Problem 1 Solve the recurrence relationship for the factorial function. Problem 2 The tower of Hanoi is a puzzle invented in 1883 by E. Lucas. A stack of n disks arranged from largest on the bottom to smallest on top placed on a rod along with two empty rods The objective of the puzzle is to find the minimum number of moves required to move the entire stack to an empty rod. However moves are allowed only if they place smaller disks on top of larger disks and only one disk can be moved at a time. Figure 1 shows a solution for a 4 disk puzzle Solve the recurrence relationship for the number of moves. Figure 1: Solution for the Tower of Hanoi where N = 4. Problem 3 Consider the following algorithm: int S(int n) if (n1) return 1: return S(n 1) n*nn a. What does this algorithm do? b. Solve the recurrence relationship for the algorithm's basic operation c. How does this algorithm compare with a non-recursive algorithm