#Rules

We can follow some rules to determine in a simple way the time of complexity of the operations:

• Simplify and remove the constants → When we have multiple constants that belong to a singe BigO family (O(3n)), no matter how much we increase the size of the input, we are going to fin that the time cost of complexity remains linear, so we can reduce and simplify the term to O(n). The same concept applies to the other notations.
• Use worst-case cost of complexity → It does not matter if our operation sometimes gives us results of O(1), if it presents higher operation costs, we must calculate the notation based on it.
• Multiple inputs == multiple names → We assign a name to our input (commonly n), when we present multiple inputs (input1, input2), we must assign a different name to each one (input1 is n, input2 is m) and we could say that our notation is O(2n+m).
• Drop Non Dominants → In our algorithms we can find diversity of operations, multiple consecutive loops O(2n), nested loops O(n^2), no loops O(1) loops, etc. In order to calculate our BigO more easily, we must focus on the operation that has the highest cost in relation to scalability. If we present the following calculation with O(2n + n^2 + 100), we can find that as our input increases, the cost of (n^2) is greater, therefore we can say that the BigO is of O(n^2).