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Almost every week, it seems, another part of our world is analyzed in an as-a-service package. This growing trend should not surprise anyone. As hardware, software, bandwidth, and protocols evolve, more processes and resources can be outsourced. This subsequent development is driving digitalization that is transforming industries around the world. Financial services are no exception. Banking as a Service (BaaS) brings banking to the world. However, as with almost everything related to finance, BaaS is surrounded by mystery. In this article, we want to overview banking as a service to shed light on its benefits, uses, and challenges. What is Banking as a Service? BaaS is a model that allows online banks and third parties to connect directly to banking systems through APIs, building banking offerings on top of a regulated vendor infrastructure, and unlocking new experiences. Digital-savvy traditional firms can fend off the looming fintech threat by moving into the BaaS space to share their data and infrastructure. In a few years, access to this level of information will guarantee digitally accustomed clients, so banks that start now will be ahead of their rivals and likely to be rewarded with solid demand. How does Bank as a Service Work? The BaaS model starts with a fintech, digital bank, or third-party provider (TPP) paying a fee to access the BaaS platform. A financial institution exposes its APIs to TPP, providing access to the systems and information needed to create new banking products or offer white-label banking services. Besides advancing open banking, traditional institutions that launch their own BaaS platforms are also opening up new revenue streams. The two main BaaS monetization strategies include charging customers a monthly fee to access the BaaS platform or charging for each used service. Layers of Banking as a Service As the image below demonstrates, BaaS can have multiple service tiers, and customers can choose numerous of them for the business. It depends on the needs of the company. BaaS vs. Open Banking vs. Banking as a Service Platform You need to distinguish between these three terms. BaaS is often confused with Open Banking as the latter also uses an API to link banks to non-banks. Although, the core functions of open banking differ significantly. Under this model, non-banks use APIs to access banking data and embed it into their financial services. For example, people use a financial management app to keep track of their monthly expenses. The app uses an API to integrate transaction data from the user’s bank account and perform analytics to help them manage finances more efficiently and improve spending habits. The itself does not provide any new banking services. It simply integrates the data already stored in the bank into the account management functions. This is how open banking business models work. app Unlike open banking, BaaS provides the user with an entirely new type of service. ​​BaaS does not give customers what has already been created but uses it as a basis for making a new banking experience. Besides, there is a difference between BaaS and a banking platform. The leading players in banking platforms are not third parties but the banks themselves. They use the power of financial technology to provide access to the services offered by the bank. For example, a bank could create an AI-powered tool to help users select the best investment opportunity and quickly complete their day-to-day banking transactions. Currently, financial institutions are using banking platforms to retain clients and enable them to immerse themselves in the fintech industry fully. In the BaaS concept, the end-user interacts not with the bank but with a third party that offers new services. The brand front-end is connected to the BaaS provider via an API, which connects the provider to the bank. This chain allows distributors, brands, and fintech companies to integrate service banking directly into their products – e-commerce websites, fintech applications, or financial services. Banking as a Service Advantages Benefits for a Client BaaS brings innovation and customization to fund product development. Clients receive the following benefits: Excellent Services are Offered If there were no BaaS providers, customers would use banking services directly. So, it’s not that the client needs BaaS – BaaS requires a client. That’s why BaaS providers strive to offer a truly superior experience. They are making an effort to meet the needs of banking customers who are digital natives and genuinely tech-savvy. More Products to Choose From The wider the choice, the better for the client. High competition is not good news for service providers. But for clients, it gives more flexibility. Innovative solutions strive to be customer-centric and offer all the necessary functions in one place. This enhances financial transparency and simplifies cash management compared to traditional bank accounts. Benefits for the Banks Like customers, banks offering API-based data access also have a win-win strategy. At a minimum, they lose nothing and earn more money. Most importantly, they benefit personally from sharing their data with BaaS banking providers. More people use Banking Services Banking as a service does not create an additional burden on the bank. Instead, BaaS provides new lines and revenue streams. The bank offers access to data through the API and takes a commission for this. He does not care how third-party distributors will attract the audience, where they will look for funds, whether they will outperform competitors, etc. They do not need to invest in development. Their primary responsibility is to ensure that customer data is well protected from breaches. Banks get to know the needs of their audience By analyzing the performance of a third-party BaaS provider, banks can gain insight into the needs of their customers. What features do they use, what helps them manage their finances, and what annoys them? Such insights can be obtained using machine learning solutions for finance and incorporated into developing the bank’s products. Benefits for Business Non-banks, enterprises, and fintech companies that provide BaaS play the most responsible role in this game. In addition to the benefits, they may find investing in a new solution challenging, just as it can be when developing any other product. They must build a to avoid failing their idea. But despite the threats, they can still gain a lot of strength. risk management strategy Enterprises Become Bankers, not Being Bankers As payments and settlements are the most popular startup segment among American banking investors. With the fintech industry’s growth, they all see great potential in investing in banking solutions. To offer banking services themselves and circumvent banking laws, businesses prefer to act as a third party and earn money by acting as an intermediary between the financial institution and the customer. FinancesOnline states, Customer Recognition Yes, it is not easy for clients to entrust their financial data to a third-party business they have never heard of. By linking with well-known banking institutions, BaaS providers build on the bank’s reputation in customers’ eyes and quickly gain their trust. Disadvantages of Banking as a Service Competition can shrink banks’ customer base For banks, BaaS means they face the constant danger of losing some of their market share to better-serving non-banks. Usually, no one-on-one relationships If you prefer digital banking but want to interact with your financial institution in person, you generally won’t get it with BaaS accounts. Your information is less secure Because you use two companies for your banking transactions (the account offering company and the bank), your information is exposed in two ways instead of one. Banking as a Service Examples To get a better understanding of BaaS, let’s take a look at a couple of real-world applications. This list is not definitive and is growing every day, so we will analyze three options for using banking as a service: Platforms and marketplaces with a large user base can benefit significantly by offering their customers the e-wallet functionality through deposit accounts. For example, crowdfunding platforms can use a BaaS solution to create unique IBAN accounts for individual users and hit two birds with one stone. Firstly, it contributes to a better user experience as they do not need to make a bank transfer every time they make a transaction on the platform as the funds are securely stored there. Secondly, it is easier for the platform to convince customers to reinvest, significantly increasing client retention. Almost any service provider can benefit from BaaS and offer white-label payment cards to their clients. Customers take advantage of individual card programs, and businesses create an additional revenue stream. However, fintech startups are taking full advantage of BaaS services. They can use the infrastructure and functionality of banks (also known as banking software as a service) and data banks about their customers. This opens up a whole new spectrum of startup opportunities, from personal finance apps to real-time payments, from targeting niche customers to focusing on mainstream adoption. What is paramount for startups is that BaaS can save you a ton of money and at least a couple of years in business and product development. Not to mention that they would not need to have the funds to acquire a license. The earlier they enter the market, the happier their investors are. How to Choose a Banking as a Service provider? So you’ve decided to integrate your business with a financial services platform. When searching for the ideal BaaS provider candidate, we suggest considering the following: Reputation In the global network, nothing stays a secret for long. Look for reviews and testimonials to form an objective opinion. Relevance of services Take a close look at the services offered by a particular provider to ensure they meet your business requirements. Ownership of services Are the proposed APIs and solutions provided by the company or owned by third parties? This issue will become necessary as the partnership develops. Scalability Does the potential partner have the tech stack, resources, and stamina to play the long game? Will they be able to stay up-to-date as their customer base expands and business needs grow? Compatibility and speed to market How quickly and reliably can the supplier deliver the solution you need? There is one more small difference that we should mention to avoid any confusion. Top Banking as a Service Companies As BaaS gains momentum, new providers are entering the market along with platforms created by banks. While BaaS providers use a closed architecture, platforms are designed to share APIs with clients. Here are some of the leading players. The Bancorp With $6.2 billion in assets and $232 billion in annual cumulative processing volume, started as a branchless bank and is now a leader in digital financial services. The company provides private banking and technology solutions for non-banking businesses. It has been holding the number one position in prepaid card volume in the US for eight consecutive years and specializes in institutional banking and commercial lending. The Bancorp Fidor Bank This German company, founded in 2009, has gone as far as creating its own BaaS platform. It runs on a proprietary OS and is a cloud-based modular system. teams have created over 40 standardized, forward-thinking APIs that integrate seamlessly with any customer service. The Fidor mobile banking app covers everything from standard accounts and card transactions to loans and crypto investments. Fidor’s Treezor is a Paris-based banking platform as a service, a “one-stop payment solution.” Recently acquired by , thanks to their innovative expertise, the startup is accredited to provide personalized payment services to its customers. Treezor Societe Generale Group Challenges of Banking as a Service The challenges of implementing a BaaS strategy are numerous. Fortunately, related solutions pave the way for user-friendly financial products and solutions. Let’s dig deeper. Modernization of traditional banks The core systems of most traditional banks are outdated. They are incompatible with modern technology. This can be a significant problem when implementing a BaaS model, as it can interfere with third-party integration. The future of banking as a service will include a modernized architecture of traditional banks. This will help expose services, products, and processes such as APIs. Changing roles of players in the financial industry Recent research shows that traditional banks are slowly losing the “customer trust” advantage over fintech players. On the other hand, many tech companies like Apple Card enter the financial space because they have customer trust. Moreover, BaaS involves cooperation with third-party players. Naturally, there are many coincidences in terms of functionality. In addition, many companies use ‘white labeling’ when offering their products. This can confuse end customers. Given these points, the future of BaaS shows a massive shift in player responsibilities. A well-defined API strategy Opening a bank or business (middleware) via an API is no small feat. Operational processes and business opportunities must be presented optimally. However, most organizations face challenges when creating an API strategy. The main goal when creating an API strategy should be ease of integration. It should provide maximum business value by limiting the cumbersome aspects of integration. The future of the financial industry may include a global standardization of the API strategy. Considering all factors, the BaaS sector shows no signs of stopping. It would be interesting to see how technological progress will affect the BaaS model in the next decade. The Banking as a Service Future The financial sector is rapidly changing, and BaaS is paving the way for a new reality. Banks, fintech, service providers, and brands can achieve synergy by creating functional and efficient integrated solutions. In an interconnected environment, everyone will reap their respective benefits if they quickly adjust their strategy. As financial services more closely reflect consumer needs, BaaS providers will attract new customers. Better customer profiling and additional revenue streams will give merchants a well-deserved bonus. All vendors need to do is establish relationships with a few relevant merchants and manage them effectively. The benefits for the banking sector from merging with providers and brands and reaching a much wider audience are even more apparent. Conclusion As you can see, BaaS has its benefits and challenges, just like any other development case. But it is a relatively vacant niche that gives you higher chances to stand out from the rivals. If the banking industry in your country is well-developed, you can create a BaaS solution and expand your market share. Also published here .

