Consider a simple function that adds the first N natural numbers. (e.g. sum(5) = 0 + 1 + 2 + 3 + 4 + 5 = 15
).
Here is a simple JavaScript implementation that uses recursion:
function recsum(x) {
if (x === 0) {
return 0;
} else {
return x + recsum(x - 1);
}
}
If you called recsum(5)
, this is what the JavaScript interpreter would evaluate:
recsum(5)
5 + recsum(4)
5 + (4 + recsum(3))
5 + (4 + (3 + recsum(2)))
5 + (4 + (3 + (2 + recsum(1))))
5 + (4 + (3 + (2 + (1 + recsum(0)))))
5 + (4 + (3 + (2 + (1 + 0))))
5 + (4 + (3 + (2 + 1)))
5 + (4 + (3 + 3))
5 + (4 + 6)
5 + 10
15
Note how every recursive call has to complete before the JavaScript interpreter begins to actually do the work of calculating the sum.
Here's a tail-recursive version of the same function:
function tailrecsum(x, running_total = 0) {
if (x === 0) {
return running_total;
} else {
return tailrecsum(x - 1, running_total + x);
}
}
Here's the sequence of events that would occur if you called tailrecsum(5)
, (which would effectively be tailrecsum(5, 0)
, because of the default second argument).
tailrecsum(5, 0)
tailrecsum(4, 5)
tailrecsum(3, 9)
tailrecsum(2, 12)
tailrecsum(1, 14)
tailrecsum(0, 15)
15
In the tail-recursive case, with each evaluation of the recursive call, the running_total
is updated.
Note: The original answer used examples from Python. These have been changed to JavaScript, since Python interpreters don't support tail call optimization. However, while tail call optimization is part of the ECMAScript 2015 spec, most JavaScript interpreters don't support it.
Best Answer
It is a guard against a stack overflow, yes. Python (or rather, the CPython implementation) doesn't optimize tail recursion, and unbridled recursion causes stack overflows. You can check the recursion limit with
sys.getrecursionlimit
:and change the recursion limit with
sys.setrecursionlimit
:but doing so is dangerous -- the standard limit is a little conservative, but Python stackframes can be quite big.
Python isn't a functional language and tail recursion is not a particularly efficient technique. Rewriting the algorithm iteratively, if possible, is generally a better idea.