Solving Coding Problems through Case by Case Analysis of Input[Technique Tuesdays]

This will help you a lot with the proofs and designing large scale solutions

Jun 08, 2022

Hello hello,

Today I will share with you a deceptively powerful technique to really boost your problem-solving. It’s one of those techniques that are extremely simple, so they often blend into the background. Nevertheless, without this technique, I would have a hard time coming up with solutions in a clear and efficient way.

This technique is one of the reasons that my tutoring/approach has been so successful.

OG readers will know how much I love this technique since it shows up in a lot during our solutions. This magic technique is the mighty case-by-case analysis. What does this mean? Let’s cover that.

Highlights

This post will cover the following-

What is it- Simply put, we will take a problem and split it into different cases. This is typically done by analyzing the domain of inputs to our problem and spotting how each of these could be solved.
How to get good at it- You probably already are. All we need to do is get you used to this. Comes from practice. That’s why we this newsletter/my coaching.

Sound exciting? Let’s get into it.

Splitting things into cases

Some of you might be a little confused by what I meant by the statement, “we will take a problem and split it into different cases”. Let me elaborate on that statement.

You know how in Software Engineering, people talk about how we should break our problems into easier sub problems and solve them? That is exactly what we do here. We take our complex input/problem and look at how we can carve it into easier subproblems. This is done by analyzing the input and breaking it into the kinds of input we can recieve. Then we try to solve for the individual different cases. For example, if we were solving a problem over integers, we might benefit from solving the problem for even and odd numbers respectively and trying to combine the results.

This technique is something I use a lot. In fact, last week’s solution used this to figure out the details of the optimal solution. Take a look below for another example of how I used this technique.

Taken from the post [Solution]Problem 26: Remove K digits to create smallest number[Microsoft]

Go through other solutions I have posted here. You will see that I rely on this technique quite a bit. I like it for many reasons-

I get to pick the low-hanging fruit by solving the easier cases. This was the reason I started using this technique.
Gives me a clear next step instead of getting stuck. Remember awkward silences are a death sentence in your interviews.
Easier cases can provide you hints on harder ones. This makes it better for solving problems, as opposed to trying to solve everything at once.
It looks really neat and logical. That’s because it is.

This might seem like I’m overhyping a simple thing, but this is something that many of my students and premium subs were able to use with great success.

Getting Good at this

So how can you get good at this technique? Short answer, practice. This is one of those techniques that can be implemented in a lot of Leetcode questions so that is a pretty clear avenue. Using this kind of analysis in your normal projects will be extremely helpful as well.

I became familiar with this technique through Math. Many Geometry, Theoretical Computer Science and Algebra proofs use this technique. I thought it felt like cheating at first, but it has been a game changer. People looking to be more advanced might benefit from implementing this approach in those subjects.

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Happy Prep. I’ll see you at your dream job.

Go kill all you magnificent maestro,

Devansh <3

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