Mastering Delphi Programming: A Complete Reference Guide

Looking at code through the Big O eyes

We can tell more about the program, about its good and bad parts, if we look at it through the eyes of time complexity, in terms of the Big O notation.

We'll start where the code starts—in the SlowMethod method. It has a loop iterating from 2 to the user-specified upper bound, for i := 2 to highBound do. The size of our data, or n, is therefore equal to highBound and this for loop has time complexity of O(n):

for i := 2 to highBound do  if not ElementInDataDivides(temp, i) then    temp.Add(i);

Inside this loop, the code calls ElementInDataDivides followed by an occasional temp.Add. The latter will execute in O(1), but we can't say anything about the ElementInDataDivides before we examine it.

This method ...