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Jim Siwek

Jim Siwek

3 years ago

In 2022, can a lone developer be able to successfully establish a SaaS product?

More on Entrepreneurship/Creators

Sanjay Priyadarshi

Sanjay Priyadarshi

3 years ago

Meet a Programmer Who Turned Down Microsoft's $10,000,000,000 Acquisition Offer

Failures inspire young developers

Photo of Jason Citron from Marketrealist.com

Jason citron created many products.

These products flopped.

Microsoft offered $10 billion for one of these products.

He rejected the offer since he was so confident in his success.

Let’s find out how he built a product that is currently valued at $15 billion.

Early in his youth, Jason began learning to code.

Jason's father taught him programming and IT.

His father wanted to help him earn money when he needed it.

Jason created video games and websites in high school.

Jason realized early on that his IT and programming skills could make him money.

Jason's parents misjudged his aptitude for programming.

Jason frequented online programming communities.

He looked for web developers. He created websites for those people.

His parents suspected Jason sold drugs online. When he said he used programming to make money, they were shocked.

They helped him set up a PayPal account.

Florida higher education to study video game creation

Jason never attended an expensive university.

He studied game design in Florida.

“Higher Education is an interesting part of society… When I work with people, the school they went to never comes up… only thing that matters is what can you do…At the end of the day, the beauty of silicon valley is that if you have a great idea and you can bring it to the life, you can convince a total stranger to give you money and join your project… This notion that you have to go to a great school didn’t end up being a thing for me.”

Jason's life was altered by Steve Jobs' keynote address.

After graduating, Jason joined an incubator.

Jason created a video-dating site first.

Bad idea.

Nobody wanted to use it when it was released, so they shut it down.

He made a multiplayer game.

It was released on Bebo. 10,000 people played it.

When Steve Jobs unveiled the Apple app store, he stopped playing.

The introduction of the app store resembled that of a new gaming console.

Jason's life altered after Steve Jobs' 2008 address.

“Whenever a new video game console is launched, that’s the opportunity for a new video game studio to get started, it’s because there aren’t too many games available…When a new PlayStation comes out, since it’s a new system, there’s only a handful of titles available… If you can be a launch title you can get a lot of distribution.”

Apple's app store provided a chance to start a video game company.

They released an app after 5 months of work.

Aurora Feint is the game.

Jason believed 1000 players in a week would be wonderful. A thousand players joined in the first hour.

Over time, Aurora Feints' game didn't gain traction. They don't make enough money to keep playing.

They could only make enough for one month.

Instead of buying video games, buy technology

Jason saw that they established a leaderboard, chat rooms, and multiplayer capabilities and believed other developers would want to use these.

They opted to sell the prior game's technology.

OpenFeint.

Assisting other game developers

They had no money in the bank to create everything needed to make the technology user-friendly.

Jason and Daniel designed a website saying:

“If you’re making a video game and want to have a drop in multiplayer support, you can use our system”

TechCrunch covered their website launch, and they gained a few hundred mailing list subscribers.

They raised seed funding with the mailing list.

Nearly all iPhone game developers started adopting the Open Feint logo.

“It was pretty wild… It was really like a whole social platform for people to play with their friends.”

What kind of a business model was it?

OpenFeint originally planned to make the software free for all games. As the game gained popularity, they demanded payment.

They later concluded it wasn't a good business concept.

It became free eventually.

Acquired for $104 million

Open Feint's users and employees grew tremendously.

GREE bought OpenFeint for $104 million in April 2011.

GREE initially committed to helping Jason and his team build a fantastic company.

Three or four months after the acquisition, Jason recognized they had a different vision.

He quit.

Jason's Original Vision for the iPad

Jason focused on distribution in 2012 to help businesses stand out.

The iPad market and user base were growing tremendously.

Jason said the iPad may replace mobile gadgets.

iPad gamers behaved differently than mobile gamers.

People sat longer and experienced more using an iPad.