BaaS (Banking as a Service): Everything You Need to Know

In the tech world, hackathons are like rock concerts—full of energy, innovation, and a bit of chaos. Stanford's TreeHacks is the Glastonbury of them all, drawing the brightest minds and wildest ideas from Silicon Valley and around the world. This year’s edition, however, took center stage not just for its usual vibe of cutting-edge creations but for its focus on AI. The mood? Electrifying. Unleashing AI's Power at TreeHacks Walking through the aisles of TreeHacks was like peering into the future. From AI-powered diagnostic tools to social media bots that can outshine any influencer, it became clear that AI is ready to reshape every nook and cranny of society. Projects like Baymax and TherapEase.ai offered a tantalizing glimpse into healthcare’s future with personalized treatment plans, while MindMint took a swing at tailoring education to individual learning styles. Not to be outdone, Show and Tell, a fusion of wearable tech and language models, broke down barriers between American Sign Language users and non-ASL speakers, leaving the judges starstruck. And Zorg didn’t just come up with a catchy name but a decentralized system to securely handle medical records, balancing accessibility with airtight data protection. Insights From the Judges' Panel Judges like Deepita Pai played a critical role in evaluating these ambitious projects, using her extensive experience in building AI applications to guide hackers towards refining their work. Deepita stood out not just for her expertise but as a symbol of women's increasing leadership in technology. Her background at Square and Brainlab equipped her with an insider’s view on the importance of balancing innovation with ethical considerations and usability. Her lens sharpened on the necessity of collaboration, ensuring that these dazzling AI models weren’t just flashy toys but robust tools that could solve real-world issues. "Always keep the end user at the heart of your innovation," she emphasized. "Involve domain experts, prioritize inclusivity, and ensure your solutions reach those who need them most." Projects to Watch The hackers didn’t hold back on creativity either. Kaleido showed how biases in political news articles could be identified and counteracted, giving readers a fuller perspective on the stories they consume. ShaScam took on the rising menace of spam calls, using LLMs to protect vulnerable seniors from fraud. Meanwhile, EcoSynth saved analysts from spreadsheet nightmares by automating sustainability reports in a matter of seconds. Some projects aimed for the stars. Shard sought to challenge Sam Altman’s massive $8 trillion network by harnessing idle computing power worldwide. Their scrappy prototype earned them the “Most Likely to Get Funded” award and $1.5k in cash. Another moonshot, llm2graph, tried to fix LLMs’ text comprehension issues by crafting a dynamic knowledge graph, tackling the underlying problem head-on. TreeHacks Takeaways TreeHacks 2024 wasn’t just a showcase of technological achievements but a lively conversation about AI’s societal impact and ethical dimensions. If these projects are any indicator, the future will be a blend of audacity, empathy, and, as Deepita puts it, “innovation balanced with usability.” The success of AI will ultimately hinge not on algorithmic finesse but on the lives it touches and the positive change it inspires. So, here’s a tip for founders and hackers alike: solve a problem you’ve personally faced. EcoSynth did it with sustainability reports, and Instant-gram, born out of the founders’ social media frustrations, now creates engaging content that could save you hours of scrolling through stock photos. TreeHacks 2024 has spoken, and the future of AI is bright, inclusive, and beaming with possibility. In the tech world, hackathons are like rock concerts—full of energy, innovation, and a bit of chaos. Stanford's TreeHacks is the Glastonbury of them all, drawing the brightest minds and wildest ideas from Silicon Valley and around the world. This year’s edition, however, took center stage not just for its usual vibe of cutting-edge creations but for its focus on AI. The mood? Electrifying. Unleashing AI's Power at TreeHacks Unleashing AI's Power at TreeHacks Walking through the aisles of TreeHacks was like peering into the future. From AI-powered diagnostic tools to social media bots that can outshine any influencer, it became clear that AI is ready to reshape every nook and cranny of society. Projects like Baymax and TherapEase.ai offered a tantalizing glimpse into healthcare’s future with personalized treatment plans, while MindMint took a swing at tailoring education to individual learning styles. Not to be outdone, Show and Tell, a fusion of wearable tech and language models, broke down barriers between American Sign Language users and non-ASL speakers, leaving the judges starstruck. And Zorg didn’t just come up with a catchy name but a decentralized system to securely handle medical records, balancing accessibility with airtight data protection. Insights From the Judges' Panel Insights From the Judges' Panel Judges like Deepita Pai played a critical role in evaluating these ambitious projects, using her extensive experience in building AI applications to guide hackers towards refining their work. Deepita stood out not just for her expertise but as a symbol of women's increasing leadership in technology. Her background at Square and Brainlab equipped her with an insider’s view on the importance of balancing innovation with ethical considerations and usability. Her lens sharpened on the necessity of collaboration, ensuring that these dazzling AI models weren’t just flashy toys but robust tools that could solve real-world issues. "Always keep the end user at the heart of your innovation," she emphasized. "Involve domain experts, prioritize inclusivity, and ensure your solutions reach those who need them most." Projects to Watch Projects to Watch The hackers didn’t hold back on creativity either. Kaleido showed how biases in political news articles could be identified and counteracted, giving readers a fuller perspective on the stories they consume. ShaScam took on the rising menace of spam calls, using LLMs to protect vulnerable seniors from fraud. Meanwhile, EcoSynth saved analysts from spreadsheet nightmares by automating sustainability reports in a matter of seconds. Some projects aimed for the stars. Shard sought to challenge Sam Altman’s massive $8 trillion network by harnessing idle computing power worldwide. Their scrappy prototype earned them the “Most Likely to Get Funded” award and $1.5k in cash. Another moonshot, llm2graph, tried to fix LLMs’ text comprehension issues by crafting a dynamic knowledge graph, tackling the underlying problem head-on. TreeHacks Takeaways TreeHacks Takeaways TreeHacks 2024 wasn’t just a showcase of technological achievements but a lively conversation about AI’s societal impact and ethical dimensions. If these projects are any indicator, the future will be a blend of audacity, empathy, and, as Deepita puts it, “innovation balanced with usability.” The success of AI will ultimately hinge not on algorithmic finesse but on the lives it touches and the positive change it inspires. So, here’s a tip for founders and hackers alike: solve a problem you’ve personally faced. EcoSynth did it with sustainability reports, and Instant-gram, born out of the founders’ social media frustrations, now creates engaging content that could save you hours of scrolling through stock photos. TreeHacks 2024 has spoken, and the future of AI is bright, inclusive, and beaming with possibility.

