RecursionExamples with Iterative Versions

Numerical examples:

FACTORIAL

/*  recursive   */
int fact (n) {
   if (n == 1) return 1;
   return n * fact(n-1);
   |
  
/*   iterative   */
int fact(n) {
    retValue = 1;
    for (int i = n; i > 0; i--) {
       retValue *= i;
       }
    return retValue;
    }
    
        
// tail recursion version 

int factorial(n) {
   return tfact(n, 1);
   }
   
int tfact(n, acc){
   if (n==0) return acc;
   return tfact(n-1, n*acc);
   }
   
/* iterative version of tail recursion */

int iTfact(n) {
    acc = 1;
    for (i = 1; i <= n; i++) {
       acc = i * acc;
       }
    return acc;
    }
    
/********************************************/

LIST EXAMPLES

Definition of list:
  empty list: ()
  an element pushed onto a list:  push a onto () -> (a)
  
Definition of list from the perspective of dynamic linked list:
   a list is linked nodes. 
   head points to the first element of the list.
   Each node points to the following node in the list.
   The final node in the list has null in the next field.
   
Operations on a list:
  head(list) returns the first element of the list
  tail(list) returns the list with the first element removed
  append(a, list) returns the list formed by adding a as the new first element
Examples:
  list = ( 1, 2, 3 )
  head(list) --> 1
  tail(list) --> ( 2, 3 )
  append(4, list) --> ( 4, 1, 2, 3 )
  
 
 /*******************************************************/
 
 NUMBER OF ELEMENTS IN A LIST
 
 // recursive
 
 int length(list) {
   if ( isEmpty(list) )  return 0;   
   return 1 + length ( tail(list) );
   }
 
 // iterative
 
 int length(list) {
    retValue = 0;