java - Generate n random numbers whose sum is m and all numbers should be greater than zero

Question

I want to generate 9 non zero random numbers whose sum is 250. I have tried following code it gives me 9 random numbers but some numbers are zero.

 public void n_random()
{
  Random r = new Random();
ArrayList<Integer> load = new ArrayList<Integer>();
    int temp = 0;
    int sum = 0;
    for (int i = 1; i <= 9; i++) {
        if (!(i == 9)) {
            temp = r.nextInt(250 - sum);
            System.out.println("Temp " + (i) + "    " + temp);
            load.add(temp);
            sum += temp;

        } else {
            int last = (250 - sum);
            load.add(last);
            sum += last;
        }
    }

    System.out.println("Random arraylist " + load);
    System.out.println("Sum is "+ sum);

}

Where is my mistake or where i should improve my code or any other solution?

Answer 1

I would suggest using:

temp = r.nextInt((250 - sum) / (9 - i)) + 1;

That will make sure that:

• each number is strictly positive
• you won't use the full "250 allowance" before reaching the 9th number

However the distribution of the results is probably biased.

Example output:

Random arraylist [18, 28, 22, 19, 3, 53, 37, 49, 21]

Explanation:

• (250 - sum) is the amount left to reach 250, so you don't want to go over that
• / (9 - i) if your sum has reached for example 200 (need 50 more) and you have 5 more to go, make sure the next random number is not more than 10, to leave some room for the next 4 draws
• + 1 to prevent 0

---

An alternative which probably gives a better distribution is to take random numbers and scale them to get to the desired sum. Example implementation:

public static void n_random(int targetSum, int numberOfDraws) {
    Random r = new Random();
    List<Integer> load = new ArrayList<>();

    //random numbers
    int sum = 0;
    for (int i = 0; i < numberOfDraws; i++) {
        int next = r.nextInt(targetSum) + 1;
        load.add(next);
        sum += next;
    }

    //scale to the desired target sum
    double scale = 1d * targetSum / sum;
    sum = 0;
    for (int i = 0; i < numberOfDraws; i++) {
        load.set(i, (int) (load.get(i) * scale));
        sum += load.get(i);
    }

    //take rounding issues into account
    while(sum++ < targetSum) {
        int i = r.nextInt(numberOfDraws);
        load.set(i, load.get(i) + 1);
    }

    System.out.println("Random arraylist " + load);
    System.out.println("Sum is "+ (sum - 1));
}