# Confusion in eloquent javascript power recursion sample

this recursion code is from the book of eloquent javascript

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

console.log(power(2, 3));
``````

obviously the exponent is decreased until it reached 0, if it is not zero, it adds power call on the stack, if it is zero, I start to see the return value of 1 then 2 then 4 then 8. But how did base got multiplied by exponent, how did base see the exponent value? it's on else and on power call? But how did base got multiplied by exponent

It doesn't multiply by the `exponent`.

The `exponent` is being used as a counter to end the recursive cycle once it's been reduced to `0`. The `base` is instead being multiplied by itself an `exponent` number of times.

This is supported by each call to `power()` returning either `1` or the value of `base`. In the latter case, `power()` is called again to get `1` or another copy of `base` to multiply by. And, this repeats until it does finally return `1` as the final multiplier.

``````            power(2, 3) ==
2 * power(2, 2) == // base * ...
2 * 2 * power(2, 1) == // base * (base * ...)
2 * 2 * 2 * power(2, 0) == // base * (base * (base * ...))
2 * 2 * 2 * 1              // base * (base * (base * (1)))
``````

The same steps could also be defined with a loop, though using `1` as the initial value rather then at the end:

``````function power(base, exponent) {
var result = 1;

while (exponent) {
result *= base;
exponent--;
}

return result;
}

console.log(power(2, 3)); // 1 * base * base * base == 1 * 2 * 2 * 2 == 8
`````` What you have to notice is that the power function returns 1 when exponent is 0 and
return base * power() on another case.

Pay attention to power function

In the following code

``````power(base, exponent - 1);
``````

you have to appreciate some things

1) If exponent is 1 the function power returns 1 so in here

``````return base * power(base, exponent - 1);
``````

Whether base is 2

``````return 2 * 1
``````

The function power is returning 2, so in the next step

``````return base * power(base, exponent - 1);
``````

means

``````return 2 * 2;
``````

which is 4, that means that function power is returning 4

I think you can catch up from here.

Let me know if you understood :) I find it easy to understand recursive procedures by looking at their base case first, then building up from there – here's the function we're studying...

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

So here, the base case is `exponent == 0`. We'll keep `2` as the input for `base`:

``````power(2, 0) => 1
``````

Well that was really easy! All we had to do was evaluate an `if` statement and we arrived at our answer. Looking ahead, we see that `power` arrives at its base case by subtracting 1 from the exponent (`exponent - 1`), we'll reverse this to get our next input – so instead of `power(2, 0)` we will do `power(2, 1)`

``````power(2, 1) => 2 * power(2, 0)
=> but wait! don't re-evaluate power(2,0)! we already know that answer from above
=> 2 * 1
=> 2
``````

Ok, we'll keep doing the same thing by incrementing exponent by 1 each time. But be careful not to do unnecessary work – if we've already evaluated one of the expressions earlier, just replace that expression with it's evaluated value

``````power(2,2) => 2 * power(2, 1)
=> we already know power(2,1) == 2 ...
=> 2 * 2
=> 4

power(2,3) => 2 * power(2,2)
=> we already know power(2,2) == 4, etc
=> 2 * 4
=> 8

power(2,4) => 2 * power(2,3)
=> 2 * 8
=> 16

power(2,5) => 2 * power(2,4)
=> 2 * 16
=> 32
``````

Now we can easily see a pattern and how the recursive procedure works in general