Question 10494 – Time-Complexity

Consider the function F(n) for which the pseudo code is given below:

     Function F(n)
     begin
     F1 ← 1
     if(n=1) then F ← 3
     else For i = 1 to n do
                       begin
                       C ← 0
     For               j = 1 to F(n – 1) do
                       begin C ← C + 1 end
                       F1 = F1 * C
     end
                       F = F1
     end
     [n is a positive integer greater than zero] 

(a) Derive a recurrence relation for F(n)
(b) Solve the recurrence relation for a closed form solutions of F(n).

Correct Answer: A