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About Me

 Hello everyone, I am Joshua Adrian Cahyono. I am a curious learner who is interested in the field of mathematics and computer science. In the past two years, I have dedicated myself to competitive programming. Thankfully, I won a silver medal in Indonesia's national informatics competition and also got the opportunity to join the national training camp. Currently, I am preparing for the next IOI in 2022. Every so often, I am also interested in solving math problems and making AI projects. 

I figured that keeping all this knowledge for myself would be a waste, so I want to share the experience and knowledge I gained from my years of study with this blog. I would mainly discuss problems and strategies in competitive programming. Occasionally, I might discuss math and AI topics as well. I would love to hear any advice on improvements to the blog and topics you would like to know more about. I hope you will enjoy reading my blog!


Also, feel free to check out some of my accounts:

Codeforces profile

TLX profile

Youtube account

IG account

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Popular posts from this blog

Proof for fun!

This post will be about several proofs of random theorems or formulas that I enjoy proving and I would like to share them with everyone. I hope that everyone could see the beauty of mathematical proofs from this post. Formula 1 For a positive integer $n$, it always holds true that: [\lim_{x \to 0} \frac{1-\prod_{i=1}^n cos(a_i x)}{x^2} = \frac{1}{2} \cdot \sum_{i=1}^n a_i^2] Note for some who might not be used to the notation, $\prod$ here is just like $\sum$ but instead of summation of terms, it is the product of all the terms. For example $\prod_{i=1}^3 i = 1 \cdot 2 \cdot 3 = 6$ Simple Example: [\lim_{x \to 0} \frac{1-cos3x \cdot cos4x \cdot cos5x}{x^2} = \frac{3^2+4^2+5^2}{2} = 25] Proof: In dealing with problem where there exist $n$ term products, we should try to build it from the most simple case of $n=1$, and then try to prove for $n=k+1$ using the equality from $n=k$ (similar to a domino effect ). In mathematics, we call this method as  induction . First step i...
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Binary Search the Answer (BSTA)

 First and foremost, this post serves as my first ever competitive programming-related post and also as a testing of the equations and code snippets in this blog. Therefore, tips and advice are highly appreciated. In this post, I would like to write about a commonly used Divide and Conquer algorithm called Binary Search The Answer (BSTA). Many programmers might already know about binary search but some might not be familiar with BSTA.  What is BSTA? To recall, binary search is an algorithm for searching a value in a static sorted array by considering the median value and reducing the problem's scope by half, as shown  here . Binary search the answer uses a similar principle to a normal binary search of halving the range of the problem. However, we do not binary search a position with a certain value. Instead, we binary search the maximum/minimum value that satisfies the given constraints. In one iteration, we consider the average $mid$ of the current possible range and ...
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Integral Problems Discussion

In this post, I would like to write a solution to an integral problem (possibly more problems in the future) as well as give insights that are usually not taught, in spite of its importance. Without any longer, let us delve into the problem. Problem 1 Find the value of the integral: [ \int \frac{\sqrt{4x-x^2}}{x} dx ] Insight 1 First of all, in dealing with integrals, we should usually try to avoid forms with square roots . Moreover, it is usually harder to manipulate the equation if we have multiple $x$ terms in a square root. Thus, in this problem, the most troublesome part is $\sqrt{4x-x^2}$. After knowing this, several ideas to simplify this form might come up.  The first most common ways to deal with $x$ and $x^2$ terms is by completing the square . In this case, $4x-x^2$ can be written as $-(x-2)^2+4$. However, the problem with this approach is that the denominator is $x$, so if we want to do a substitution of $u=x-2$, the denominator would be in the form of $u+2$, which...
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