## Tail-Recursive Functions

Tail-recursion is a type of recursion where the last statement executed is the recursive call and, therefore, there are no instructions after that call. When the return from the recursive call is made, the calling function terminates, in which case the return address to the calling function is not necessary. Some compilers and some languages do not save the return address back to the recursive calling function and translate tail recursion into machine instructions for a loop, which saves space on the stack and execution time. However, implementation of source tail recursion using machine code for a loop is compiler and/or language dependent.

Tail-recursive functions are functions in which all recursive calls are tail calls and hence do not build up any deferred operations. For example, the gcd function (shown again below) is tail-recursive. In contrast, the factorial function (also below)
is **not** tail-recursive; because its recursive call is not in tail position, it builds up deferred multiplication operations that must be performed after the final recursive call completes. With a compiler or interpreter that treats
tail-recursive calls as jumps rather than function calls, a tail-recursive function such as gcd will execute using constant space. Thus the program is essentially iterative, equivalent to using imperative language control structures like the "for"
and "while" loops.

Tail recursion: | Augmenting recursion: |
---|---|

//INPUT: Integers x, y such that x >= y and y > 0 int gcd(int x, int y) { if (y == 0) return x; else return gcd(y, x % y); } |
//INPUT: n is an Integer such that n >= 0 int fact(int n) { if (n == 0) return 1; else return n * fact(n - 1); } |

The significance of tail recursion is that when making a tail-recursive call (or any tail call), the caller's return position need not be saved on the call stack; when the recursive call returns, it will branch directly on the previously saved return position. Therefore, in languages that recognize this property of tail calls, tail recursion saves both space and time.

Source: Wikipedia, https://en.wikipedia.org/wiki/Recursion_(computer_science)#Tail-recursive_functions

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