Evaluate students' ability to analyze time and space trade-offs among quicksort, mergesort, heapsort, and insertion sort across input characteristics (sorted, reverse-sorted, random, nearly-sorted, small arrays). Assess understanding of best/average/worst-case time complexities, auxiliary space (in-place vs extra memory), stability, recursion/iterative overhead, cache and constant-factor effects, and practical algorithm selection. Tasks should include comparing algorithms for given scenarios, justifying choices with theoretical and empirical reasoning, and interpreting simple performance measurements.