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## Tail Recursion

A recursive function is said to be tail recursive if all recursive calls within it are tail recursive. A recursive call is tail recursive when it is the last statement that will be executed within the body of a function and its return value is not a part of an expression. Tail-recursive functions are characterized as having nothing to do during the unwinding phase. This characteristic is important because most modern compilers automatically generate code to take advantage of it.

When a compiler detects a call that is tail recursive, it overwrites the current activation record instead of pushing a new one onto the stack. The compiler can do this because the recursive call is the last statement to be executed in the current activation; thus, there is nothing left to do in the activation when the call returns. Consequently, there is no reason to keep the current activation around. By replacing the current activation record instead of stacking another one on top of it, stack usage is greatly reduced, which leads to better performance in practice. Thus, we should make recursive functions tail recursive whenever we can.

To understand how tail recursion works, let’s revisit computing a factorial recursively. First, it is helpful to understand the reason the previous definition was not tail recursive. Recall that the original definition computed n! by multiplying n times (n - 1)! in each activation, repeating this for n = n - 1 until n = 1. This definition was not tail recursive ...

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