“The idea I had was what if we built a gaming business that was more like traditional video games but played on tablets as opposed to some kind of mobile game that I’ve been doing before.”

Unexpected insight after researching the video game industry

Jason learned from studying the gaming industry that long-standing companies had advantages beyond a single release.

Previously, long-standing video game firms had their own distribution system. This distribution strategy could buffer time between successful titles.

Sony, Microsoft, and Valve all have gaming consoles and online stores.

So he built a distribution system.

He created a group chat app for gamers.

He envisioned a team-based multiplayer game with text and voice interaction.

His objective was to develop a communication network, release more games, and start a game distribution business.

Remaking the video game League of Legends

Jason and his crew reimagined a League of Legends game mode for 12-inch glass.

They adapted the game for tablets.

League of Legends was PC-only.

So they rebuilt it.

They overhauled the game and included native mobile experiences to stand out.

Hammer and Chisel was the company's name.

18 people worked on the game.

The game was funded. The game took 2.5 years to make.

Was the game a success?

July 2014 marked the game's release. The team's hopes were dashed.

Critics initially praised the game.

Initial installation was widespread.

The game failed.

As time passed, the team realized iPad gaming wouldn't increase much and mobile would win.

Jason was given a fresh idea by Stan Vishnevskiy.

Stan Vishnevskiy was a corporate engineer.

He told Jason about his plan to design a communication app without a game.

This concept seeded modern strife.

“The insight that he really had was to put a couple of dots together… we’re seeing our customers communicating around our own game with all these different apps and also ourselves when we’re playing on PC… We should solve that problem directly rather than needing to build a new game…we should start making it on PC.”

So began Discord.

Online socializing with pals was the newest trend.

Jason grew up playing video games with his friends.

He never played outside.

Jason had many great moments playing video games with his closest buddy, wife, and brother.

Discord was about providing a location for you and your group to speak and hang out.

Like a private cafe, bedroom, or living room.

Discord was developed for you and your friends on computers and phones.

You can quickly call your buddies during a game to conduct a conference call. Put the call on speaker and talk while playing.

Discord wanted to give every player a unique experience. Because coordinating across apps was a headache.

The entire team started concentrating on Discord.

Jason decided Hammer and Chisel would focus on their chat app.

Jason didn't want to make a video game.

How Discord attracted the appropriate attention

During the first five months, the entire team worked on the game and got feedback from friends.

This ensures product improvement. As a result, some teammates' buddies started utilizing Discord.

The team knew it would become something, but the result was buggy. App occasionally crashed.

Jason persuaded a gamer friend to write on Reddit about the software.

New people would find Discord. Why not?

Reddit users discovered Discord and 50 started using it frequently.

Discord was launched.

Rejecting the $10 billion acquisition proposal

Discord has increased in recent years.

It sends billions of messages.

Discord's users aren't tracked. They're privacy-focused.

Purchase offer

Covid boosted Discord's user base.

Weekly, billions of messages were transmitted.

Microsoft offered $10 billion for Discord in 2021.

Jason sold Open Feint for $104m in 2011.

This time, he believed in the product so much that he rejected Microsoft's offer.

“I was talking to some people in the team about which way we could go… The good thing was that most of the team wanted to continue building.”

Last time, Discord was valued at $15 billion.

Discord raised money on March 12, 2022.

The $15 billion corporation raised $500 million in 2021.

Rachel Greenberg

Rachel Greenberg

3 years ago

The Unsettling Fact VC-Backed Entrepreneurs Don't Want You to Know

What they'll do is scarier.

Photo by DESIGNECOLOGIST on Unsplash

My acquaintance recently joined a VC-funded startup. Money, equity, and upside possibilities were nice, but he had a nagging dread.

They just secured a $40M round and are hiring like crazy to prepare for their IPO in two years. All signals pointed to this startup's (a B2B IT business in a stable industry) success, and its equity-holding workers wouldn't pass that up.

Five months after starting the work, my friend struggled with leaving. We might overlook the awful culture and long hours at the proper price. This price plus the company's fate and survival abilities sent my friend departing in an unpleasant unplanned resignation before jumping on yet another sinking ship.

