Mrthdrb

I was asked this question in an interview recently and was curious as to what others thought.

"When should you calculate Big O?"

Most sites/books talk about HOW to calc Big O but not actually when you should do it. I'm an entry level developer and I have minimal experience so I'm not sure if I'm thinking on the right track. My thinking is you would have a target Big O to work towards, develop the algorithm then calculate the Big O. Then try to refactor the algorithm for efficiency.

My question then becomes is this what actually happens in industry or am I far off?

"When should you calculate Big O?"

When you care about the Time Complexity of the algorithm.

When do I care?

When you need to make your algorithm to be able to scale, meaning that it's expected to have big datasets as input to your algorithm (e.g. number of points and number of dimensions in a nearest neighbor algorithm).

Most notably, when you want to compare algorithms!

You are asked to do a task, for which several algorithms can be applied to. Which one do you choose? You compare the Space, Time and development/maintenance complexities of them, and choose the one that best fits your needs.

It represents the upper bound.
Big-oh is the most useful because represents the worst-case behavior. So, it guarantees that the program will terminate within a certain time period, it may stop earlier, but never later.

It gives the worst time complexity or maximum time require to execute the algorithm

Big O or asymptotic notations allow us to analyze an algorithm's running time by identifying its behavior as the input size for the algorithm increases.

So whenever you need to analyse your algorithm's behavior with respect to growth of the input, you will calculate this. Let me give you an example -

Suppose you need to query over 1 billion data. So you wrote a linear search algorithm. So is it okay? How would you know? You will calculate Big-o. It's O(n) for linear search. So in worst case it would execute 1 billion instruction to query. If your machine executes 10^7 instruction per second(let's assume), then it would take 100 seconds. So you see - you are getting an runtime analysis in terms of growth of the input.

When we are solving an algorithmic problem we want to test the algorithm irrespective of hardware where we are running the algorithm. So we have certain asymptotic notation using which we can define the time and space complexities of our algorithm.

1. Theta-Notation: Used for defining average case complexity as it bounds the function from top and bottom




2. Omega-Notation: Bounds the function from below. It is used for best-time complexity




3. Big-O Notation: This is important as it tells about worst-case complexity and it bounds the function from top.

Now I think the answer to Why BIG-O is calculated is that using it we can get a fair idea that how bad our algorithm can perform as the size of input increases. And If we can optimize our algorithm for worst case then average and best case will take care for themselves.

I assume that you want to ask "when should I calculate time complexity?", just to avoid technicalities about Theta, Omega and Big-O.

Right attitude is to guess it almost always. Notable exceptions include piece of code you want to run just once and you are sure that it will never receive bigger input.

The emphasis on guess is because it does not matter that much whether complexity is constant or logarithmic. There is also a little difference between O(n^2) and O(n^2 log n) or between O(n^3) and O(n^4). But there is a big difference between constant and linear.

The main goal of the guess, is the answer to the question: "What happens if I get 10 times larger input?". If complexity is constant, nothing happens (in theory at least). If complexity is linear, you will get 10 times larger running time. If complexity is quadratic or bigger, you start to have problems.
Secondary goal of the guess is the answer to question: 'What is the biggest input I can handle?". Again quadratic will get you up to 10000 at most. O(2^n) ends around 25.

This might sound scary and time consuming, but in practice, getting time complexity of the code is rather trivial, since most of the things are either constant, logarithmic or linear.