Question 1 Show,
Show that if merge-sort was done by dividing the array into 3 equal parts, rather than 2, the asymptotic time required to solve it wouldn't change.
Note: To completely solve this problem, you need to first explain how the algorithm (esp. merge) works with 3 sub-problems (and compute the runtime of merge), and then solve the recursion.
Solve the recurrence .
Rewrite the counting sort algorithm such that the last loop iterates from the first item to the last item. Make sure that it is still a stable sorting algorithm. Demonstrate the working of your algorithm.