Algorithms *

The Mandelbrot set. And it's a program! I made it in g++, a freely distributable C++ compiler. Read it! Very interesting. Using OpenMP, you do parallel programming at the multithreading level. And I decided - this would be a completely different level of quality! I implemented honest supersampling (antialiasing) - with 8x8 antialiasing (64 passes per pixel!!!) That is, not 1920 by 1080 pixels, but 8x8 more! 15360 by 8640 pixels! And then these 64 passes reduce by one pixel, but smoothly - and no longer 8-bit, but 24-bit TrueColor!

Short video apps have completely reshaped how people consume entertainment. Instead of sitting down for a two-hour movie or a 45-minute TV episode, viewers are now hooked on bite-sized videos that fit into their busy schedules. This shift has been accelerated by Gen Z and Millennials, who prefer quick storytelling formats that are both interactive and engaging.

In 2025, the OTT and short video industry is projected to see over 1.5 billion monthly active users worldwide, with an average revenue per user (ARPU) of nearly $12. The reasons are clear: affordability, accessibility, and convenience. The success of apps like DramaBox shows that people are willing to spend money on shorter dramas as long as they deliver strong storytelling.

For entrepreneurs, this presents a golden opportunity to build OTT platforms like DramaBox and tap into this global demand.

Complex systems often appear chaotic or incomprehensible, yet closer examination reveals that such complexity can frequently be reduced to a simple underlying mechanism. By systematically removing layers of emergent behavior, one can uncover a fundamental rule or equation from which the entire system originates.

Armenia is a lucky country. Back in the 1990s somebody lobbied Synopsys, the #1 leader in the Electronic Design Automation market, to create a division there. It was joined by Mentor Graphics / Siemens EDA, another EDA leader, then NVidia. Synopsys Armenia became the largest Synopsys division outside the US Silicon Valley and Boston, although the Taiwanese may tell you otherwise. Since Synopsys and Mentor make software used by chip designers in Apple, Samsung, AMD and all other electronic companies, Armenia has an unfair advantage over all their neighbors in Caucasus and Central Asia.

In addition, Armenia has friendly relations with Russia, and most Armenians speak Russian as well. This has facilitated the move of many Russian companies to Armenia, for example, a RISC-V semiconductor IP provider Syntacore. Finally, as we can see from the recent conference EDA Connect, Armenia is attracting the attention of electronic and EDA companies from China.

EDA Connect featured not only academic and industrial papers but also a hackathon on FPGA design, attended by local students from Yerevan State University, the American University of Armenia, the Russian-Armenian University, the French University in Armenia and others.

The most common types of software bugs are memory management bugs. And very often they lead to the most tragic consequences. There are many types of memory bugs, but the only ones that matter now are memory leaks due to circular references, when two or more objects directly or indirectly refer to each other, causing the RAM available to the application to gradually decrease because it cannot be freed.

Memory leaks due to circular references are the most difficult to analyze, while all other types have been successfully solved for a long time. All other memory bugs can be solved at the programming language level (for example, with garbage collectors, borrow checking or library templates), but the problem of memory leaks due to circular references remains unsolved to this day.

But it seems to me that there is a very simple way to solve the problem of memory leaks due to circular references in a program, which can be implemented in almost any typed programming language, of course, if you do not use the all-permissive keyword unsafe for Rust or std::reinterpret_cast in the case of C++.

A lot of people around me spend time trading on the stock market. Some trade crypto, some trade stocks, others trade currencies. Some call themselves investors, others call themselves traders. I often see random passersby in various cities and countries checking their trading terminals on their phones or laptops. And at night I sometimes write analytical or backtesting software—well, I did up until recently. All these people share a common faith and a set of misconceptions about the market.

In today's interconnected development world, secure authentication is not just a luxury—it's a necessity. Whether you're a seasoned DevOps engineer or a junior developer just starting your journey, understanding SSH key pairs is crucial for your daily workflow. They're the unsung heroes that keep our git pushes secure, our server access protected, and our deployments safe from prying eyes.

But let's be honest: SSH keys canbe confusing. With terms like “public key infrastructure,” “cryptographic algorithms,” and “key fingerprints” floating around, it's easy to feel overwhelmed. This guide aims to demystify SSH key pairs, breaking down complex concepts into digestible pieces that will help you make informed decisions about your security setup.

OpenStreetMap (OSM) is a global project formed around a geographic information database which is being filled by all comers — both enthusiasts and interested companies. Anybody can contribute, but the openness has its downside: incorrect edits often get into the database. Hence plenty of validators of OSM data have been written which allow to maintain the data quality at an acceptable level.

