# Tail Recursion

What is tail recursion?
A recursive function is tail recursive when recursive call is the last thing executed by the function. For example the following C++ function print() is tail recursive.

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

Why do we care?
The tail recursive functions considered better than non tail recursive functions as tail-recursion can be optimized by compiler. 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 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. `

## Python 3

 `# 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 ` `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

 ` `

Output :

```120
```

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 second argument. When n reaches 0, return the accumulated value.

## C++

 `#include ` `using` `namespace` `std; ` ` `  `// A tail recursive function to calculate factorial ` `unsigned factTR(unsigned ``int` `n, unsigned ``int` `a) ` `{ ` `    ``if` `(n == 0)  ``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. `

## Python 3

 `# A tail recursive function ` `# to calculate factorial ` `def` `fact(n, a ``=` `1``): ` ` `  `    ``if` `(n ``=``=` `0``): ` `        ``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" `

## 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

 ` `

Output :

```120
```

Next articles on this topic:
Tail Call Elimination
QuickSort Tail Call Optimization (Reducing worst case space to Log n )

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