Does the abstract in-place merge produce proper output if and only if the two input subarrays are in sorted order? Prove your answer, or provide a counterexample.

Question 3  Full explain this question and text typing work only have

Create a compare-based MinPQ API implementation where the minimum deletion requires 2 log N comparisons and the minimum insert uses log log N compares.Hint: To locate the ancestor in swim(), use binary search on parent pointers.

Dr. Sponge thinks it's too hard to implement Merge. So, he wants to replace Merge with Insertion Sort (yes, the insertion sort you learned in class). The following is the pseudo-code of the new Merge-Sort, Merge-Sort(p, r) 1. if p == r return 2. q = floor of (p+ r) / 2 3. Merge-Sort(p, q) 4. Merge-Sort(q+1, r) 5. Insertion-Sort(p, r) Give the recurrence for the running time of this new Merge-Sort and solve it. We let T(n) denote the running time when input array has n elements. By solving the recurrence (no need to show how you solved it), we obtain T(n) =