where each algorithm excels or fails.