Since 2016 there exists an open source subway preprocessor that validates (generates error reports) rapid transit routes in OSM for completeness and logical/topological errors, and converts them into formats that are suitable for routing and rendering, e.g. GTFS. Besides OSM data it takes a list of public transport (PT) networks which contains the checking information about the number of lines, stations etc. per a PT network. The preprocessor has successfully proven itself in the preparation of PT data for applications such as Maps.me and Organic Maps.

In this article, I would like to share an approach to detecting one of the types of errors that occur quite often in OSM data and automatic detection of which is somewhat challenging. It's an accidental loss of a station from a route. The source code of the validator and the described algorithm are open source. But first, let's define the concepts used to represent PT data in OpenStreetMap.

The traditional definition for the operation of exponentiation to a natural power (or a positive integer) had introduced approximately as follows:

Exponentiation is an arithmetic operation originally defined as the result of multiple multiplications a number by itself.

But the more precise formulation is still different:

Raising a number X to an integer power N is an arithmetic operation defined as the result of multiple [N by mod times] multiplications or divisions one by number X.

Surprisingly, there are strict mathematical methods that literally allow to hear visual geometric forms and, conversely, to see the beauty of musical harmonies...

[Read on Russian]

The intuition is to employ a depth-first search (DFS) approach through the tree.

During each step in the traversal, we perform the following key calculations:

1. Determine the path that ends at the current node.

2. Compute two different subtree paths that traverse the current node.

3. Maintain an array that keeps track of the cases where paths contain either 0 or 1 prime number.

This method allows us to efficiently count the valid paths in the tree while considering the presence of prime numbers.

Time complexity: O(max(nums) * log(max(nums)) + n * log(n)). Accounting for computing prime scores, using the stack to compute next greater elements, and sorting the tuples.

Space complexity: O(max(nums) + n). Considering the space required for arrays and the stack used for computation.

2809. Min Time to Make Array Sum: Efficient Swift solution, using dynamic programming, for minimizing time to reach a sum in arrays A and B. Time: O(n²), Space: O(n).

2813. Max Elegance of K-Length Subseq: Swift code for elegantly selecting unique k-length subsequences with profit and categories. Solution uses sorting and iteration. Time: O(nlogn), Space: O(n).

Github: https://github.com/sergeyleschev/leetcode-swift

Hard++, Extra Category.

Amazon.

Overflow checks have been taken into consideration. The maximum time to move a box is at most 4 * 1000 (four steps to move the box, each taking 1000 time). With at most 1e4 boxes, the total time is at most 4e7, ensuring the solution is safe.

Given two positive integers low and high represented as strings, find the count of stepping numbers in the inclusive range [low, high].

A stepping number is an integer such that all of its adjacent digits have an absolute difference of exactly 1.

Return an integer denoting the count of stepping numbers in the inclusive range [low, high].

Since the answer may be very large, return it modulo 10^9 + 7.

Hard, Acceptance Level 14.5%.
Dynamic Programming (DP).
Efficiently handles large inputs (10^9 + 7).

Latest and Most Hardest Problem.

Simple Swift Math Solution.

Time complexity: O(N logN).

The time complexity of this solution is dominated by the sorting step, making it O(N logN), where N is the length of the input array usageLimits. The rest of the operations involve simple arithmetic and comparisons, which take linear time. Therefore, the overall time complexity of the function is O(NlogN).

Only 10 lines of code.

LeetCode 2612 (Hard). Minimum Reverse Operations.

The algorithm follows a breadth-first search (BFS) approach to determine the minimum number of reverse operations needed to bring the 1 to each position in the array.

To speed up the algorithm, we mark banned positions with -2 instead of using set lookups. This optimization reduces the constant coefficient and improves the speed of the algorithm, but it may still result in a time limit exceeded (TLE) error.

For each visited position, there are potentially O(k) target positions that can be reached through reverse operations. To avoid the multiplicative cost of iterating over all these potential positions, we update the nextNode2s array. This array initially points forward by 2, but we update it dynamically to point beyond all the target positions considered for each visited position. This optimization helps improve the efficiency of the algorithm and avoids unnecessary computations.

Solution of the day.
LeetCode 956 (Hard). Tallest Billboard.

The code uses dynamic programming to solve the problem. It maintains a dictionary dp, where the keys represent the possible height differences between the two billboards, and the values represent the maximum sum of heights achieved for each height difference.

Hash, salt, SHA-1, SHA-2, std::hash.. To a non-programming person that may come up as some kind of a recipe that just does not seem to add up. In a sense, this is indeed supposed to be a gibberish to any third party and a strong, helpful mechanism for us, programmers. 

At the start of writing this article, I had one clear idea to get across the table: to finally unveil this mystery of hashing in C++ for beginners. I, a beginner myself, also wanted to solidify my knowledge in this area; so let’s get started.

1 Playing Diplomacy

1.1 What this work is about

1.2 A puzzle for the talented and brave (Eccentrics are welcome: ?)