Charting New Horizons: Exploring AI Innovation at TreeHacks 2024

By Alex Korotkov, CEO @ PineOx.com Hello, everyone. My name is Alex Korotkov. I'm a serial startup founder. I've developed several social apps previously with millions of Daily Active Users, including apps for Fox Sports, Liverpool FC, PSG, RMC Sport, and more. Also, I was an internationally acknowledged political prisoner in Belarus, and that's why I chose to start a startup in the social sphere. Despite the technological and chemical advancements of the last decades, 99.9% of CO2 extraction from the atmosphere still relies on trees and soil. This fundamental reality underpins our mission at PineOx, where we harness the power of technology not to replace, but to amplify these natural processes. Our approach is simple yet profound: facilitate tree planting on a massive scale to combat climate change effectively. As the CEO of PineOx and a software developer with over a decade of experience in creating apps, I have directed our efforts toward developing a platform that empowers individuals worldwide to participate in environmental preservation. Our application not only makes it easier for anyone to contribute to stopping climate change but also ensures that their efforts are transparent and impactful. Tech-Driven Solutions At PineOx, we leverage emerging technologies to enhance our tree-planting efforts. These technologies allow us to track the growth and carbon sequestration impact of each tree, ensuring every participant can see the tangible results of their contributions. We initiated PineOx because polls showed a significant increase in demand for solutions that enable widespread participation in climate action. The services currently available on the market, primarily from non-profits, lack the transparency and social components necessary for a B2C tool to succeed. By filling this gap, we aim to engage as many people as possible in becoming more environmentally responsible. Every tree planted through our app comes with a digital twin, represented by an image and location data. This feature allows our users to verify the progress of their seedlings either by visiting the planting sites or by viewing satellite imagery available on platforms like Google Maps. Engagement Through Innovation One of our core challenges is differentiating ourselves in a crowded market. At PineOx, we bet on a unique and engaging user experience through simple yet unorthodox mechanics. Users engage with our platform by completing sustainability quizzes, and PineOx commits to planting a real tree for every two quizzes completed. We then send the user an image and location of the planted tree, thus maintaining a transparent and direct connection between our users' actions and their environmental impact. Our app educates users about their CO2 footprint through an intuitive interface that calculates their annual emissions. We then translate these figures into the number of trees needed to offset their footprint, usually one tree every 7-14 days, depending on their lifestyle habits. This educational tool has surprised many of our users, who often don't realize the extent of their impact on the environment. To keep users engaged and informed about the importance of their contributions, especially during significant events like Earth Day, PineOx sends push notifications reminding them to plant more trees to maintain their CO2 neutrality. This reminder is not just a nudge; it's an invitation to participate further in quizzes that deepen their understanding of their environmental impact. Future Outlook Looking forward, PineOx is committed to expanding our technological capabilities to further enhance our environmental impact. Our future roadmap includes integrating more advanced digital solutions to enable broader participation in tree planting, addressing the urgent need to counteract rapid deforestation. By focusing on scalable solutions, PineOx aims to plant billions of trees each year, bridging the gap between deforestation and reforestation rates and ensuring a healthier planet for future generations. This story was distributed under HackerNoon’s Business Blogging Program. Learn more about the program here. By Alex Korotkov, CEO @ PineOx.com By Alex Korotkov, CEO @ PineOx.com By Alex Korotkov, CEO @ PineOx.com Hello, everyone. My name is Alex Korotkov. I'm a serial startup founder. I've developed several social apps previously with millions of Daily Active Users, including apps for Fox Sports, Liverpool FC, PSG, RMC Sport, and more. Also, I was an internationally acknowledged political prisoner in Belarus, and that's why I chose to start a startup in the social sphere. Despite the technological and chemical advancements of the last decades, 99.9% of CO2 extraction from the atmosphere still relies on trees and soil. This fundamental reality underpins our mission at PineOx, where we harness the power of technology not to replace, but to amplify these natural processes. Our approach is simple yet profound: facilitate tree planting on a massive scale to combat climate change effectively. As the CEO of PineOx and a software developer with over a decade of experience in creating apps, I have directed our efforts toward developing a platform that empowers individuals worldwide to participate in environmental preservation. Our application not only makes it easier for anyone to contribute to stopping climate change but also ensures that their efforts are transparent and impactful. Tech-Driven Solutions Tech-Driven Solutions At PineOx, we leverage emerging technologies to enhance our tree-planting efforts. These technologies allow us to track the growth and carbon sequestration impact of each tree, ensuring every participant can see the tangible results of their contributions. We initiated PineOx because polls showed a significant increase in demand for solutions that enable widespread participation in climate action. The services currently available on the market, primarily from non-profits, lack the transparency and social components necessary for a B2C tool to succeed. By filling this gap, we aim to engage as many people as possible in becoming more environmentally responsible. Every tree planted through our app comes with a digital twin, represented by an image and location data. This feature allows our users to verify the progress of their seedlings either by visiting the planting sites or by viewing satellite imagery available on platforms like Google Maps. Engagement Through Innovation Engagement Through Innovation One of our core challenges is differentiating ourselves in a crowded market. At PineOx, we bet on a unique and engaging user experience through simple yet unorthodox mechanics. Users engage with our platform by completing sustainability quizzes, and PineOx commits to planting a real tree for every two quizzes completed. We then send the user an image and location of the planted tree, thus maintaining a transparent and direct connection between our users' actions and their environmental impact. Our app educates users about their CO2 footprint through an intuitive interface that calculates their annual emissions. We then translate these figures into the number of trees needed to offset their footprint, usually one tree every 7-14 days, depending on their lifestyle habits. This educational tool has surprised many of our users, who often don't realize the extent of their impact on the environment. To keep users engaged and informed about the importance of their contributions, especially during significant events like Earth Day, PineOx sends push notifications reminding them to plant more trees to maintain their CO2 neutrality. This reminder is not just a nudge; it's an invitation to participate further in quizzes that deepen their understanding of their environmental impact. Future Outlook Future Outlook Looking forward, PineOx is committed to expanding our technological capabilities to further enhance our environmental impact. Our future roadmap includes integrating more advanced digital solutions to enable broader participation in tree planting, addressing the urgent need to counteract rapid deforestation. By focusing on scalable solutions, PineOx aims to plant billions of trees each year, bridging the gap between deforestation and reforestation rates and ensuring a healthier planet for future generations. This story was distributed under HackerNoon’s Business Blogging Program. Learn more about the program here. This story was distributed under HackerNoon’s Business Blogging Program. Learn more about the program here . here

Tech-Driven Tree Planting: How PineOx Moves Beyond Traditional Methods

টেক-চালিত বৃক্ষ রোপণ: কিভাবে PineOx প্রথাগত পদ্ধতির বাইরে চলে যায়

Technologiegestützte Baumpflanzung: Wie PineOx über traditionelle Methoden hinausgeht

Plantación de árboles impulsada por la tecnología: cómo PineOx va más allá de los métodos tradicionales

Plantation d'arbres basée sur la technologie : comment PineOx va au-delà des méthodes traditionnelles

तकनीक-संचालित वृक्षारोपण: पाइनऑक्स कैसे पारंपरिक तरीकों से आगे बढ़ता है

テクノロジーを活用した植樹: PineOx が従来の方法を超える方法

기술 중심 나무 심기: PineOx가 전통적인 방법을 뛰어넘는 방법

Plantio de árvores baseado em tecnologia: como o PineOx vai além dos métodos tradicionais

Посадка деревьев на основе технологий: как PineOx выходит за рамки традиционных методов

Teknoloji Odaklı Ağaç Dikimi: PineOx Geleneksel Yöntemlerin Ötesine Nasıl Geçiyor?

