a). Implement these two algorithms in the Java programming language and confirm that they give the same result (for the values they apply to!).

b). Show (by algebra!) That the recursive formula in the second recursive algorithm is correct, ie. that she gives n!

Consider the following classical recursive algorithm for computing the factorial n! of a non-negative integer n: FACTORIALn If n = 0 return 1 else return n FaCToriaL(n-1) The following recursive algorithm also computes the factorial function, but using a different grouping of the multiplications: FALLING(n,m): Compute ny (n-m)! return 1 else if m 1 return n else return FALLING(n, Lm/21) . FALLING (n--Lm/2],m/2) Consider the following classical recursive algorithm for computing the factorial n! of a non-negative integer n: FACTORIALn If n = 0 return 1 else return n FaCToriaL(n-1) The following recursive algorithm also computes the factorial function, but using a different grouping of the multiplications: FALLING(n,m): Compute ny (n-m)! return 1 else if m 1 return n else return FALLING(n, Lm/21) . FALLING (n--Lm/2],m/2)