Category:Recursion: Difference between revisions

[[Category:Solutions by Programming Task]][[Category:Encyclopedia]]'''Recursion''' is the idea that a function can come to an answer by repeatedly calling itself with new arguments until a "base case" or "end condition" is met. One simple example is a [[factorial function]] (for positive integers only). The base case for factorial is "0!" (some people like to use 1 or 2, but 0 is OK for instructional purposes). When 5 is sent as an argument to a recursive factorial function, the function does not know the answer right away. AllBut it knowsdoes isknow that 5! = 5 * 4!. So it calls itself to find out what 4! is. This process continues until it gets to 0!, which is 1. Now it has built up a train of answers: 5! = 5 * 4! = 5 * 4 * 3! etc., and it can find the final answer. Other common examples include [[tree traversal]] and the [[wp:Minimax|min/max algorithm]]. Anyone who can convert the likes of 12,345 into "twelve thousand, three hundred and forty-five" is engaging in the recursive use of language.

More than one end condition is allowed. More than one recursion condition is allowed. More generally, the function may be able to deliver the result for some arguments but not for others, and for those cases it is able to compose the result from some combination of function calls with different arguments. Simple recursion is when it invokes itself, but a group of functions may be involved in mutual recursion. The analyst's task is to devise a plan that will always end with a result for the desired initial invocations. In the case of the factorial function, this is easily seen since factorial(n) invokes factorial(n - 1) and so on, and: for every positive integer this sequence must eventually reach zero and the result for factorial(0) is directly available. A more complex example is provided by the [[wp:Ackermann_function]]