Calculating sum 1 to N by adding 1 to N/2 with N/2 to N in a recursive method

Question

I am having trouble making a recursive method that calculates the sum of 1,2,3 to N, but does it by adding (1,2,3... to N/2) with (N/2+1... to N).

The code i manage so far is this:

public static void main(String[] args) {

    System.out.println(sum(10, 1));
}

public static int sum(int n, int start) {

    if (start == n){
        return n;
    }

    if (start > n / 2){
        return start + sum(n, start + 1);
    }

    return start + sum(n, start + 1);

}

I believe this is wrong, It is an assignment in school where we have to motivate how splitting the recursion up into to parts is a more/lesser efficient way of calculating the sum. (adding numbers from 1 to N/2 with N/2 to N, instead of just from 1 to N directly).

He made us do this way to make it harder for us but i cannot grasp the idea on how to do this at all. Is it correct?

Thanks

Answer 1

Might be helpful in some cases to reduce recursion depth.

You need to take start into account when calculating n/2 for inner steps, the code should probably look similar to this:

public static int sum(int n, int start) {
  if (start > n) {
    return 0;
  }

  if (start == n){
      return n;
  }

  int n2 = (start + n) / 2;
  return sum(n2, start) + sum(n, n2 + 1);
} 

The start > n check just avoids extra checks at the end for the case where start and n are less than 2 apart.

Answer 2

I believe, that this piece of code is as simple as possible, you can check performance in a loop. I don't see any difference in complexity.

class Sums {

    public static int sumHelp(int n, int start){
        if (n == start) return;
        else return (n + sumHelp(n - 1, start));
    }

    public static int sumByHalf(int n){
        return sumHelp(n/2, 0) + sumHelp(n, n/2);
    }

    public static int sum(int n){
        return sumHelp(n, 0);
    }

    public static void main(String[] args) {
        System.out.println(sumByHalf(100));
        System.out.println(sum(100));
    }
}    

Answer 3

Check out that you got declare n as an int. n/2 not always will give to you the expected value. I think that's the trick your teacher wants you to observe.