How to write a O(n^2) method that finds the largest distance between two points

Question

I have an array int [] nums = {5, 1, 6, 10, 4, 7, 3, 9, 2}

I want to find the distance between the smallest and largest number in that array in O(n^2) time.

Answer 1

For numbers (as opposed to points on a plane) You can do that in linear time. Find maximum, find minimum, then subtract. So, no nested loops required.

Answer 2

You're overwriting the max and mins.

if (nums[i] > nums[j])
    max = nums[i];
else if (nums[i] < nums[j])
    min = nums[i];  
}

You need to compare the current number with the max/min that is set already. Instead you're comparing the current number with another number, and then overwriting max/min if the condition is true. In this example, at one point 10 was the max, but then you later checked if(9>2), which is true, so you changed max = 10 to max = 9.

Here it is in O(n^2) time, with the outer loop being completely useless.

public static int quadratic(int[] nums) {

    int max = Integer.MIN_VALUE;
    int min = Integer.MAX_VALUE;

    for (int i = 0; i < nums.length; i++) {
        for (int j = 0; j < nums.length; j++) {

            if (nums[j] > max)
                max = nums[j];
            if (nums[j] < min)
                min = nums[j];  
            }
        }
    System.out.println(max + " " + min);
    int maxDifference = max - min;
    return maxDifference; 
}