Or is it a longer-term project? And how important is it? Be straightforward If you realize you have neither the desire nor the bandwidth to help, and, therefore, need to turn down the request, be honest and up front about your reasons, advises Weeks. Or they come across as disingenuous. Be empathetic.

## Urban Dictionary: The Big O

Be compassionate. Perhaps you can attend brainstorming sessions, read first drafts, or simply serve as a sounding board. Adjust your expectations Even if you follow all the steps above, you should prepare for negative feedback. But it may not be personal. Practice To get better at saying no, Dillon suggests practicing saying it out loud — either alone, behind closed doors, or with a trusted friend or colleague.

Your tone should be clear and your demeanor diplomatic. The average case complexity describes the expected performance of the algorithm. Sometimes involves calculating the probability of each scenarios. It can get complicated to go into the details and therefore not discussed in this article. Below is a cheat-sheet on the time and space complexity of typical algorithms. By inspecting the functions, we should be able to immediately rank the following polynomials from most complex to lease complex with rule 3.

Where the square root of n is just n to the power of 0. Then by applying rules 2 and 6, we will get the following. Base 3 log can be converted to base 2 with log base conversions. Base 3 log still grows a little bit slower then base 2 logs, and therefore gets ranked after. And then since we know 2 to the power of log n with based 2 is equal to n, we can convert the following. The log with 0. The one with n to the power of log log n is actually a variation of the quasi-polynomial , which is greater than polynomial but less than exponential. Since log n grows slower than n, the complexity of it is a bit less.

The factorials can be represented by multiplications, and thus can be converted to additions outside the logarithmic function. Well you probably have guessed that the answer is false. To demonstrate, check out this trinket.

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It compares the time for quick sort and merge sort. I have only managed to test it on arrays with a length up to , but as you can see so far, the time for merge sort grows faster than quick sort. I have also made the below graph to compare the ratio between the time they take, as it is hard to see them at lower values. And as you can see, the percentage time taken for quick sort is in a descending order. The moral of the story is, Big O notation is only a mathematical analysis to provide a reference on the resources consumed by the algorithm.

Practically, the results may be different. But it is generally a good practice trying to chop down the complexity of our algorithms, until we run into a case where we know what we are doing. I like coding, learning new things and sharing them with the community. If there is anything in which you are particularly interested, please let me know. I generally write on web design, software architecture, mathematics and data science. You can find some great articles I have written before if you are interested in any of the topics above.

Learn Forum News. Welcome to Developer News. This is a free, open source, no-ads place to cross-post your blog articles. Read about it here. Tweet this to your followers. Picture of a Mandelbrot set, which relates to Complex Numbers and Recursions, Pixabay In this article, we will have an in-depth discussion about Big O notation. It is a member of a family of notations invented by Paul Bachmann, Edmund Landau, and others, collectively called Bachmann—Landau notation or asymptotic notation. Formal Definition of Big O notation Once upon a time there was an Indian king who wanted to reward a wise man for his excellence.

Question: An image is represented by a 2D array of pixels. If you use a nested for loop to iterate through every pixel that is, you have a for loop going through all the columns, then another for loop inside to go through all the rows , what is the time complexity of the algorithm when the image is considered as the input?

Little O o describes the upper bound excluding the exact bound. Complexity Comparison Between Typical Big Os When we are trying to figure out the Big O for a particular function g n , we only care about the dominant term of the function. There are actually quite a few rules. O log n is more complex than O 1 , but less complex than polynomials As complexity is often related to divide and conquer algorithms, O log n is generally a good complexity you can reach for sorting algorithms.

Factorials have greater complexity than exponentials If you are interested in the reasoning, look up the Gamma function , it is an analytic continuation of a factorial. Multiplying terms When multiplying, the complexity will be greater than the original, but no more than the equivalence of multiplying something that is more complex. Question: Rank following functions from the most complex to the lease complex. Examples taken from Textbook Problems Solution to Section 2 Question: It was actually meant to be a trick question to test your understanding.

The math of Big-O isn't that hard and the article while having good intentions misses the point. Big-O is about asymptotic behaviour and the graphs are misleading in that regard well, they're simply wrong, not misleading. There are algorithms where if you just look at the Big-O you'd think one has faster run time than the other but because the constants fall out that wouldn't be the case for any practical problem size.

