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# What is Tail Recursion

Tail recursion is defined as a recursive function in which the recursive call is the last statement that is executed by the function. So basically nothing is left to execute after the recursion call.

For example the following C++ function print() is tail recursive.

## C

 `// An example of tail recursive function` `void` `print(``int` `n)``{``    ``if` `(n < 0)``        ``return``;``    ``printf``(``"%d "``, n);` `    ``// The last executed statement is recursive call``    ``print(n - 1);``}`

## C++

 `// An example of tail recursive function` `static` `void` `print(``int` `n)``{``    ``if` `(n < 0)``        ``return``;``    ``cout << ``" "` `<< n;`` ` `    ``// The last executed statement is recursive call``    ``print(n - 1);``}` `// This code is contributed by Aman Kumar`

## Java

 `// An example of tail recursive function` `static` `void` `print(``int` `n)``{``    ``if` `(n < ``0``)``        ``return``;` `    ``System.out.print(``" "` `+ n);` `    ``// The last executed statement``    ``// is recursive call``    ``print(n - ``1``);``}` `// This code is contributed by divyeh072019`

## Python3

 `# An example of tail recursive function`  `def` `prints(n):` `    ``if` `(n < ``0``):``        ``return``    ``print``(``str``(n), end``=``' '``)` `    ``# The last executed statement is recursive call``    ``prints(n``-``1``)` `    ``# This code is contributed by Pratham76``    ``# improved by ashish2021`

## C#

 `// An example of tail recursive function` `static` `void` `print(``int` `n)``{``    ``if` `(n < 0)``        ``return``;` `    ``Console.Write(``" "` `+ n);` `    ``// The last executed statement``    ``// is recursive call``    ``print(n - 1);``}` `// This code is contributed by divyeshrabadiya07`

## Javascript

 ``

## C

 `// An example of tail recursive function` `void` `print(``int` `n)``{``    ``if` `(n < 0)` `        ``return``;``    ``<< ``" "` `<< n;` `    ``// The last executed statement is recursive call``    ``print(n - 1);``}`

## C++

 `// An example of tail recursive function` `static` `void` `print(``int` `n)``{``    ``if` `(n < 0)``        ``return``;``    ``cout << ``" "` `<< n;`` ` `    ``// The last executed statement is recursive call``    ``print(n - 1);``}` `// This code is contributed by Aman Kumar`

## Java

 `// An example of tail recursive function` `static` `void` `print(``int` `n)``{``    ``if` `(n < ``0``)``        ``return``;` `    ``System.out.print(``" "` `+ n);` `    ``// The last executed statement``    ``// is recursive call``    ``print(n - ``1``);``}` `// This code is contributed by divyeh072019`

## Python3

 `# An example of tail recursive function`  `def` `prints(n):` `    ``if` `(n < ``0``):``        ``return``    ``print``(``str``(n), end``=``' '``)` `    ``# The last executed statement is recursive call``    ``prints(n``-``1``)` `    ``# This code is contributed by Pratham76``    ``# improved by ashish2021`

## C#

 `// An example of tail recursive function` `static` `void` `print(``int` `n)``{``    ``if` `(n < 0)``        ``return``;` `    ``Console.Write(``" "` `+ n);` `    ``// The last executed statement``    ``// is recursive call``    ``print(n - 1);``}` `// This code is contributed by divyeshrabadiya07`

## Javascript

 ``

Time Complexity: O(n)
Auxiliary Space: O(n)

## Need for Tail Recursion:

The tail recursive functions are considered better than non-tail recursive functions as tail-recursion can be optimized by the compiler.

Compilers usually execute recursive procedures by using a stack. This stack consists of all the pertinent information, including the parameter values, for each recursive call. When a procedure is called, its information is pushed onto a stack, and when the function terminates the information is popped out of the stack. Thus for the non-tail-recursive functions, the stack depth (maximum amount of stack space used at any time during compilation) is more.

The idea used by compilers to optimize tail-recursive functions is simple, since the recursive call is the last statement, there is nothing left to do in the current function, so saving the current function’s stack frame is of no use (See this for more details).

## Can a non-tail-recursive function be written as tail-recursive to optimize it?

Consider the following function to calculate the factorial of n.

It is a non-tail-recursive function. Although it looks like a tail recursive at first look. If we take a closer look, we can see that the value returned by fact(n-1) is used in fact(n). So the call to fact(n-1) is not the last thing done by fact(n).

