factorial recursive algorithm analysis code example

Example 1: complexity analysis of factorial using recursion

T(n) = T(n-1) + 3   (3 is for As we have to do three constant operations like 
                 multiplication,subtraction and checking the value of n in each recursive 
                 call)

     = T(n-2) + 6  (Second recursive call)
     = T(n-3) + 9  (Third recursive call)
     .
     .
     .
     .
     = T(n-k) + 3k
     till, k = n

     Then,

     = T(n-n) + 3n
     = T(0) + 3n
     = 1 + 3n

Example 2: recursion factorial algorithm

FUNCTION FACTORIAL (N: INTEGER): INTEGER
(* RECURSIVE COMPUTATION OF N FACTORIAL *)

BEGIN
  (* TEST FOR STOPPING STATE *)
  IF N <= 0 THEN
    FACTORIAL := 1
  ELSE
    FACTORIAL := N * FACTORIAL(N - 1)
END; (* FACTORIAL *)