This affects founders. This affects VC-backed companies (and all businesses). This affects anyone starting, buying, or running a business.

Here's the under-the-table approach that's draining VC capital, leaving staff terrified (or jobless), founders rattled, and investors upset. How to recognize, solve, and avoid it

The unsettling reality behind door #1

You can't raise money off just your looks, right? If "looks" means your founding team's expertise, then maybe. In my friend's case, the founding team's strong qualifications and track records won over investors before talking figures.

They're hardly the only startup to raise money without a profitable customer acquisition strategy. Another firm raised money for an expensive sleep product because it's eco-friendly. They were off to the races with a few keywords and key players.

Both companies, along with numerous others, elected to invest on product development first. Company A employed all the tech, then courted half their market (they’re a tech marketplace that connects two parties). Company B spent millions on R&D to create a palatable product, then flooded the world with marketing.

My friend is on Company B's financial team, and he's seen where they've gone wrong. It's terrible.

Company A (tech market): Growing? Not quite. To achieve the ambitious expansion they (and their investors) demand, they've poured much of their little capital into salespeople: Cold-calling commission and salary salesmen. Is it working? Considering attrition and companies' dwindling capital, I don't think so.

Company B (green sleep) has been hiring, digital marketing, and opening new stores like crazy. Growing expenses should result in growing revenues and a favorable return on investment; if you grow too rapidly, you may neglect to check that ROI.

Once Company A cut headcount and Company B declared “going concerned”, my friend realized both startups had the same ailment and didn't recognize it.

I shouldn't have to ask a friend to verify a company's cash reserves and profitability to spot a financial problem. It happened anyhow.

The frightening part isn't that investors were willing to invest millions without product-market fit, CAC, or LTV estimates. That's alarming, but not as scary as the fact that startups aren't understanding the problem until VC rounds have dried up.

When they question consultants if their company will be around in 6 months. It’s a red flag. How will they stretch $20M through a 2-year recession with a $3M/month burn rate and no profitability? Alarms go off.

Who's in danger?

In a word, everyone who raised money without a profitable client acquisition strategy or enough resources to ride out dry spells.

Money mismanagement and poor priorities affect every industry (like sinking all your capital into your product, team, or tech, at the expense of probing what customer acquisition really takes and looks like).

This isn't about tech, real estate, or recession-proof luxury products. Fast, cheap, easy money flows into flashy-looking teams with buzzwords, trending industries, and attractive credentials.

If these companies can't show progress or get a profitable CAC, they can't raise more money. They die if they can't raise more money (or slash headcount and find shoestring budget solutions until they solve the real problem).

The kiss of death (and how to avoid it)

If you're running a startup and think raising VC is the answer, pause and evaluate. Do you need the money now?

I'm not saying VC is terrible or has no role. Founders have used it as a Band-Aid for larger, pervasive problems. Venture cash isn't a crutch for recruiting consumers profitably; it's rocket fuel to get you what and who you need.

Pay-to-play isn't a way to throw money at the wall and hope for a return. Pay-to-play works until you run out of money, and if you haven't mastered client acquisition, your cash will diminish quickly.

How can you avoid this bottomless pit? Tips:

  • Understand your burn rate

  • Keep an eye on your growth or profitability.

  • Analyze each and every marketing channel and initiative.

  • Make lucrative customer acquisition strategies and satisfied customers your top two priorities. not brand-new products. not stellar hires. avoid the fundraising rollercoaster to save time. If you succeed in these two tasks, investors will approach you with their thirsty offers rather than the other way around, and your cash reserves won't diminish as a result.

Not as much as your grandfather

My family friend always justified expensive, impractical expenditures by saying it was only monopoly money. In business, startups, and especially with money from investors expecting a return, that's not true.

More founders could understand that there isn't always another round if they viewed VC money as their own limited pool. When the well runs dry, you must refill it or save the day.

