Time complexity of a combination function

Question

I have this function that creates pairs from a list of numbers. We know that there will be a total of n choose 2 iterations every time. So does that make the time complexity O(nC2)? or is it O(n^2)?

If it is O(n^2) why is it O(n^2)? The function does not iterate that many times and it never will.

def find_pairs(nums):
    pairs = []
    for i in range(len(nums)):
        current = nums[i]

        for n in nums[i+1:]:
            pairs.append((current, n))

    return pairs

Answer 1

Time complexity isn't about exactly how many times an algorithm is run, it's how the algorithm scales.

In your case n choose 2 is equal to:

n! / (2 * (n - 2)!)

This can be simplified to

n * (n-1) / 2 = (n^2 - n) / 2

As you can see we have a 2nd degree polynomial function (quadratic). Therefore we consider the time complexity to be O(n^2) since it will scale quadratically.