嵌套循环的复杂性

Question

I've this C# method:

private void Process()
{

  foreach (Vat vat in vats) // n elements
  {
    foreach (ProcessResultRow row in processResultRows) // m elements
    {
      // something here
    }

    foreach (KeyValuePair<int, Shop> entry in _shopsList) // j elements
    {
      // something else here
    }
  }

}

I know two nested loops have a O(n^2) complexity. Is it right in this example?

I am undecided because of the fact that within the external cycle I have two for cicles at the same level.

Answer 1

Prividing that loops don't have return , break and alike (eg throwing exception) the compleixity is

O(n * (m + j)) == O(n * m) + O(n * j)

if both m and j are constants we have

O(n*m + n*j) == m * O(n) + j * O(n) == O(n)  

if at least one m or j such that m ~ n or j ~ n then we have

// here m ~ n and j is some const
O(n * m) + O(n * j) == O(n * n) + j * O(n) == O(n**2) + O(n) == O(n**2)

Answer 2

As @RobinBennet said, the answer is O(n * (m + j)) .

The outer loop iterates n times (one for each element). For each element within the outer loops, the first inner loop iterates m times and the second j times - so for each element you perform O(m + j) steps. Iterate over n elements, O(n * (m + j).

That is, assuming that m, j are not related to n - if, for example m = j = n, you'd get O(n^2)