Venture financing isn't your grandpa's money. A discerning investor has entrusted you with dry powder in the hope that you'll use it wisely, strategically, and thoughtfully. Use it well.

Vanessa Karel

Vanessa Karel

3 years ago

10 hard lessons from founding a startup.

Here is the ugly stuff, read this if you have a founder in your life or are trying to become one. Your call.

#1 You'll try to talk yourself to sleep, but it won't always work.

As founders, we're all driven. Good and bad, you're restless. Success requires resistance and discipline. Your startup will be on your mind 24/7, and not everyone will have the patience to listen to your worries, ideas, and coffee runs. You become more self-sufficient than ever before.

#2 No one will understand what you're going through unless they've been a founder.

Some of my closest friends don't understand the work that goes into starting a business, and we can't blame them.

#3 You'll feel alienated.

Your problems aren't common; calling your bestie won't help. You must search hard for the right resources. It alienates you from conversations you no longer relate to. (No 4th of July, no long weekends!)

#4 Since you're your "own boss," people assume you have lots of free time.

Do you agree? I was on a webinar with lots of new entrepreneurs, and one woman said, "I started my own business so I could have more time for myself." This may be true for some lucky people, and you can be flexible with your schedule. If you want your business to succeed, you'll probably be its slave for a while.

#5 No time for illness or family emergencies.

Both last month. Oh, no! Physically and emotionally withdrawing at the worst times will give you perspective. I learned this the hard way because I was too stubborn to postpone an important interview. I thought if I rested all day and only took one call, I'd be fine. Nope. I had a fever and my mind wasn't as sharp, so my performance and audience interaction suffered. Nope. Better to delay than miss out.

Oh, and setting a "OoO" makes you cringe.

#6 Good luck with your mental health, perfectionists.

When building a startup, it's difficult to accept that there won't be enough time to do everything. You can't make them all, not perfectly. You must learn to accept things that are done but not perfect.

#7 As a founder, you'll make mistakes, but you'll want to make them quickly so you can learn.

Hard lessons are learned quicker. You'll need to pivot and try new things often; some won't work, and it's best to discover them sooner rather than later.

#8 Pyramid schemes abound.

I didn't realize how bad it was until I started a company. You must spy and constantly research. As a founder, you'll receive many emails from people claiming to "support" you. Be wary and keep your eyes open. When it's too good to be true. Some "companies" will try to get you to pay for "competitions" to "pitch at events." Don't do it.

#9 Keep your competitor research to a minimum.

Actually, competition is good. It means there's a market for those solutions. However, this can be mentally exhausting too. Learn about their geography and updates, but that's it.

#10 You'll feel guilty taking vacation.

I don't know what to say, but I no longer enjoy watching TV, and that's okay. Pay attention to things that enrich you, bring you joy, and have fun. It boosts creativity.

Being a startup founder may be one of the hardest professional challenges you face, but it's also a great learning experience. Your passion will take you places you never imagined and open doors to opportunities you wouldn't have otherwise. You'll meet amazing people. No regrets, no complaints. It's a roller coaster, but the good days are great.

Miss anything? Comment below

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CNET

CNET

3 years ago

How a $300K Bored Ape Yacht Club NFT was accidentally sold for $3K

The Bored Ape Yacht Club is one of the most prestigious NFT collections in the world. A collection of 10,000 NFTs, each depicting an ape with different traits and visual attributes, Jimmy Fallon, Steph Curry and Post Malone are among their star-studded owners. Right now the price of entry is 52 ether, or $210,000.

Which is why it's so painful to see that someone accidentally sold their Bored Ape NFT for $3,066.

Unusual trades are often a sign of funny business, as in the case of the person who spent $530 million to buy an NFT from themselves. In Saturday's case, the cause was a simple, devastating "fat-finger error." That's when people make a trade online for the wrong thing, or for the wrong amount. Here the owner, real name Max or username maxnaut, meant to list his Bored Ape for 75 ether, or around $300,000. Instead he accidentally listed it for 0.75. One hundredth the intended price.

