Question

Hello it has been some time sins i have used Big O notation, so i’m a bit rusty.

I know that having 1 loop, that loops n times is O(n), and having 1 loop that loops n time within another loop that loops n times is O(n^2).

But in the following code snippet do i have a loop that loops n times, and within that a loop that loops n-i times.

What will the Worst and Best O notation be for this code?

The worst is where it runs without finding a collision, and the best will be when there are a collission between the 2 first rectangles.

class TestClass
{
    bool Run(List<Rectangle> R)
    {
        var b = false;
        var i = 0;
        var n = R.Count;
        var j = 0;
        while ((i < n-1 ) && !b )
        {
            j = i + 1;
            while (j<n && !b)
            {
                if ((R[i].x >= R[j].x - R[i].w) && (R[i].x <= R[j].x + R[j].w))
                    if ((R[i].y <= R[j].y + R[i].h) && (R[i].y >= R[j].y - R[j].h))
                        b = true;
                j++;
            }
            i++;
        }

        return b;
    }
}

public class Rectangle
{
    public int x;
    public int y;
    public int w;
    public int h;
}

Answer 1

Your actual worst case running time is n X n/2 = n²/2. Throw away the constants, and it’s O(n²)