Leaving aside actual errors pointed out in other comments, is this article even understandable to a beginner? Having learned and absorbed this stuff years ago,

Leaving aside actual errors pointed out in other comments, is this article even understandable to a beginner? Having learned and absorbed this stuff years ago, it's hard for me to be sure, but my impression was that it assumed the reader knew lots of things few beginners would. One example: "O(1) describes an algorithm that will always execute in the same time (or space) regardless of the size of the input data set." What does always executing in the same time (or space) really mean? I know, but I doubt a beginner would. (As an aside, the use of "complexity" here is unfortunate. It's a wretched term for what it describes. Computer science is full of lousy terminology, but "complexity" is surely among the worst.) Aside from undefined vocabulary, the common O values are introduced out of order. O(n) is by far the easiest to understand; it should therefore go first, with both a contrived example and a real one. The rest of the document should follow on from there, comparing to O(n).