Tail vs. Non-Tail Recursion

Tail recursion and Non-tail recursion are two types of recursive functions in computer programming. In this post we will deep dive into what are the major differences between the tail and non-tail recursion.

1) Definition:

• Tail recursion is defined by having the recursive call as the last operation in the function before returning

function factorial (currentNumber , previousMultiplication):

if currentNumber is less or equal to 0 then

return previousMultiplication

else

return factorial( currentNumber – 1, currentNumber * previousMultiplication ) // Tail Recursion

end

end

• While non-tail recursion involves other operations after the recursive call

function factorial ( n ):

if n is less or equal to 0 then

return 1

else

return n * factorial ( n – 1 ) // Non-Tail Recursion

end

end

2) Base Case Handling:

• In tail recursion, the base case is typically handled at the end of the function.
• whereas in non-tail recursion, it can be handled before making the recursive call. 

3) Stack Usage:

• Tail recursion can often be optimized to use a constant amount of stack space, as the current function’s stack frame can be reused for the recursive call.
• Non-tail recursion typically uses more stack space because each recursive call creates a new stack frame. 

4) Optimization Potential:

• Tail recursion has the potential to be optimized by compilers/interpreters for tail call elimination, which improves stack space efficiency.
• Non-tail recursion may not benefit from this optimization. 

5) Examples:

• Examples of tail recursion include factorial calculations and some tree traversal algorithms.
• Non-tail recursion is common in algorithms like Fibonacci sequence generation and recursive algorithms without tail call optimization.

6) Which One is Better? Tail or Non-Tail Recursion?

“Tail recursion” is considered better than non-tail recursion because tail recursive functions can be optimized by modern compilers.

In summary, the key difference between tail and non-tail recursion lies in where the recursive call occurs within the function and how it impacts stack space usage and potential optimizations. Tail recursion is often preferred when possible due to its potential for stack space optimization.

7) Can We Convert a Non-tail Recursion to a Tail Recursion?

The answer is “YES“, We can convert any Non-tail recursive function to a Tail recursive function by passing additional parameters to maintain the state of the recursive call.

Difference Between Tail and Non-Tail Recursion:

Below is the comparison of these two types in tabular format:

Feature	Tail Recursion	Non-Tail Recursion
Definition	A recursive function is said to be tail-recursive if the recursive call is the last thing done in the function before returning.	A recursive function is said to be non-tail-recursive if the recursive call is not the last thing done in the function before returning.
Base Case Handling	Usually, the base case is handled at the end of the function after the recursive call.	Usually, the base case is handled before making the recursive call.
Stack Usage	Typically, tail recursion can be optimized by compilers/interpreters to use a constant amount of stack space.	Typically, non-tail recursion uses more stack space because each recursive call creates a new frame on the call stack.
Optimization Potential	Can be optimized for tail call elimination, improving stack space efficiency.	May not be optimized for tail call elimination, which can lead to stack overflow errors.
Examples	Factorial function, some tree traversals, mutual recursions with multiple recursive calls.	Fibonacci sequence, recursive algorithms without the tail call optimization.