Category:Recursion: Difference between revisions

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'''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 good example is a [[factorial function]]. 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. All it knows is 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 [~~http~~:~~//en.wikipedia.org/wiki/~~Minimax min/max algorithm].

'''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 good example is a [[factorial function]]. 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. All it knows is 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]].

A pseudocode function to demonstrate recursion would look something like this:

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More than one end condition is allowed. More than one recursion condition is allowed.

Many recursion problems can be solved with an iterative method, or using a [[~~Loops|~~loop]] of some sort (usually recursion and iteration are contrasted in programming, even though recursion is a specific type of iteration). In some languages, the factorial example is best done with a loop because of function call overhead. Some other languages, like [[Scheme]], are designed to favor recursion over explicit looping, using ''tail-recursion optimization'' to convert recursive calls into loop structures. If loop structures are not available (or not allowed) in your language, recursion is a good way to go.

Many recursion problems can be solved with an iterative method, or using a [[loop]] of some sort (usually recursion and iteration are contrasted in programming, even though recursion is a specific type of iteration). In some languages, the factorial example is best done with a loop because of function call overhead. Some other languages, like [[Scheme]], are designed to favor recursion over explicit looping, using ''tail-recursion optimization'' to convert recursive calls into loop structures. If loop structures are not available (or not allowed) in your language, recursion is a good way to go.

Below is a list of examples of recursion in computing.