Editing Iteration (section)

=== Relation with recursion ===
Recursions and iterations have different algorithmic definitions, even though they can generate identical effects/results.  The primary difference is that recursion can be employed as a solution without prior knowledge as to how many times the action will have to repeat, while a successful iteration requires that foreknowledge. 

Some types of programming languages, known as [[functional programming languages]], are designed such that they do not set up a block of statements for explicit repetition, as with the ''for'' loop.  Instead, those programming languages exclusively use [[recursion]].  Rather than call out a block of code to be repeated a pre-defined number of times, the executing code block instead "divides" the work to be done into a number of separate pieces, after which the code block executes itself on each individual piece.  Each piece of work will be divided repeatedly until the "amount" of work is as small as it can possibly be, at which point the algorithm will do that work very quickly.  The algorithm then "reverses" and reassembles the pieces into a complete whole.

The classic example of recursion is in list-sorting algorithms, such as [[merge sort]].  The merge sort recursive algorithm will first repeatedly divide the list into consecutive pairs; each pair is then ordered, then each consecutive pair of pairs, and so forth until the elements of the list are in the desired order.

The code below is an example of a recursive algorithm in the [[Scheme (programming language)|Scheme]] programming language that will output the same result as the pseudocode under the previous heading.  
<syntaxhighlight lang="scheme">
(let iterate ((i 1) (a 0))
  (if (<= i 3)
    (iterate (+ i 1) (+ a i))
    (display a)))
</syntaxhighlight>