Hi there. What would you suggest to a person who loves these kind of stuff (data structures and algorithms) but finds it hard to develop the underlying intuitions for coming up with these data-structure and algorithm? I personally just hammer down on deliberate practice to recognise patterns and underlying concepts to solve as many problems as I can on my own. I was wondering apart from general DS and Algo what topics in Mathematics might supplement this process?
I recently had someone ask me about a problem in machine learning. The algorithm for it turned out to be something I had read about 30 years earlier, where it was being used to accelerate the simulation of the motion of stars in galaxies. I had never expected to use that algorithm, but its existence, if not details, was there in my long term memory, waiting to surface.
So, I suggest you just read everything you can, getting the gist of things so if you encounter something similar you know where to look.
I also suggest looking for little tricks you can apply again and again. For example, some of the data structures in that course use a trick where you break the structure into a top part, using one algorithm, and a bunch of leaf parts, each of size maybe O(log n), that are handled using another algorithm. Often this combination does better than either algorithm by itself.
1. Where can I find that algorithm you are talking about?
2. The algorithm which you stated seems a bit complex from the algos taught in the undergrad level, so what are the pre-requisites for understanding it that I must be aware of?
3. What books or papers you would suggest for reading?
4. How the hell you remember something you read decades ago :)?
The ML problem involved, for a set of points on a line, computing the sum (over all the pairs of distinct points) of a function d(x_i,x_j) that is, in some sense, well behaved. The purpose was to compute the similarity of two sets of real numbers.
It turns out this can be done (to sufficient accuracy) in nearly linear time using something called the fast multipole method.
Really, to quote the old "How do I get to Carnegie Hall?" it's "practice practice practice" - it's doing this stuff often enough so that the correct data structure becomes obvious is how you get good at this game
