Big Bad O

When I first started programming, I considered big O(n) notation to be the single most intimidating aspect of programming. This formal system to characterize the performance of algorithms does not have to cause headaches sending an interviewee into oblivion if one remembers these four rules:

When a function is said to be independent of the size of its data input, then that method operates under constant time. Here are two examples where the execution speed of the method is independent of the arguments.

Algorithms that are said to behave in log linear time are ones where ten times the input data size only slows the execution twofold. Two classic examples are a binary search tree and a merge sort.

When a enumerable stuck into another enumerable when you were working on a project at three in the morning prior to a code review, it’s alright. So your code smells? So what?

Although there may be times when you write code that breaks your computer. It is difficult to deliberately write a method that is in exponential time. Two classic examples are a K-D tree that utilizes a nearest neighbor search and a brute force algorithm attempting to guess an encrypted password. To fully demonstrate how much slower the growth rate of these processes are, I compiled all of them on the same plot.

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