when would a statement inside a loop affect the complexity?

Question

for example, if I have

for(int i = 1; i < 500; i++){
  for (int j = 0; j < N; j++){
    if (array[j] == someNumber && i == someNumber)
      counter++;
}
  }

if all numbers were the same in the array, hence counter would increase for each of them, would this make the complexity O(2N), O(N squared) or still just O(N), where it never became O(2N)? I hope the question makes sense. I find it hard to understand how statements might affect the complexity.

Answer 1

Since the statements inside your loop take constant time, they don't have any impact on the overall complexity of your algorithm. The complexity of the code you posted is just O(N), since your outer loop is executed a constant number of times, and your inner loop executes N times.

An example of when it would matter would be if you did something inside a loop like call a function that searches for a value in an array, or sorts a list. Since those operations depend on the size of the array (or list), you'd have to take them into account when calculating the complexity of your algorithm.