What O N means is there is some large enough number where the run-time edit: or any function really is bounded by a constant times the input size for any input size larger than that number see, math, not hard. As a data point, I have no idea what you just said. He's saying that big O only matters for big input sizes, because big O is specifically about the algorithm's asymptotic performance, which means its performance for a large value of n.

If you have a small value of n then the other constant time operations in the algorithm may affect the running time more. Depends on how big n is, right? Big O notation just assumes that n is big enough to make the answer "yes. More or less, yes. What he is saying is that there is a constant hidden in the big O. So the first algorithm A is clearly faster asymptotically. This is because of the constant that is hidden in the big O.

A good implementation could check problem sizes beforehand and chose the algorithm accordingly. What I don't agree with is that "big O only matters for big input sizes". Big is not really a well-defined term. The problem here is that "big" depends entirely on the algorithms. There's nothing in the definition of the landau symbols that prevents that. The definition of a "big" input size is somewhat circular, yes. YZF on July 27, Can you be more specific?

That's not hard to explain either. If I already lost you here let me know. I just proved this function is O N. Retric on July 27, Suppose you had three functions. This is the only useful comment in this entire thread. But sometimes this is overkill, because if n is small, you probably aren't going to notice the speed difference anyway. So yes, Big O is all about asymptotic behavior, which basically means, the rate of growth as n approaches infinity.

Because a large value of n is when the choice of algorithm starts to really matter for performance. I think that Sedgewick's tilde notation [1] is nice if you want to include more information about constant factors. His tilde notation is also more informative than the big-O one. The canonical example is Quicksort. KennyCason on July 27, Well stated :.

This sort of contributes to giving self-taught programmers a rather bad name. The writeup is good, but the idea that Big O is "scary" is just absurd. It's an elementary concept that every working programmer should be familiar with, regardless of whether they're self-taught. Algorithms are not "scary". If you can't reason about algorithms, you may not be a very good programmer yet. To be clear, I really appreciate the writeup. I just wish it had been framed better.

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It should be clear that this is for beginner programmers, regardless of whether they have a degree or whether they're self-taught. Ahh yes. Let's berate the OP for being intimidated by a topic and then diving in and learning it on their own. This will really encourage others to learn on their own and contribute back. Well, whether we like it or not, self-taught programmers are held to a higher standard. It doesn't help us to further the stereotype that self-taught programmers are afraid of the basics, haven't attained a general education in computer science on their own, or are less reliable than their peers who have degrees.

Not trying to berate the OP. I'm trying to say I wish OP had framed it better. Being familiar with big O notation is not that same thing as being familiar with a few basic complexity classes. I wouldn't be surprised or disappointed if a self-taught programmer was intimidated by big O notation, but I would be surprised if they were unfamiliar with the concept that hash map lookups are much faster than array searches, or that searching a sorted array is much faster than an unsorted array.

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You seem to be using "big O notation" to refer to fundamental competency about basic data structures. It's even quite possible and understandable for a self-taught programmer to, over time, figure out that certain big O classes refer to certain algorithms while still not understanding the meaning of the mathematical notation. To you. I never studied things like these in school and getting to a point of "Oh that's what that means" was long and arduous as it pertained to a lot of scientific literature.

Plain English, it seems, isn't in the tool set for a lot of very smart people who, coincidentally, feel that it's their duty to Explain All the Things. It's unfortunate that so many of them are deluded by the "x should be elementary" mindset or the like without regard to the language they use or the specificities of notation Big-O in this case.

I wish computer scientists can be more like Neil deGrasse Tyson. Ixiaus on July 27, I'm as autodidactic as they come high school drop out, self-taught in math, comp sci, psychology and I to think this is elementary stuff. The correct way to "understand these things" is to learn the math, the theory, and do the exercises. Would you take a scientist seriously if they didn't understand what the scientific method was?

You're right. English is not the tool to use here in explaining theory, it's not capable of it. Mathematics and programming languages are! It's unfortunate you've read my post as a claim to avoid actually learning these. I was pointing out that the "x is elementary" attitude doesn't help the process and I thought from the video at least some empathy in communication is warranted.

