Freek Lijten has put together a new post to his blog looking at a method for showing how complex an algorithm is without having to get too deep into how it works - the big O notation (with examples written in PHP).

I'd like to share a topic today which was re-introduced to me by a lightningtalk of a colleague of mine. His talk was on the "big O notation". The big O notation is a tool you can use to express the order of complexity of an algorithm. It is useful because it lets you express the order of complexity of an algorithm without taking a lot of time profiling or researching the underlying algorithm. In other words: it gives you a quick way to gain an understanding of what might be wrong (or right) with a specific algorithm.

He introduces the notation as the result of a series of steps needed to solve a problem (ex. 2+2 is less complex than 2+2+2). He illustrates with PHP examples that show adding complexity to a class, adding sets of numbers, looping to find needles in haystacks and finding duplicates in an array of strings. Each of these expand on the theory and show more complexity as the article progresses.