Question

I have a treesort function which performs two distinct tasks, each with its own time complexity. I figured out the avg. case time complexity of the two tasks but how do I find the overall complexity of the algorithm.

For example the algorithm takes in a random list of “n” keys x:

Sort(x):
    Insert(x):
        #Time complexity of O(nLog(n))
    Traverse(x):
        #Time complexity of O(n)

Do I just add the two complexities together to give me O(n + nLog(n)) or do I take the dominant task (in this case Insert) and end up with an overall complexity of O(nLog(n))

Answer 1

or do I take the dominant task (in this case Insert) and end up with an over complexity of O(nLog(n))
That’s right. As n grows, first element in O(n + nLog(n)) sum will become less and less significant. Thus, for sufficiently large n, its contribution can be ignored.