Question

Here is what I have for my solution:

 public int powerN(int base, int n) {

    if(n == 0)
       return 1;

    else if(n % 2 == 0)
       return base * base;

    else
       return base * powerN(base, n-1); 

 }

However, if n > 3 then this function doesn’t work.
For instance, powerN(2, 4) yields 4 and powerN(2, 5) yields 8.
I know that a much simpler solution exists, but it just bothers me that I can’t figure out why this is not working correctly.

Answer 1

Into pseudocode

Let me translate your code into pseudocode:

public int powerN(int base, int exponent)  {
    if the exponent is 0
        then return 1
    otherwise, if the exponent is even
        then return base * base
    otherwise
        base * powerN(base, exponent - 1)
}

The second branch has a logic error. What your code is saying is this: “As long as the exponent is even, the result should be base * base (that is, base squared)”. You’ve already mentioned that this is the result you get when you run your code.

How to solve it

What you probably want to do is to raise base to half the exponent (base * base * base * ... for exponent / 2 times), and then multiply that number by itself. That way, you get base multiplied by itself exponent times.

In pseudocode:

otherwise, if the exponent is even
    then return powerN(base, exponent / 2) * powerN(base, exponent / 2)

Realistically, this would actually be the following:

otherwise, if the exponent is even
    then {
        let x = powerN(base, exponent / 2)
        return x * x
    }

Done. Mostly.

Translate that back to Java and you’ll be set.