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.

// 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); } 

// 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); } 

// 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); } 

# 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) 

// 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); } 

function prints(n) {  if (n < 0) {  return;  }  console.log(n);    // The last executed statement  // is recursive call  prints(n - 1); } 

Need for Tail Recursion:

• Tail-recursive functions are better than non-tail-recursive ones because they can be optimized by the 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 can be avoided by simply sending the control back to the beginning of the function either using a loop or goto statement.(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).

#include <iostream> using namespace std; // Non-tail-recursive factorial function unsigned int fact(unsigned int n) {  if (n <= 0)  return 1;  // Recursive call is not the last operation  return n * fact(n - 1); } int main() {  // Testing the factorial function  cout << fact(5);  return 0; } 

#include <stdio.h> // Non-tail-recursive factorial function unsigned int fact(unsigned int n) {  if (n <= 0)  return 1;  // Recursive call is not the last operation  return n * fact(n - 1);   } int main() {  // Testing the factorial function  printf("%u", fact(5));    return 0; } 

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. 

# 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)) 

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 

// 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) function fact(n) {  if (n === 0) {  return 1;  }  return n * fact(n - 1); } // Driver program to test // above function console.log(fact(5)); 

<?php // 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) function fact( $n) { if ($n == 0) return 1; return $n * fact($n - 1); } // Driver Code echo fact(5); ?> 

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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.

#include <iostream> 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; } 

#include <stdio.h> // A tail recursive function to calculate factorial unsigned int 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); } int main() {  printf("%u", fact(5));  return 0; } 

// 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. 

# 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# 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. 

<script> // Javascript Code for Tail Recursion // A tail recursive function // to calculate factorial function factTR(n, a) {  if (n <= 0)  return a;    return factTR(n - 1, n * a); }   // A wrapper over factTR function fact(n) {  return factTR(n, 1); } // Driver code  document.write(fact(5)); // This code is contributed by rameshtravel07   </script> 

<?php // A tail recursive function // to calculate factorial function factTR($n, $a) { if ($n <= 0) return $a; return factTR($n - 1, $n * $a); } // A wrapper over factTR function fact($n) { return factTR($n, 1); } // Driver program to test  // above function echo fact(5); // This code is contributed // by Smitha ?> 

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Next articles on this topic: 

• Tail Call Elimination 
• QuickSort Tail Call Optimization (Reducing worst case space to Log n )