Question

I’m trying to learn how to use recursive functions, but am not understanding what is happening at all.

function power(base, exponent) {
    return base * power(base, exponent - 1);
};

alert(power(4,4));

I’m getting:

RangeError: Maximum call stack size exceeded.

From the example that I’m going off of, it has:

function power(base, exponent) {
  if (exponent == 0)
    return 1;
  else
    return base * power(base, exponent - 1);
}

alert(power(4,4));

Could someone explain to me why the if statement is needed? I suspect that I’m missing something.

Answer 1

A recursive function calls itself. That’s the definition of it.

This brings a problem: it will indefinitely call itself. So it will go forever which is why you’re getting stack overflows.

Instead, you should stop at a certain point. This is where the if clause comes in. When exponent == 0, you don’t call the function, but stop the process.

So when executing power(3, 3) it will go like:

   power(3, 3) is equal to:

   3 * power(3, 2)
or 3 * 3 * power(3, 1)
or 3 * 3 * 3 * power(3, 0)
or 3 * 3 * 3 * 1            // no additional calls anymore; can be calculated now

---

Seen from a little different angle:

• power(4, 4) is defined as 4 * power(4, 3) by the function.
• power(4, 3) is defined as 4 * power(4, 2) by the function.
• power(4, 2) is defined as 4 * power(4, 1) by the function.
• power(4, 1) is defined as 4 * power(4, 0) by the function.
• power(4, 0) is defined as 1 by the function.

If you substitute everything into each previous one, you’ll obtain:

                         power(4, 4)
equals               4 * power(4, 3)
equals           4 * 4 * power(4, 2)
equals       4 * 4 * 4 * power(4, 1)
equals   4 * 4 * 4 * 4 * power(4, 0)
equals   4 * 4 * 4 * 4 *      1   
equals   256