Trồng cây dựa trên công nghệ: PineOx vượt xa các phương pháp truyền thống như thế nào

科技驱动的植树：PineOx 如何超越传统方法

Daily Coding Problem Hello everyone and welcome back with another problem to solve! Today we’ll be dealing with paths, calculating the greatest path in a triangle of numbers starting from the top to the bottom! Today’s problem comes from the archives of : a super cool website to look at if you are in the mood for some head scratching! There are more than 800 math and coding problems to solve and a vast archive of discussions about them. It is the perfect tool to train your math skills and learn something new. Go check it out and try to solve your challenges too! ProjectEuler.net Let’s jump to the action! The problem By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23. That is,3+7+4+9=23. Find the maximum total from top to bottom of the triangle below: As there are only 16384 routes, it is possible to solve this problem by trying every route. However, , is the same challenge with a triangle containing one hundred rows; it cannot be solved by brute force, and requires a clever method! ;o) NOTE: Problem 67 So, to recap a bit: we are given a triangle with numbers. Each number is connected to the two directly below it, . What we need to do is go from top to bottom and find the maximum possible path value. The sum of its values will be our answer. Also, as the problem states, since the routes are limited, we could try the solution out from calculating every possible route. As we’ll see just in a moment, , so we should scrap our heads a bit and find a better solution. forming a path directly to solve it by brute-forcing that would not be an efficient solution Ready then? Let’s solve it! Brute forcing the solution Since the problem advises that the brute force solution is not an efficient one, let’s take a moment to understand why is by looking at some smaller triangles. To know which path is the most valuable one, we first need to . It would be nice to know how many of them there are in the first place. walk over all the possible paths So, let’s try to count them: When there is one row (just one element) we have only one possible path. With two rows there are two possible paths we can take, with three rows there are 4 paths, and so on. Hopefully, you can see what’s happening here: : so for instance, with 4 rows we have 2³ = 8. In the problem’s example, the triangles have 15 rows so we count 2¹⁴ possible paths, which are 16384 possible routes, just as the problem states. the number of paths grows like 2ⁿ⁻¹ Given this, to calculate the maximum path by brute force, we would need to calculate the value of all the 16384 routes and then compare them. Besides the hassle of calculating all those possible paths, for the next similar problem mentioned by the text, which has 100 lines, we are going to have 2⁹⁹ possible paths, meaning roughly a total of 63.382.530.010.000.000.000.000.000.000 possible routes: inconvenient to say the least. Finally, , which is one of the worst results we could hope for. brute forcing the solution would force us with an algorithm with a time complexity of O(2ⁿ) We need a better method. The better method As we saw, the main problem in brute-forcing the solution is that there are so too many steps that our algorithm should do to calculate them all. . Since the number of routes depends on the number of elements in the triangle, we have no control over that variable. way too many possible routes, A better solution should involve either fewer routes or fewer steps to calculate them So, s needed for the algorithm to complete. What if we could calculate the maximum path possible of every given triangle … with just one step? our only chance is to reduce the number of step Let’s take a triangle and reason about it. This is the triangle from the sample given by the problem, for which we already know that the maximum path is 23 (the one in red), or 3 + 7 +4 + 9. This is our first hint: This means that we could track the growing value of each path while we go down the triangle and choose the maximum at the end. We can do this by . we don’t need intermediate values, we just want the sum of them. updating intermediate numbers with their actual path value As you can see we can apply this process row by row, updating all the values until, in the last row, we obtain the exact solution: 23. This is why I called it the avalanche algorithm: ! it’s like a snowball rolling down the mountain, which takes the route with the most snow on it and collects it to grow and grow again We have a problem though: for certain values inside the triangle we obtain multiple values. Take the middle 4, for example, the one in the third line of the first graph. If we come to the 4 from the 10 we are going to get 14 as a result, but if we come from the 7 we are going to obtain 11. If we think about it though, 10 and 7 in the second row are already “path values” updated from the previous row, since we’ve done 3+7=10 and 3+4=7 to get them. This means that the path coming from the 10 has already a higher value than the one coming from the 7 and, since we jump on the 4 only from those two values and from 4 we can only go to 5 and 9, we can conclude that the 10 path has an higher value than the 7 one, at least up to that point, and then we will always choose the route coming from the 10. It’s much clearer if you look it like this: Since we are coming only from 10 and 5, no matter if we are going to 5 or 9, we will always choose the path that already has a value of 10 because it’s higher than the one with a value of 7. This is our second hint: We could also store it, as we’ll do if we want to take the inverse road and print out the final path. besides adding the “path value” row by row and number by number, for each number we can choose the highest previous path value and move on. Each element in the triangle will have two values then: its real value and an “updated value” to keep track of the path value up to that point. OK: we have everything we need to start coding then. Let’s jump to the code! The code As with every good coder out there, I learned during the years to innately hate . Given this though, I feel like that for this project a solid OOP language was needed, to wrap everything up in a clear form. Go, even if is by far my first choice on almost every project, was not that suitable for this kind of task: its lack of a proper class object would have been a pain to deal with. Python is similar, since it has classes but it becomes messy to work with them after a while, in my opinion at least. , which is sold as Java 2.0: much less boilerplate but the same code potential for its interoperability with Java code. If you never used it, you’ll love it in a moment. Java So for this problem, we are going for Kotlin Also, this solution requires building a : if you are not familiar with that kind of data structure go check some resources online if you feel this solution is not clear! tree Let’s write the code then. https://gist.github.com/NicolaM94/81f57ae53d2c79012926047528ea492b?embedable=true We’ll start writing a class, which will be the blueprint for each number inside the triangle. This class must be built with two parameters, , the actual value of the number, and , the list of previous Nodes from which you can jump to this value (always at most 2). Then, inside the class we are going to build two other attributes: , which will hold the updated value of the path up to that point, and , which will hold the biggest parent of that node. We initially set to be equal to . Node value parents updatedValue chosenParent updatedValue value After that, we call the block, which will be the first block executed when the class gets created. In that block, we loop over the two parents (the loop there it’s a bit useless since there always are two parents, but it’s useful to show the idea behind it) and we update the with the found. Finally, we update to be equal to the value of this node plus the updated value of its bigger parent. init chosenParent biggestParent updatedValue We can also write a simple function which recursively print out the chain of values that brought us here. PrintChain That’s it, really: you have everything you need to solve the problem! Of course, you need a wrapper to collect all the numbers and instantiate all of them as nodes. Here’s the one I wrote, but of course you should build one yourself for your implementation. https://gist.github.com/NicolaM94/756a0d5fa2477454f16c4c23537a9b22?embedable=true Lastly, in the main function, we can wrap everything up and loop over the last line to get our solution. As always, for the problems given by ProjectEuler.net, besides presenting math riddles and problems, . And I love that: they are so committed that publishing results and guides for their problems is forbidden (this is one of the first 100 problems, so I understand it is permitted). Given this, . You have everything you need to start working on it! I won’t give out the solution: you need to build this by yourself, if you want to know it! ProjectEuler.net is a lovely project: their main focus is to provide a tool to start learning, thinking, and reasoning about math and algorithms I don’t feel it would be fair to just give out the solution to copy-paste and get the achievement Have a nice coding guys! 😎 Time complexity It’s not that easy to model the time complexity for an algorithm like this one, but we can try to by comparing it with the brute-force solution. reason a bit more generally First off, in both cases, we need to parse the numbers in the triangle somehow, either to collect them as nodes or to store them in lists, arrays, or any other method you can think of. Let’s suppose we use the same parsing algorithm for both solutions, the brute force one and the smart one, and let’s suppose this parsing algorithm takes O(n) time, where n is the number of rows in the triangle. After parsing the elements, in solution, we must calculate the value of each one of the 2ⁿ⁻¹ possible routes. This, again, . the brute force leaves us with a time complexity of O(2ⁿ⁻¹) With the smart solution though we don’t need to do anything else besides parsing the elements correctly. . Since we are using the same parsing algorithm for both solutions, we can discard the time used for parsing while comparing. Thus, Given that we must pass on each element to parse it as a Node, we’ll do exactly n(n+1)/2 operations After this we only need to loop over the last row to find the maximum path, requiring O(n) time. the smarter solution requires only O(n) time while the brute force requires O(2ⁿ⁻¹) time! Conclusion That’s it! As always, I hope you liked the article and found it somehow useful. If so, consider leaving a clap or two or sharing it: it would make my day! I also have a page, if you want to contribute to the redaction of these articles by sharing a coffee with me! Ko-Fi Also, feel free to share your thoughts or questions about this in the comment section: we’re all here to learn! As always, thanks for reading. Nicola

