1. The factorial of 0 is defined to be 1. The factorial of a positive integer is defined to be the product of that integer times the factorial of the next smaller nonnegative integer. We use the notation n! to express the factorial of the integer n. Thus the factorial of 3 (written 3!) is 3 × (2!) = 3 × (2 × (1!)) x 3 × (2 × (1 × (0!))) = 3 × (2 × (1 × (1))) = 6. Design a recursive algorithm that computes the factorial of a given value.

2. a. Suppose you must sort a list of five names, and you have already designed an algorithm that sorts a list of four names. Design an algorithm to sort the list of five names by taking advantage of the previously designed algorithm. b. Design a recursive algorithm to sort arbitrary lists of names based on the technique used in (a).