It was bought instantaneously. The buyer paid an extra $34,000 to speed up the transaction, ensuring no one could snap it up before them. The Bored Ape was then promptly listed for $248,000. The transaction appears to have been done by a bot, which can be coded to immediately buy NFTs listed below a certain price on behalf of their owners in order to take advantage of these exact situations.

"How'd it happen? A lapse of concentration I guess," Max told me. "I list a lot of items every day and just wasn't paying attention properly. I instantly saw the error as my finger clicked the mouse but a bot sent a transaction with over 8 eth [$34,000] of gas fees so it was instantly sniped before I could click cancel, and just like that, $250k was gone."

"And here within the beauty of the Blockchain you can see that it is both honest and unforgiving," he added.

Fat finger trades happen sporadically in traditional finance -- like the Japanese trader who almost bought 57% of Toyota's stock in 2014 -- but most financial institutions will stop those transactions if alerted quickly enough. Since cryptocurrency and NFTs are designed to be decentralized, you essentially have to rely on the goodwill of the buyer to reverse the transaction.

Fat finger errors in cryptocurrency trades have made many a headline over the past few years. Back in 2019, the company behind Tether, a cryptocurrency pegged to the US dollar, nearly doubled its own coin supply when it accidentally created $5 billion-worth of new coins. In March, BlockFi meant to send 700 Gemini Dollars to a set of customers, worth roughly $1 each, but mistakenly sent out millions of dollars worth of bitcoin instead. Last month a company erroneously paid a $24 million fee on a $100,000 transaction.

Similar incidents are increasingly being seen in NFTs, now that many collections have accumulated in market value over the past year. Last month someone tried selling a CryptoPunk NFT for $19 million, but accidentally listed it for $19,000 instead. Back in August, someone fat finger listed their Bored Ape for $26,000, an error that someone else immediately capitalized on. The original owner offered $50,000 to the buyer to return the Bored Ape -- but instead the opportunistic buyer sold it for the then-market price of $150,000.

"The industry is so new, bad things are going to happen whether it's your fault or the tech," Max said. "Once you no longer have control of the outcome, forget and move on."

The Bored Ape Yacht Club launched back in April 2021, with 10,000 NFTs being sold for 0.08 ether each -- about $190 at the time. While NFTs are often associated with individual digital art pieces, collections like the Bored Ape Yacht Club, which allow owners to flaunt their NFTs by using them as profile pictures on social media, are becoming increasingly prevalent. The Bored Ape Yacht Club has since become the second biggest NFT collection in the world, second only to CryptoPunks, which launched in 2017 and is considered the "original" NFT collection.

Mike Tarullo

Mike Tarullo

3 years ago

Even In a Crazy Market, Hire the Best People: The "First Ten" Rules

The Pareto Principle is a way of life for First Ten people.

Hiring is difficult, but you shouldn't compromise on team members. Or it may suggest you need to look beyond years in a similar role/function.

Every hire should be someone we'd want as one of our first ten employees.

If you hire such people, your team will adapt, initiate, and problem-solve, and your company will grow. You'll stay nimble even as you scale, and you'll learn from your colleagues.

If you only hire for a specific role or someone who can execute the job, you'll become a cluster of optimizers, and talent will depart for a more fascinating company. A startup is continually changing, therefore you want individuals that embrace it.

As a leader, establishing ideal conditions for talent and having a real ideology should be high on your agenda. You can't eliminate attrition, nor would you want to, but you can hire people who will become your company's leaders.

In my last four jobs I was employee 2, 5, 3, and 5. So while this is all a bit self serving, you’re the one reading my writing — and I have some experience with who works out in the first ten!

First, we'll examine what they do well (and why they're beneficial for startups), then what they don't, and how to hire them.

First 10 are:

  • Business partners: Because it's their company, they take care of whatever has to be done and have ideas about how to do it. You can rely on them to always put the success of the firm first because it is their top priority (company success is strongly connected with success for early workers). This approach will eventually take someone to leadership positions.