The Avalanche Algorithm — How To Calculate the Maximum Possible Path in a Binary Tree

Have you ever thought about why databases are so complex internally and why we can’t use a text file to store the data? This blog post aims to go from the most basic database that writes data to text files to a more complex setting where we use LSM-tree and B-tree. We will understand why we need these data structures and more. World’s Simplest Key-Value Store What does the world’s simplest key-value store look like? 2 bash functions that write data to a text file and get data from the text file. db_set(){
	echo "$1, $2" >> database
}

db_get(){
	grep "^$1," database | sed -e "s/^$1,//" | tail -n 1
} Let me explain both the functions. The db_set() function appends to the end of the file without any logic. That means if you update the value of a key, it will not overwrite the value but create a new key value at the end of the file. The db_get() function gets the last occurrence of the key. What’s the problem with this implementation? Doesn’t deal with concurrency control, reclaiming disk space, handling errors, and partially written records. db_get() function has terrible performance as it takes O(n) to lookup for a record. To efficiently find the value of a key, we need a different data structure: . The general idea behind indexes is to keep some additional metadata on the side, which acts as a signpost and helps you locate the data you want. But this comes with a tradeoff as it slows down writes but offers fast reads. an index Hash Indexes I am not planning to dive deep into the workings of hash indexes in this particular blog. I plan on covering it in a future blog, but till then, you can refer to to understand more about it. this blog Let’s again go back to our key-value store. The strategy to improve the lookup speed is to keep an in-memory hash map where every key is mapped to a byte offset in the file. Whenever a new key is appended to the file, the hash map is also updated to reflect the offset. How do we avoid running out of disk space as we are only appending to the file? We break the files into smaller segments and perform on each segment. Compaction is throwing away the duplicate keys in the file and keeping only the most recent update for each key. We can perform compaction over multiple segments together at the same time. Segments are never modified, so the merged segment is written to a new file. It is done in the background while we serve read and write requests using the old segment files. But there are some things to take care of with the implementation and limitations of the hash table index: compaction The hash table must fit in memory because, on disk, it is hard to get the same performance We can’t do range queries efficiently If the database is restarted, the in-memory hash maps are lost. We rebuild the index by reading the entire segment file from beginning to end. It will take a lot of time. We can have a snapshot of each segment’s hash map on disk to solve this issue The database may crash halfway through appending a record that can be resolved by including checksums Writes are appended to the file in a strictly sequential order. A common implementation is to have only 1 write thread and multiple read threads When merging segments, the tells the merging process to discard any previous values for the deleted key tombstone SSTables A simple change to our segment files can help us get rid of maintaining the hash index with all keys. We store the key-value pairs in a sorted-by-key order. We call this format SSTable What advantages do we gain over the hash index? Merging the segment files gets simple and efficient even if the files are larger than the available memory. The merge sort algorithm is used to create new merged segment files, also sorted by key. We now don’t need to maintain an index of all keys in memory. We build a sparse index where we get the keys between which our key lies. It saves disk space and I/O bandwidth. How is this SSTable constructed and maintained? When writes come in we add them to the in-memory tree . When it gets bigger than a threshold, we write all the data from the memtable to the SSTable file. The new SSTable file becomes the most recent segment of the database. While we write to SSTable, writes continue to the new memtable instance. When read requests come in we first search for the key in memtable then in the most recent on-disk segment, then in the next older segment, and so on. And from time to time we run compaction in the background. We can also keep a separate log on disk to which every write is immediately appended for durability purposes. memtable LSM Tree Log-structure merge-tree or LSM tree is a clever algorithm based on the above principle of merging and compacting sorted files. LSM is append-only as we only append all the modifications to the SSTable. The LSM tree algorithm can be slow when looking up keys that do not exist in the database. We first check the memtable and then all the segments. Storage engines use to optimize the algorithm. Bloom Filters A bloom filter is a memory-efficient data structure for approximating the contents of a set. It can tell if a key exists in the database and thus save many unnecessary disk reads for keys that don’t exist. B Tree B Tree keeps key-value pairs sorted by keys like SSTable, which allows efficient key lookups and range queries. It breaks down the database into fixed-size blocks or pages, traditionally 4Kb in size, and reads or writes one page at a time. This design corresponds closely to the underlying hardware, as disks are also arranged in fixed-size blocks. An append-only file where we capture all B tree modifications before applying them to the pages of the tree itself. It is a (WAL or redo log) that helps make the database crash-resilient. We use latches (lightweight locks) to protect our B tree when multiple threads try to access the B tree at the same time. write-ahead log Which one is better? LSM Tree vs B Tree B Tree writes every piece of data at least twice: once to the write-ahead log and once to the tree page itself (and sometimes again when the pages split). The log-structure index rewrites data multiple times due to the repeated compaction and merging of SSTable. It results in one write to the database and multitudinous writes to the disk throughout the database’s lifetime - known as . It is a concern on SSDs as a limited number of overwrites can perform before wearing out. write amplification LSM trees can be compressed better, resulting in smaller files on disk than B trees. B tree storage engine leaves some disk space unused due to fragmentation when the page is split or the row cannot fit in an existing table. LSM trees aren’t page-oriented and periodically rewrite SSTables to remove fragmentation. The compaction process can sometimes interfere with the performance of ongoing reads and writes. At high throughput, the disk’s finite bandwidth is shared between the initial write and the compaction threads running in the background. The bigger the database gets, the more disk bandwidth is required for compaction. In B trees, each key only exists in exactly one place in the index, whereas a log-structured storage engine may have multiple copies of the same key in different segments. It makes B trees attractive in databases that want to offer strong transactional semantics. LSM trees are typically able to sustain a higher write throughput than B trees. But B trees are thought to offer faster read throughput. Parting Words There are more data structures that power databases like skiplist, inverted index, R tree, suffix tree, etc. This blog merely introduces the more famous ones and helps you understand the way they work. If you liked the blog don’t forget to share it on , LinkedIn, Peerlist, and other social platforms and tag me. You may also write to me at to share your thoughts about the blog. Twitter guptaamanthan01@gmail.com References Designing Data-Intensive Applications: The Big Ideas Behind Reliable, Scalable, and Maintainable Systems by Martin Kleppmann Originally published . here

Decoding Database Complexity: A Journey from Text Files to LSM Trees and B-Trees

The Noonification: How to Implement a Merkle Tree in Solidity (11/19/2023)

