Mergesort does have a worst-case time of (NlgN) but its overhead (hidden in the constant factors) is high and this is manifested near the bottom of the recursion tree where many merges are made. Someone proposed that we stop the recursion once the size reaches K and switch to insertion sort at that point. Analyze this proposal (by modifying the recurrence analysis of standard mergesort) and prove that its running time is (NK + Nlg(N/K)).

4. Mergesort does have a worst-case time of (NigN) but its overhead (hidden in the constant factors) is high and this is manifested near the bottom of the recursion tree where many merges are made. Someone proposed that we stop the recursion once the size reaches K and switch to insertion sort at that point. Analyze this proposal (by modifying the recurrence analysis of standard mergesort) and prove that its running time is (NK + Nlg(N/K))