  • High Speed Learners: They process knowledge quickly and can reach 80%+ competency in a new subject matter rather quickly. A growing business that is successful tries new things frequently. We have all lost a lot of money and time on employees who follow the wrong playbook or who wait for someone else within the company to take care of them.

  • Autodidacts learn by trial and error, osmosis, networking with others, applying first principles, and reading voraciously (articles, newsletters, books, and even social media). Although teaching is wonderful, you won't have time.

  • Self-scaling: They figure out a means to deal with issues and avoid doing the grunt labor over the long haul, increasing their leverage. Great people don't keep doing the same thing forever; as they expand, they use automation and delegation to fill in their lower branches. This is a crucial one; even though you'll still adore them, you'll have to manage their scope or help them learn how to scale on their own.

  • Free Range: You can direct them toward objectives rather than specific chores. Check-ins can be used to keep them generally on course without stifling invention instead of giving them precise instructions because doing so will obscure their light.

  • When people are inspired, they bring their own ideas about what a firm can be and become animated during discussions about how to get there.

  • Novelty Seeking: They look for business and personal growth chances. Give them fresh assignments and new directions to follow around once every three months.


Here’s what the First Ten types may not be:

  • Domain specialists. When you look at their resumes, you'll almost certainly think they're unqualified. Fortunately, a few strategically positioned experts may empower a number of First Ten types by serving on a leadership team or in advising capacities.

  • Balanced. These people become very invested, and they may be vulnerable to many types of stress. You may need to assist them in managing their own stress and coaching them through obstacles. If you are reading this and work at Banza, I apologize for not doing a better job of supporting this. I need to be better at it.

  • Able to handle micromanagement with ease. People who like to be in charge will suppress these people. Good decision-making should be delegated to competent individuals. Generally speaking, if you wish to scale.

Great startup team members have versatility, learning, innovation, and energy. When we hire for the function, not the person, we become dull and staid. Could this person go to another department if needed? Could they expand two levels in a few years?

First Ten qualities and experience level may have a weak inverse association. People with 20+ years of experience who had worked at larger organizations wanted to try something new and had a growth mentality. College graduates may want to be told what to do and how to accomplish it so they can stay in their lane and do what their management asks.

Does the First Ten archetype sound right for your org? Cool, let’s go hiring. How will you know when you’ve found one?

  • They exhibit adaptive excellence, excelling at a variety of unrelated tasks. It could be hobbies or professional talents. This suggests that they will succeed in the next several endeavors they pursue.

  • Successful risk-taking is doing something that wasn't certain to succeed, sometimes more than once, and making it do so. It's an attitude.

  • Rapid Rise: They regularly change roles and get promoted. However, they don't leave companies when the going gets tough. Look for promotions at every stop and at least one position with three or more years of experience.

You can ask them:

  • Tell me about a time when you started from scratch or achieved success. What occurred en route? You might request a variety of tales from various occupations or even aspects of life. They ought to be energized by this.

  • What new skills have you just acquired? It is not required to be work-related. They must be able to describe it and unintentionally become enthusiastic about it.

  • Tell me about a moment when you encountered a challenge and had to alter your strategy. The core of a startup is reinventing itself when faced with obstacles.

  • Tell me about a moment when you eliminated yourself from a position at work. They've demonstrated they can permanently solve one issue and develop into a new one, as stated above.

  • Why do you want to leave X position or Y duty? These people ought to be moving forward, not backward, all the time. Instead, they will discuss what they are looking forward to visiting your location.

  • Any questions? Due to their inherent curiosity and desire to learn new things, they should practically never run out of questions. You can really tell if they are sufficiently curious at this point.

People who see their success as being the same as the success of the organization are the best-case team members, in any market. They’ll grow and change with the company, and always try to prioritize what matters. You’ll find yourself more energized by your work because you’re surrounded by others who are as well. Happy teambuilding!