## C++

 `#include ``using` `namespace` `std;` `// A NON-tail-recursive function.  The function is not tail``// recursive because the value returned by fact(n-1) is used``// in fact(n) and call to fact(n-1) is not the last thing``// done by fact(n)``unsigned ``int` `fact(unsigned ``int` `n)``{``    ``if` `(n <= 0)``        ``return` `1;` `    ``return` `n * fact(n - 1);``}` `// Driver program to test above function``int` `main()``{``    ``cout << fact(5);``    ``return` `0;``}`

## Java

 `class` `GFG {` `    ``// A NON-tail-recursive function.``    ``// The function is not tail``    ``// recursive because the value``    ``// returned by fact(n-1) is used``    ``// in fact(n) and call to fact(n-1)``    ``// is not the last thing done by``    ``// fact(n)``    ``static` `int` `fact(``int` `n)``    ``{``        ``if` `(n == ``0``)``            ``return` `1``;` `        ``return` `n * fact(n - ``1``);``    ``}` `    ``// Driver program``    ``public` `static` `void` `main(String[] args)``    ``{``        ``System.out.println(fact(``5``));``    ``}``}` `// This code is contributed by Smitha.`

## Python3

 `# A NON-tail-recursive function.``# The function is not tail``# recursive because the value``# returned by fact(n-1) is used``# in fact(n) and call to fact(n-1)``# is not the last thing done by``# fact(n)`  `def` `fact(n):``    ``if` `(n ``=``=` `0``):``        ``return` `1``    ``return` `n ``*` `fact(n``-``1``)`  `# Driver program to test``# above function``if` `__name__ ``=``=` `'__main__'``:``    ``print``(fact(``5``))` `# This code is contributed by Smitha.`

## C#

 `using` `System;` `class` `GFG {` `    ``// A NON-tail-recursive function.``    ``// The function is not tail``    ``// recursive because the value``    ``// returned by fact(n-1) is used``    ``// in fact(n) and call to fact(n-1)``    ``// is not the last thing done by``    ``// fact(n)``    ``static` `int` `fact(``int` `n)``    ``{``        ``if` `(n == 0)``            ``return` `1;` `        ``return` `n * fact(n - 1);``    ``}` `    ``// Driver program to test``    ``// above function``    ``public` `static` `void` `Main() { Console.Write(fact(5)); }``}` `// This code is contributed by Smitha`

## PHP

 ``

## Javascript

 ``

Output

`120`

Time Complexity: O(n)
Auxiliary Space: O(n)

The above function can be written as a tail-recursive function. The idea is to use one more argument and accumulate the factorial value in the second argument. When n reaches 0, return the accumulated value.

Below is the implementation using a tail-recursive function.

## C++

 `#include ``using` `namespace` `std;` `// A tail recursive function to calculate factorial``unsigned factTR(unsigned ``int` `n, unsigned ``int` `a)``{``    ``if` `(n <= 1)``        ``return` `a;` `    ``return` `factTR(n - 1, n * a);``}` `// A wrapper over factTR``unsigned ``int` `fact(unsigned ``int` `n) { ``return` `factTR(n, 1); }` `// Driver program to test above function``int` `main()``{``    ``cout << fact(5);``    ``return` `0;``}`

## Java

 `// Java Code for Tail Recursion` `class` `GFG {` `    ``// A tail recursive function``    ``// to calculate factorial``    ``static` `int` `factTR(``int` `n, ``int` `a)``    ``{``        ``if` `(n <= ``0``)``            ``return` `a;` `        ``return` `factTR(n - ``1``, n * a);``    ``}` `    ``// A wrapper over factTR``    ``static` `int` `fact(``int` `n) { ``return` `factTR(n, ``1``); }` `    ``// Driver code``    ``static` `public` `void` `main(String[] args)``    ``{``        ``System.out.println(fact(``5``));``    ``}``}` `// This code is contributed by Smitha.`

## Python3

 `# A tail recursive function``# to calculate factorial`  `def` `fact(n, a``=``1``):` `    ``if` `(n <``=` `1``):``        ``return` `a` `    ``return` `fact(n ``-` `1``, n ``*` `a)`  `# Driver program to test``# above function``print``(fact(``5``))` `# This code is contributed``# by Smitha``# improved by Ujwal, ashish2021`

## C#

 `// C# Code for Tail Recursion` `using` `System;` `class` `GFG {` `    ``// A tail recursive function``    ``// to calculate factorial``    ``static` `int` `factTR(``int` `n, ``int` `a)``    ``{``        ``if` `(n <= 0)``            ``return` `a;` `        ``return` `factTR(n - 1, n * a);``    ``}` `    ``// A wrapper over factTR``    ``static` `int` `fact(``int` `n) { ``return` `factTR(n, 1); }` `    ``// Driver code``    ``static` `public` `void` `Main()``    ``{``        ``Console.WriteLine(fact(5));``    ``}``}` `// This code is contributed by Ajit.`

## PHP

 ``

## Javascript

 ``

Output

`120`

Time Complexity: O(n)
Auxiliary Space: O(1)

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