Question

Is there any cheapest way to compare an ICollection with itself.

Here is my code:

        public IEnumerable<Pet> speciesChecker()
        {
            foreach (Pet pet in _pets)
            {
                bool wantedSpecies = true;
                foreach (Pet pet2 in _pets)
                {
                    if (pet2 != pet && pet.Species == pet2.Species)
                    {
                        wantedSpecies = false;
                        break;
                    }
                }
                if (wantedSpecies) yield return pet;
            }
        }

What is the time complexity of my code, all I know is this that it is less than O(N^2) and if I’ll remove ‘break’ from inner foreach loop, the time complexity will be O(N^2). Please correct me if I am wrong.

Answer 1

let n is the length of _pets collection

number of required steps with break:

1+2+3+...+n = n*(n+1)/2 =n^2/2 + n/2 = O(n^2) (for each pet in _pets);

There are two simple rules how to calculate O from wiki:

1. If f(x) is a sum of several terms, the one with the largest
   growth rate is kept, and all others omitted.

2. If f(x) is a product of several factors, any constants (terms in
   the product that do not depend on x) are omitted.

number of required steps without break:

n+n+n+...+n = n^2 = O(n^2)