Big O Notation – Explained as easily as possible
If you are the kind of person that want to read an article titled "explained as easily as possible", I think you should just avoid saying the phrase "big oh" but instead talk about algorithm runtime more informally, like "quicksort has a worst case quadratic but average case n log n runtime".<p>The risk is otherwise you will shoot yourself in the foot, maybe during an interview or other situation, as Big O is just one out of many members in a family of notations that has a very specific mathematical definition, other common ones being small-o and big-theta.<p>Analysis of algorithms is more difficult than it appears. If you implement an algorithm in a high level language like Python you may get much worse runtime than you thought because some inner loop does arithmetic with bignum-style performance instead of hardware integer performance, for example. In such case you could talk of big-omega (your analysis is bounded-below instead of bounded-above, asymptotically).