Comparison between recursion and iteration

Some methods implemented using recursion can also be directly implemented using iteration.

Example: Iterative implementation of the factorial, exploiting the following iterative definition:

fact(n) = n ^. (n - 1) ^. (n - 2) ^{.   ...   .} 2 ^. 1

public static long factorialIterative(long n) {
  int res = 1;
  while (n > 0) {
    res = res * n;
    n--;
  }
  return res;
}

Characteristics of the iterative implementation:

• initialization:
  Ex. res = 1;
• loop operation, executed a number of times equal to the number of repetitions of the loop:
  Ex. res = res * n;
• termination:
  Ex. n--; allows the condition (n > 0) of the while loop to become false

Recursive implementation of the factorial, exploiting the recursive definition shown previously:

public static long factorial(long n) {
  if (n == 0)
    return 1;
  else
    return n * factorial(n-1);
}

Characteristics of the recursive implementation:

• base step:
  Ex. return 1;
• recursive step:
  Ex. return n * factorial(n-1) ;
• termination is guaranteed by the fact that the recursive call factorial(n-1) decreases by one the value passed as parameter; hence, if initially we have n>0, sooner or later we reach an activation in which the condition n==0 is true and hence only the code for the base step is executed.

Actually, it is not always possible to implement a recursive method in a simple way without using recursion. However, all recursive methods can be implemented iteratively by simulating recursion through the use of a specific data structure (a stack).