Decision Trees theory is a method used in and data analysis that allows building decision-making models with tree-shaped hierarchy. In each node of the tree, a certain criterion is being checked, and leaves represent final decisions or predicted outcomes. Such trees have high interpretability and can be used for solving classification and regression tasks. machine learning Digging a bit deeper into this theory, it’s pretty easy to find out that: Nodes can be split not just by one criterion but by several as well. It is not necessary to use just one of the criteria implemented in the commonly used sci-kit-learn library for branching. The node can be split into more than two branches. Logical question to arise would be: isn’t there anything better than regular decision trees? And the answer to this question would be: yes, there is—but with its own nuances. Despite the great popularity of deep learning, researchers are still widely working on improving the . Among these “upgrades” are so-called oblique decision trees. In a regular tree, each node has a splitting rule by a single feature, while in oblique trees, each node contains rules based on a combination of several features. The simplest example of a combination is linear—let’s take a closer look at it. decision trees Oblique decision trees Oblique decision trees allow performing node splitting based on a combination of features instead of just one feature. This linear combination can improve the generalization performance of the model by combining the advantages of individual trees. Let us imagine that we have a classification task based on two features with the elements of the training sample that are distributed like in the image below (different classes are marked by different colors). Understandably, the researchers will be eager to identify such situations and use tilted or oblique, straight lines—which represent a linear combination of features—to divide the space. In regular trees, the splitting rules are interpreted in the graphic form as horizontal or vertical straight lines. Oblique tree types, on the other hand, can create diagonal decision boundaries in the space of features, which may be more appropriate for certain datasets. It is because of the oblique division lines these types of trees are called oblique. Oblique decision trees can be used in various fields of machine learning and data analysis, where regular decision trees don’t bring significant results. Here are some examples of such areas: In datasets where decision boundaries are not axially parallel, oblique trees may be more effective at separating classes or detecting nonlinear dependencies. Complex data spaces. In situations where you have many attributes and some of them may be correlated, oblique trees can provide more accurate models because they can account for combinations of attributes. High-dimensional data. Oblique trees may be more complex than regular decision trees, but they still retain a tree structure that can be visualized and interpreted. Areas that require interpretability. , oblique trees can be used for both classification and regression tasks. Classification and regression tasks. Similar to standard decision trees It is worth noting that, as a rule, oblique trees are lower in height yet require significantly more time for training to reach the quality of regular trees. But if you are willing to sacrifice time on training in favor of better quality predictions, you can experiment with them as well. Random trees Considering random trees, ), we can tell that the methodology is well developed. There are algorithms for creating optimal random trees, but in practice, such methods as random forest and, to a higher extent, boosting outperform individual trees. For a random forest to perform effectively, it is important that the trees are uncorrelated and have good generalization performance. Under these conditions, oblique trees show statistically significantly superior results. when we see that a splitting occurs in a tree node, a random subset of features is selected as candidates for the splitting rather than all available features Advantages of Double Random Forest (DRaF) Let’s take a closer look at the method of building a DRaF-LDA (Rotation-based double random forest with linear discriminant analysis). It is different from a classic random forest (Classification and regression trees, or CART) in two ways. In the CART algorithm, bootstrapping is supposed to be performed at the initial step, and start building a tree using the resulting dataset and reducing the sample at each step down on the tree. In DRaF, bootstrapping of all data is performed directly for each individual node, taking into account the limitations of the previous node splitting occurrences. Bootstrapping. In the case of CART, a subset of features is selected for node splitting, among which the best possible node splitting variant is chosen. In DRaF-LDA, as it is easy to guess, the Linear Discriminant Analysis (LDA) algorithm is used for node partitioning. LDA allows performing better splitting than one single feature. Node splitting. Using these two “deviations” from the classic tree-building algorithm for a random forest allows for generating trees that are better in quality and uncorrelated. This gives a gain in quality for the random forest algorithm. There are numerous approaches to forming linear combinations of features for splitting. To learn more about the existing variants you can read the article titled “ ,” written by M.A. Ganaie, M. Tanveer, P.N. Suganthan and V. Snasel. Oblique and rotation double random forest In the article, the researchers proposed a new variant of the forest (trees) that has a statistically significant improvement in prediction quality compared to a common implementation. The research of classic is still ongoing, sometimes even making interesting advances. This is why it’s better not to stick to the default libraries and instead keep studying the subject area and choosing the most suitable algorithms for your tasks. Perhaps it is oblique trees that will work well in your case. machine learning algorithms

Complexity Simplified: How Oblique Decision Trees are Transforming Data Interpretation

The TechBeat: How to Implement a Merkle Tree in Solidity (11/13/2023)

The Noonification: How to Implement a Merkle Tree in Solidity (11/12/2023)

We figured out how the search and insert operation works in the red-black tree in the . In this part, we figure out how the delete operation works. The delete operation is more complicated than the insert operation. first part The Delete Operation The delete operation as well as the insert operation ensures O(log(n)) time complexity. First, we must implement an auxiliary transplant method that transplants y’s node to x’s node place. func (tree *Tree[K, V]) transplant(x *TreeNode[K, V], y *TreeNode[K, V]) {
	if x.parent == tree.leaf {
		tree.root = y
	} else if x == x.parent.left {
		x.parent.left = y
	} else {
		x.parent.right = y
	}

	y.parent = x.parent
} The delete operation is similar to the delete operation in the binary search tree but has several differences. We have to keep the original color of the deleted node. If the deleted node is red, we don’t violate any properties of the red-black tree, but if the deleted node is black, we can violate the red-black properties. We might violate the first property: the root is black, if a transplanted node is red, and the deleted node is black. We might violate the third property: there cannot be two neighboring red nodes if the parent of the deleted node is red and the transplanted node is red. We will violate the fifth property: having the same number of black nodes from the root to each leaf. We must run the auxiliary method to restore the red-black properties. The algorithm for deleting a node in a red-black tree is as follows. 1. We need to declare a variable that will store the color of the node to be deleted. 2. If the node has no children or only one child, we can transplant this node or leaf in case the node has no children to the node to be deleted. If the color of the node to be deleted is black, we need to run the deleteFixup helper method. 3. If the node to be deleted has two children, it is necessary to find a successor of this node. The successor of the node is the leftmost node of its right child. It is essential to save the color of the descendant to a variable, as there may be violations there after the transplantation. If the successor is not the right child of the node being deleted, we need to transplant the right subtree of the successor to the successor. Then we must transplant the successor into the node to be deleted and set the color of the node to be deleted. Then we must run the method deleteFixup if it is required. func (tree *Tree[K, V]) Delete(key K) {
	x := tree.lookup(key)

	if x == tree.leaf {
		return
	}

	var y *TreeNode[K, V]
	originalColor := x.color

    
	if x.left == tree.leaf { 
		y = x.right
		tree.transplant(x, x.right)
	} else if x.right == tree.leaf {
		y = x.left
		tree.transplant(x, x.left)
	} else {
		successor := tree.leftmost(x.right)
		originalColor = successor.color
    
		y = successor.right

		if successor != x.right {
			tree.transplant(successor, successor.right)
			successor.right = x.right
			successor.right.parent = successor
		} else {
			y.parent = successor
		}

		tree.transplant(x, successor)
		successor.left = x.left
		successor.left.parent = successor
		successor.color = x.color
	}

	tree.len--

	if originalColor == black {
		tree.deleteFixup(y)
	}
} 4 cases are used to rebalance the red-black tree after deleting the node. Case one occurs when the sibling of the node is red. We must exchange the color of the current node’s parent and the current node’s sibling and rotate the node’s parent to the left if the node belongs to a left subtree, or rotate to the right if the node belongs to the right subtree and then updating the sibling. Case two occurs when both sibling’s children have the black color. The sibling is also black. We must change the color of the sibling to red and leave the current node. If the node’s parent is red, the cycle terminates. Case 3 occurs when both the sibling and its right child have the black color, and the left child has the red color. Need to exchange colors of the sibling’s left child and sibling and rotate the sibling to the right if the node belongs to the left subtree, and rotate to the left if the node belongs to the right subtree and update the sibling. Then we go to the fourth case. 4. Case 4 occurs when the right child of the sibling is red and the sibling has a black color. We must change the color of the sibling’s right child to black, and change the current node’s parent to black. Then we must rotate the node’s parent to the left if the node belongs to the left subtree, or rotate to the right if the node belongs to the right subtree. Then we set the current node as the root tree. func (tree *Tree[K, V]) deleteFixup(x *TreeNode[K, V]) {
	for x != tree.root && x.color == black {
		if x == x.parent.left {
			y := x.parent.right

			if y.color == red {
				y.color = black
				x.parent.color = red
				tree.leftRotate(x.parent)
				y = x.parent.right
			}

			if y.left.color == black && y.right.color == black {
				y.color = red
				x = x.parent
			} else {

				if y.right.color == black {
					y.left.color = black
					y.color = red
					tree.rightRotate(y)
					y = x.parent.right
				}

				y.color = x.parent.color
				x.parent.color = black
				y.right.color = black
				tree.leftRotate(x.parent)
				x = tree.root
			}
		} else {
			y := x.parent.left

			if y.color == red {
				y.color = black
				x.parent.color = red
				tree.rightRotate(x.parent)
				y = x.parent.left
			}

			if y.left.color == black && y.right.color == black {
				y.color = red
				x = x.parent
			} else {

				if y.left.color == black {
					y.right.color = black
					y.color = red
					tree.leftRotate(y)
					y = x.parent.left
				}

				y.color = x.parent.color
				x.parent.color = black
				x.left.color = black
				tree.rightRotate(x.parent)
				x = tree.root
			}
		}
	}
	tree.root.color = black
} I hope it is now more clear how node deleting works in the red-black tree.

