Tail Recursion

2.4

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)

#include<iostream>
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;
}

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.

#include<iostream>
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;
}

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

References:
http://en.wikipedia.org/wiki/Tail_call
http://c2.com/cgi/wiki?TailRecursion

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