### aryanc403's blog

By aryanc403, 11 hours ago,

Update 1 -
Let's consider this problem -
We have a function subset_convolution(A,B) it gives us Subset Sum Convolution of two sets $A, B$.
Let's say we array $A$ with $A[0]=1$ and we want to find A^K defined as $A$ convoluted with itself $K$ times.
A^2 = subset_convolution(A,A)
A^3 = subset_convolution(A^2,A)
...
A^k = subset_convolution(A^{k-1},A)
The best I can think right now is using something on lines of fast exponential to achieve $O(log K*N^2*2^N)$ time where $2^N$ is the size of A.
But it can be done in $O(N^2*2^N)$ using tricks well known at some places. Idk why it works tho.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

TLDR — Just me rambling about the old ARC problem I was solving for the last 3 days. Something "set power series" similar to "power series for polynomials" I came across and I have an iota idea about it right now. Also amplifying some unanswered bugaboo related to it in the discussion of that ARC round. Spoiler is just very very briefly mention different solutions I had for ARC105F problem.

Me trying to solve ARC105 F

The logarithm of 'set power series' is a function $g(x)=\sum_{S} g_{S} x^{S}$ such that $f(x) = \sum_{S} (\sum_{\mathcal{P}} \prod_{P_i \in \mathcal{P}} g_{P_i}) x^{S}$, where the inner summation goes over all unordered partitions $P$ of $S$.

dario2994 submission on the same problem implements a small library for subsets with functions namely and/or/xor/subset convolutions along with log and exp of set power series.
(First to answer dario2994 comment — Yes, there does exist a clever way (and maroonrk's submission) to compute subset convolution.)

I did asked some of my friends and seniors doing MATH major — where can I read formal definitions of "set power series" since googling it just gave me useless results and none of them ever heard it.

Q1 — What exactly is the definition of exp of set power series? (One implemented by dario2994 and mentioned by mmaxio). Where can I read about more similar definitions?

mmaxio mentions Lu Kaifeng's report, googling about his report along with keywords such as "set power series" doesn't yield helpful results. But then I came across this blog. It has a code snippet and mentions For details, please refer to the 2015 Proceedings of the National Training Team Lu Kaifeng, "The Properties and Application of Set Power Series and Its Fast Algorithm".

It's a 17 page report published in 2015 in Chinese, I wasn't able to find an English version. Hence must be a well-known problem in China and hence a "trivial solution" by Elegia. I tried auto translating it using the method mentioned by z4120 in Auto-translated Chinese national IOI training team report papers but I messed up a step somewhere and ended up with just Chinese translated into Chinese, would really appreciate it if someone can translate it for me.

Q2 — mmaxio's comment looks like you can apply any function to the set power series by applying it to a "ranked" vector for each mask independently makes me much more interested in this. It opens the door to a hell of a lot of possibilities here (a reason for this blog here) integration, derivative, inverse, square root to name some among similar operations on polynomials and series.

I do remember the day when I learnt about the inverse and square root of a polynomial and was overwhelmed by it. On that day, I just concluded that "polynomials are just numbers". Later I have seen some problems which even used dp states as polynomials instead of integers. The observation "polynomials are just numbers" makes it easy for me to understand those editorials and those problems do excite me these days. Something similar for sets will for sure generalize it further.

Publishing this blog with the expectation that I would find more material to read about it since Google isn't my friend here.

Update 1 (solution) —

O(N^2*2^N) solution of initial problem

• +63

By aryanc403, history, 3 months ago,

Notification, when someone in your friend list writes a comment or creates a blog, is too annoying. Can someone make it opt-in?
/cc geranazavr555 MikeMirzayanov

Update 1: Apologies to 1595 people who got pinged due to this blog.
Update 2: I just realised codechef advertised their upcoming contest to 9298 people without spending a single penny. GG.

• +450

By aryanc403, 7 months ago,

17 Dec 2019 -

3 March 2020 -

Finally on 16 Nov 2020 -

And the hunt continues.

• +215

By aryanc403, history, 2 years ago,

hmehta didnt made an announcement on CF :/
SRM 756 will be held today.(in less than 30 mins) Atleast topcoder site says so.

Lets discuss problems after the contest.

• +44

By aryanc403, history, 2 years ago,

MikeMirzayanov
Can you please add an unofficial checkbox on a user profiles contest page (e.g. — My Profile's Contest Page) similar to the submissions page.
Unofficial contests can include Unrated, out of competition contests. And maybe virtual participation as well.
Thank you.

• +46

By aryanc403, 3 years ago,

We are trying to add our first gym contest for members of our college in our CF group.
We have added problems on polygon platform.

For adding problem in group We came across https://codeforces.com/blog/entry/10077?locale=en . We have followed preliminaries of Polygon and up to step 2 of CF.

For the third step, we need one directory at ftp://taskbook.codeforces.com . Unfortunately, it is showing the following error.

→ External storage error
The external storage was offline or malfunctioned during the last contest update. Please wait for some time, then go to the contest edit page and click "Save changes" to synchronize data

MikeMirzayanov please fix this issue asap. So that we can add problems for our group. We are planning to start the contest by Thursday evening. And we have less than 24 hrs.

We express gratitude to MikeMirzayanov and the rest of the team for the great Codeforces and the wonderful Polygon platform.

Upd: Issue was fixed within 15 minutes after this blog.
Maybe It was due to this blog or they were already working on it.

• +15

By aryanc403, history, 3 years ago,

Since ICPC season is underway. In past, Three Codeforces Trainings Seasons (in 2013-14, 14-15, 16-17) and one on codechef) were organized.
Can someone organize one for this season also?