Implementing Red-Black Tree in Go — Part 2: The Delete Operation

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The TechBeat: How to Implement a Merkle Tree in Solidity (10/30/2023)

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The TechBeat: How to Implement a Merkle Tree in Solidity (10/28/2023)

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The TechBeat: How to Implement a Merkle Tree in Solidity (10/26/2023)

The Noonification: How to Implement a Merkle Tree in Solidity (10/23/2023)

A Merkle tree is a binary tree that makes it possible to efficiently and securely verify the contents of large data structures. The concept of this tree was proposed and patented in 1982 by Ralph Merkle, an American cryptographer. The length of the hash remains the same for any amount of input data. Leaf vertices contain hashes from blocks of data, whereas inner vertices include hashes from the addition of values in two child vertices. In turn, the root vertex comprises the hash of the entire data set. Theory Initially, there is a set of data that is not related to each other in any way. For each block of data (in the context of a transaction blockchain), we need to compute a hash of the block. The number of data blocks should be , because as the tree is built, the previous blocks are hashed in pairs at each iteration. A pair of hashes is then grouped together and a new hash is created based on them. Hashing will continue as long as there is something to group at each level, and it will stop when there is only one pair left from which the root hash – the Merkle root – is obtained. 2^N H(1-2) = keccak256(H(1) + H(2)) H(3-4) = keccak256(H(3) + H(4)) H(5-6) = keccak256(H(5) + H(6)) H(7-8) = keccak256(H(7) + H(8)) H(1-2-3-4) = keccak256(H(1-2) + H(3-4)) H(5-6-7-8) = keccak256(H(5-6) + H(7-8)) H(1-2-3-4-5-6-7-8) = keccak256(H(1-2-3-4) + H(5-6-7-8)) Once we have the root, we can validate the data. If the root hash matches the original hash, everything is fine, the data is valid. It is also possible to efficiently check whether certain data is present in the tree structure. Let’s say we want to check that the hash is present in the tree. The proof will be an array of data: , , . Thanks to these hashes, we can reconstruct the root hash: H2 H1 H3-4 H5-6-7-8 H(1-2-3-4-5-6-7-8) = keccak256(keccak256(keccak256(H(1) + H(2)) + H(3-4)) + H(5-6-7-8)) Then we compare the resulting hash with the original one. If they match, it means that the hash is present in the tree. H2 Practice Let’s now see how to implement a Merkle tree and data validation in Solidity. For simplicity, we will write the array of transactions directly to the blockchain, as well as the array of hashes. Since we will be using the built-in function, which returns a hash of 32 bytes, the datatype of the hashes array will be . The array will also have a dynamic length. In general, the length of the hashes array will not be the same as the length of the transactions array, because it will hold the hashes produced. We could calculate the length in advance, but for the sake of code simplification we won’t. If you like, you can make each of these arrays and read the hashes of the transactions. keccak256 bytes32 public We will produce in the constructor. The first step is to count the hashes for blocks with in the loop. Then, at each level of the tree, the number of hashes is reduced by a factor of 2. Since we will be storing the hashes in the hashes array, the index offsets must be stored separately. The iterator in the inner loop is incremented by 2 because we will be taking a couple of elements when calculating and adding hashes. In this time we will add 2 hashes each to which we will set the indices correctly: for the left element – the value of the current shift offset + the index at the current tree level, and for the right element – the same + 1. hashes transactions abi.encodePacked So, we have built the tree, but the interest consists in validating the data. To do this, let’s write a function that takes a transaction and its index. Unfortunately, Solidity does not have a method for arrays, so it is easier to just pass the transaction index. validateTransaction find First, let’s calculate the hash of the transaction and create an array of proofs. We find the number of proofs depending on the length of the transaction array and set the length of . After it, at each level of the tree, we find the necessary element, depending on the index, taking the right or left element, bearing in mind the offsets in the . Then we go through the array of proof indices, checking the index for parity and calculating the hash depending on whether the element is left or right in the pair. Finally, we compare the resulting hash with the root hash and return the result. proofsIndexes hashes Application There are several applications of a Merkle tree in blockchain. : In Bitcoin, for example, a transaction block stores only the merkle_root of its transactions. This reduces the size of the block and the load on the network. After accumulating a certain number of transactions, it is possible to delete old transactions to save space, but the blocks themselves remain unchanged because they only store the root of the tree. Transaction storage : A bitcoin block consists of two parts – the block header and the list of transactions. To avoid having to recompute the transaction hashes each time, they are lined up in a Merkle tree, after which the block header is hashed rather than the entire block, and a random nonce number is taken. When the block is sent to other nodes, the root of the transaction list is calculated, and if it does not match the root in the header, the block is rejected. Mining : The essence of verification is auditing without having to download the entire blockchain. The process is greatly simplified and also allows the existence of data to be confirmed without disclosing information about the data, which can be useful for verifying sensitive information. Verification Summary Without Merkle trees, blockchains would be too cumbersome, and Merkle proofs allow for cost-effective verification of data authenticity. Merkle trees are actively used in blockchains (e.g., Bitcoin, Ethereum) to store transactions efficiently, but this is not the only application. For example, after the collapse of the FTX exchange, many exchanges implemented a Proof-of-Reserve mechanism, which utilizes a Merkle tree.

How to Implement a Merkle Tree in Solidity

সলিডিটিতে মার্কেল ট্রি কীভাবে প্রয়োগ করবেন

So implementieren Sie einen Merkle Tree in Solidity

Cómo implementar un árbol Merkle en Solidity

Comment implémenter un arbre Merkle dans Solidity

सॉलिडिटी में मर्कल ट्री को कैसे लागू करें

Solidity でマークル ツリーを実装する方法

Solidity에서 머클 트리를 구현하는 방법

Como implementar uma árvore Merkle no Solidity

Как реализовать дерево Меркла в Solidity

Solidity'de Merkle Ağacı Nasıl Uygulanır?

Cách triển khai cây Merkle một cách vững chắc

如何在 Solidity 中实现 Merkle 树

The binary search tree has one serious problem. They can transform into a linked list. The red-black tree solves this problem and ensures O(log(n)) time complexity for get, insert, and delete operations. To avoid this problem we can use self-balancing trees. The red-black tree is one of safe-balanced tree. It ensures that the depth between the right and left subtree does not differ by more than 1. In addition to binary search properties, the red-black tree introduces additional properties: The root of the red-black tree is black The leaf is always black The black node can have either a black or red node. If the node is red, both children are black. A simple path from a node to its descendant leaves always has the same number of black nodes. We will also keep a separate instance per tree leaf. We could create an instance for each leaf, but that would be more memory-intensive. Also, we will create a comparator that will compare keys. package util

import (
	"cmp"
)

type Comparator[T any] interface {
	Compare(a T, b T) int
}

type OrderedComparator[T cmp.Ordered] struct {
}

func (o OrderedComparator[T]) Compare(a T, b T) int {
	return cmp.Compare(a, b)
} package redblacktree

import (
	"github.com/dmitriiantonov/go-ds/tree"
	"github.com/dmitriiantonov/go-ds/util"
)

type color int

const (
	black color = iota
	red
)

type TreeNode[K any, V any] struct {
	key    K
	value  V
	color  color
	parent *TreeNode[K, V]
	left   *TreeNode[K, V]
	right  *TreeNode[K, V]
}

func (node *TreeNode[K, V]) Key() K {
	return node.key
}

func (node *TreeNode[K, V]) Value() V {
	return node.value
}

type Tree[K any, V any] struct {
	leaf       *TreeNode[K, V]
	root       *TreeNode[K, V]
	comparator util.Comparator[K]
	len        int
}

func NewTree[K any, V any](comparator util.Comparator[K]) *Tree[K, V] {
	instance := new(Tree[K, V])
	instance.leaf = &TreeNode[K, V]{color: black}
	instance.root = instance.leaf
	instance.comparator = comparator
	return instance
}

func (tree *Tree[K, V]) Len() int {
	return tree.len
} The difference from a binary search tree is that we end the search if the current node is leaf, rather than nill. The more interesting differences begin when inserting the node in our tree. We mark the new node as red and we can violate property 1 if the tree is empty, and property 4 because we can’t have two red nodes in the path. And, we must rebalance our tree. First, we need to introduce the two operations used to balance the tree. These are rotating the tree to the left and to the right. func (tree *Tree[K, V]) leftRotate(x *TreeNode[K, V]) {
	right := x.right
	x.right = right.left
	if right.left != tree.leaf {
		right.left.parent = x
	}
	right.parent = x.parent
	if x.parent == tree.leaf {
		tree.root = right
	} else if x == x.parent.left {
		x.parent.left = right
	} else {
		x.parent.right = right
	}
	right.left = x
	x.parent = right
}