It's ridiculous to expect clarity when no such thing exists in the language used to describe an idea in the first place. The OP went to the trouble of making such a post. Maybe it wasn't perfect, but it gets the ball rolling. Whatever inadequacies can be corrected with feedback and I for one would like to see more people engage in humane explanations for things pertaining to their expertise. Big-O is "technical". Understanding of it comes with clear explanations. No where did I claim anything contrary to : "The correct way to "understand these things" is to learn the math, the theory, and do the exercises.

Ixiaus on July 28, Well, I must still be misunderstanding you because I spent 30 minutes writing a whole comment explaining why Math is important then got to the bottom of your comment and realized we both believe the same thing that these subjects are important. What I will contend is that pity parties about scary topics are unhelpful and rigor is important - more so for self-taught people. Like you, I advocate humane teaching. Humane teaching, to me however, is more about adapting to learning styles while maintaining the rigor and difficulty of the material without watering it down - this article watered it down.

Clear and humane explanations are out there; this article was not one of them.

## Saying No to the Big O

The intention was noble and I respect them for that but I agree with the top commenter in that the pity party needs to end and more self-educated individuals need to be role models for those that do find it scary so that we can all as in self-educated people strive to understand difficult concepts instead of "being okay" with not fully understanding it or the language it was meant to be understood in. Much as autodidactic scholars hold themselves up to very high standards when reading about an author, they read the author's works in the original language they were written in - not in its translations this is slight speculation because I don't know any autodidactic scholars personally, but I have read some of their articles.

Then it seems, we're basically on the same page. Watering down is unacceptable. No argument here. What I do appreciate though is that advanced topics can be made reachable with a step stool, at least at first, before the full rung up the ladder.

### An Introduction to Probability & Statistics

That "being okay" with not fully understanding a concept grates me to no end too. It's honestly incredibly condescending. That said, there are ways to be more clear without being condescending and without accepting that "okay" is good enough. Take that math, for example. I've lost count of how many people I've run into who hate Calculus and the like because "it's so hard!

I hated math too, cause it was big and scary, until I came across and awesome teacher who actually sat down with me and went over the basics with very careful attention to the language she used. There are approaches to teaching like this online I'm sure, but they're very few and far between. As an aside, you can't be self-taught in psychology. It's like being a self-taught doctor: Being educated in psychology is predicated upon you having a degree in psychology, because it's a very certification-heavy field. I would actually advise you to not brag about being "self-taught in psychology" because it's a very strong indicator that you don't know what you're talking about.

Jungian psychology, freudian psychology, alchemical symbolism; ALL disciplines of personal understanding and understanding inter-personal relationships that have spanned hundreds of books on my bookshelf and years worth of self-application to become a happier more effective human being.

I guess none of that was worth it because I don't know what I'm talking about! Oy I might as well stop reading books then because claiming I'm self-taught in anything will make me look bad! No offense, but your comment made you look like you don't know what you are talking about. What the fuck would you call self-education then if reading books, becoming more intelligent, applying it to your life, and improving quality of said life isn't self-education? Self-education is something everyone does, even people that have been through a formal education. The difference is that they are choosing their subjects of study instead of having them chosen.

By the way, your analogy would be stronger if I laid claim to "psychiatry" rather than "psychology" - psychiatry is more akin to being a doctor; I do not ever claim to practice what I know on other people just as people that love studying physiology and medical text-books don't practice on people! Oh, also, I was not bragging, I was qualifying myself for the commenter as someone who is self-taught so I wouldn't appear to be someone that doesn't know what they are talking about.

I think the "scary" part is the notation. Any competent programmer, whether schooled or self-taught, is familiar with the concepts if not the notation. Thanks for the comment.

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I don't feel as though self-taught programmers have a bad name. I feel like they can lack some skills because the importance of them aren't lauded in their social circles. It wasn't until 5 years into my professional career that I was fortunate enough to work with someone with a computer science background, so the topics of Big-O never even came up.

I think computer science has a bad wrap for being useless brain-teasers used only in interviews within a subset of the target demographic of this article. Through the bits I've managed to pick up, I feel like they contribute to a better understanding of programming on a broader spectrum.