(15 pts, 3 pts for each)) Based on what we have discussed in class, give the best asymptotic running time for each of the problems below, using the "big Oh" notation. It is assumed that T(1)=d for some constant d in all the recurrences. Just state the answers- you do not need to justify them. (1) Given a rod of length n inches and a table of prices pi for i=0,1,,n, determine the maximum revenue rn obtainable by cutting the rod and selling the pieces. (2) Quicksort on n elements in the worst case. (3) Sorting nd-digit numbers in which each digit can take on up to k possible values using RadiX-Sort(). (4) Select a maximum-size subset of mutually compatible activities in a set of n activities. (5) DELETE operation on a Fibonacci heap with n elements using amortized analysis