func (tree *Tree[K, V]) rightRotate(x *TreeNode[K, V]) {
	left := x.left
	x.left = left.right
	if left.right != tree.leaf {
		left.right.parent = x
	}
	left.parent = x.parent
	if x.parent == tree.leaf {
		tree.root = left
	} else if x == x.parent.left {
		x.parent.left = left
	} else {
		x.parent.right = left
	}
	left.right = x
	x.parent = left
} We have three cases in which we must fix violations in our tree. Also, we need to denote an uncle node, that is a sibling node’s parent. If the uncle is a red node and the node’s parent is red we must make them black. Also, we must make their parent red and set it as the current node. If its parent is red, then we must fix the following violation. If the node belongs to the left subtree and the node’s right child is red or if the node belongs to the right subtree and the node’s left child is red we must make the node’s parent current node and do the left rotation in the 1 case, or the right rotation in the second case. And then we come to case 3. In the third case, we must make the current node’s parent black and its parent red, and then we must do a right rotation if the node’s parent is a left subtree, or a left rotation if the node’s parent is a right subtree. I illustrated cases for the left subtree. For the right subtree, you must change the right rotation to the left rotation, and the left rotation to the right rotation. func (tree *Tree[K, V]) Insert(key K, value V) {
    x := tree.lookup(key) // try to find a node by key

    if x != tree.leaf { // if we found it, update value and exit
       x.value = value
       return
    }
    // find the parent
    parent := tree.leaf
    current := tree.root

    for current != tree.leaf {
       parent = current

       switch tree.comparator.Compare(key, current.key) {
       case -1:
          current = current.left
       case 1:
          current = current.right
       }
    }
    // create a new node
    x = &TreeNode[K, V]{
       key:    key,
       value:  value,
       color:  red,
       parent: parent,
       left:   tree.leaf,
       right:  tree.leaf,
    }

    // send the node as child
    if parent == tree.leaf {
       tree.root = parent
    } else if tree.comparator.Compare(key, parent.key) < 0 {
       parent.left = x
    } else {
       parent.right = x
    }
    // do the rebalance
    tree.insertFixup(x)
}

func (tree *Tree[K, V]) insertFixup(x *TreeNode[K, V]) {
    for x.parent.color == red { // we must iterate only if the node's parent is red
       if x.parent == x.parent.parent.left { // if the node belongs to left subtree
          y := x.parent.parent.right // set uncle
          if y.color == red { // case 1
             x.parent.color = black
             y.color = black
             x.parent.parent.color = red // set 
             x = x.parent.parent
          } else {
             if x == x.parent.right { // case 2
                x = x.parent
                tree.leftRotate(x)
             }
             x.parent.color = black // case 3
             x.parent.parent.color = red
             tree.rightRotate(x.parent.parent)
          }
       } else { // if the node belongs to the right subtree
          y := x.parent.parent.left 
          if y.color == red { // case 1
             x.parent.color = black
             y.color = black
             x.parent.parent.color = red
             x = x.parent.parent
          } else {
             if x == x.parent.left { // case 2
                x = x.parent
                tree.rightRotate(x)
             }
             x.parent.color = black // case 3
             x.parent.parent.color = red
             tree.leftRotate(x.parent.parent)
          }
       }
    }
    tree.root.color = black // change the root color to black
} In the second part of this article, we will consider the delete operation.

Implementing Red-Black Tree in Go — Part 1, The Search and Insert Operation

What does the zkSync L2 chain have in common with Bitcoin and Ethereum? They all rely on the genius concept of Merkle Trees, born in the 1980s. But how does it apply to zkSync, you ask? Join me as I delve into the workings of and how it employs this ingenious tech to ensure the integrity and security of its data. Merkle Trees Deciphering Merkle Trees Within the zkSync protocol lies the Merkle Trees technology fashioned to help securely store information on the . The associated with Merkle Тrees help ensure the integrity of the data stored on the blockchain. blockchain cryptographic hashes Merkle Trees is a concept born in the 1980s. American computer scientist Raph Merkle proposed this binary hash tree philosophy in 1987 through a paper titled A Digital Signature Based on a Conventional Encryption Function." Note: Another name for Merkle Trees is Binary Hash Tree The mathematician and scientist Ralph Merkle is widely hailed as one of the founders of public key , the cornerstone of the blockchain space. A Merkle Tree is a data structure blockchain used to encode blockchain data more safely and efficiently. cryptography For instance, Bitcoin blocks help in generating a hash. On average, completing a block takes 10 minutes and includes thousands of transactions. To generate the hash, Bitcoin runs each transaction, then a pair of transactions; later, the pairs are linked until we get a hash for the block. This process, visualized, takes the form of a tree! Well, that is at least how Merkle Trees operate. But how do they work on the zkSync chain? zkSync and State Merkle Trees At the heart of zkSync lies the State Merkle Tree system, an iteration of the standard Merkle Tree. This system represents balances and accounts. The height of the accounts tree is represented by the symbol 'Ha' and has a value of 24, while the balance is donated by 'Hb' with a value of 8. Each of the main account trees has corresponding leaves. Balance trees are the subtrees hosted on Accounts, and each balance tree has balanced leaves. A Leaf's hash In this State Merkle Trees system, a Leaf's hash represents the of the bit string. But how do you obtain the bit string? The simplest way of obtaining the bit string is encoding each of the fields in bits, in the order from least to most significant. rescue hash The account leaf In this system, accounts can be inserted into account trees as leaves. After inserting, the account gets an AccountId, the least available ID. Account leaf comprises different fields and types, including a nonce, pubkey_hash, state tree root, and address. Notably, the state_tree_root combines the root hash of the balance_tree_root, a zero field element designated for future subtree root hash, and the rescue hash. This combination, in its entirety, is padded to 256 bits. Moreover, the empty leaf contains state_tree_root computed using the empty balances subtree. The empty balances subtree of the account has zero in each leaf. The Balance Leaf The Balance leaf, on the other hand, contains a field named value, with the type being StateAmount. An empty leaf will have a value equal to zero. zkSync Block Pub Data Format Lastly, the zkSync block pub data format consists of a Rollup operations pub data sequence, with a constant value as the maximum block size. What if the size of operations is not enough to fill the block? In that case, the remaining space is filled using an empty operation. Noop Optimistic Rollups Merkle Trees System are layer 2 solutions that offload transaction processing weight from Ethereum's L1 blockchain. They bolster transaction throughput. Optimistic Rollups These rollups leverage Merkle proofs in transaction validation while running them completely off-chain. The blocks consist of a cryptographic proof, the Merkel Tree root, and the summary for the new account. Typically, Optimistic rollups run assuming that each transaction on L2 is valid. They bring simplicity and lower transaction costs while causing an extension of withdrawal times. Notice the optimistic rollups leverage Merkel Trees to validate transactions off-chain. These rollups deploy a contract in L1, which manages the rollup state and handles deposits, balances, withdrawals, and disputes. Furthermore, these systems utilize sequencers or operators whose defined role is collecting and aggregating transactions off-chain. These operators will bundle a myriad of transactions into a single 'rollup block. The operators later submit the bundled block to the mainchain by providing the Merkle tree root and additional "call data." The data helps in verifying the rollup block's validity later. Plasma Chain Merkle proofs are also applicable in another class of L2 solutions, Plasma. Plasma's rollup solution combines fraud proofs and Merkle Trees to validate transactions off-chain. By marrying smart contracts and Merkle Trees, Plasma can create child chains, and copies of the parent blockchain (Ethereum). Offloading transactions makes the transactions cheaper and faster as each Merkle Trees-enabled Chains is independent. So transactions first occur on the mainchain. In fraud cases in the plasma child chain, users exit and return to the parent chain. However, the critical point is that Plasma mainly leverages Merkle Trees in service delivery. Final Word In summary, Merkle Trees are the fundamental technologies designed to ensure the integrity and efficiency of data stored. In Bitcoin, Merkle is vital in generating hashes for blocks, and securing the myriads of transactions. zkSync leverages State Merkle Trees, a variant of Merkle trees, to represent balances and accounts. The construction of leaves in this system, whether account or balance leaves, follows a specific procedure, promoting clarity and structural integrity. Other technologies like Optimistic Rollups and Plasma leverage Merkle Trees, which help offload transactions from the Ethereum main chain, bolstering throughput and reducing costs. Merkle Trees continue to shape the blockchain space, confirming their place as the cornerstone of the realm.

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