Shalitha Suranga

Shalitha Suranga

3 years ago

The Top 5 Mathematical Concepts Every Programmer Needs to Know

Using math to write efficient code in any language

Photo by Emile Perron on Unsplash, edited with Canva

Programmers design, build, test, and maintain software. Employ cases and personal preferences determine the programming languages we use throughout development. Mobile app developers use JavaScript or Dart. Some programmers design performance-first software in C/C++.

A generic source code includes language-specific grammar, pre-implemented function calls, mathematical operators, and control statements. Some mathematical principles assist us enhance our programming and problem-solving skills.

We all use basic mathematical concepts like formulas and relational operators (aka comparison operators) in programming in our daily lives. Beyond these mathematical syntaxes, we'll see discrete math topics. This narrative explains key math topics programmers must know. Master these ideas to produce clean and efficient software code.

Expressions in mathematics and built-in mathematical functions

A source code can only contain a mathematical algorithm or prebuilt API functions. We develop source code between these two ends. If you create code to fetch JSON data from a RESTful service, you'll invoke an HTTP client and won't conduct any math. If you write a function to compute the circle's area, you conduct the math there.

When your source code gets more mathematical, you'll need to use mathematical functions. Every programming language has a math module and syntactical operators. Good programmers always consider code readability, so we should learn to write readable mathematical expressions.

Linux utilizes clear math expressions.

A mathematical expression/formula in the Linux codebase, a screenshot by the author

Inbuilt max and min functions can minimize verbose if statements.

Reducing a verbose nested-if with the min function in Neutralinojs, a screenshot by the author

How can we compute the number of pages needed to display known data? In such instances, the ceil function is often utilized.

import math as m
results = 102
items_per_page = 10 
pages = m.ceil(results / items_per_page)
print(pages)

Learn to write clear, concise math expressions.

Combinatorics in Algorithm Design

Combinatorics theory counts, selects, and arranges numbers or objects. First, consider these programming-related questions. Four-digit PIN security? what options exist? What if the PIN has a prefix? How to locate all decimal number pairs?

Combinatorics questions. Software engineering jobs often require counting items. Combinatorics counts elements without counting them one by one or through other verbose approaches, therefore it enables us to offer minimum and efficient solutions to real-world situations. Combinatorics helps us make reliable decision tests without missing edge cases. Write a program to see if three inputs form a triangle. This is a question I commonly ask in software engineering interviews.

Graph theory is a subfield of combinatorics. Graph theory is used in computerized road maps and social media apps.

Logarithms and Geometry Understanding

Geometry studies shapes, angles, and sizes. Cartesian geometry involves representing geometric objects in multidimensional planes. Geometry is useful for programming. Cartesian geometry is useful for vector graphics, game development, and low-level computer graphics. We can simply work with 2D and 3D arrays as plane axes.

GetWindowRect is a Windows GUI SDK geometric object.

GetWindowRect outputs an LPRECT geometric object, a screenshot by the author

High-level GUI SDKs and libraries use geometric notions like coordinates, dimensions, and forms, therefore knowing geometry speeds up work with computer graphics APIs.

How does exponentiation's inverse function work? Logarithm is exponentiation's inverse function. Logarithm helps programmers find efficient algorithms and solve calculations. Writing efficient code involves finding algorithms with logarithmic temporal complexity. Programmers prefer binary search (O(log n)) over linear search (O(n)). Git source specifies O(log n):

The Git codebase defines a function with logarithmic time complexity, a screenshot by the author

Logarithms aid with programming math. Metas Watchman uses a logarithmic utility function to find the next power of two.

A utility function that uses ceil, a screenshot by the author

Employing Mathematical Data Structures

Programmers must know data structures to develop clean, efficient code. Stack, queue, and hashmap are computer science basics. Sets and graphs are discrete arithmetic data structures. Most computer languages include a set structure to hold distinct data entries. In most computer languages, graphs can be represented using neighboring lists or objects.

Using sets as deduped lists is powerful because set implementations allow iterators. Instead of a list (or array), store WebSocket connections in a set.

Most interviewers ask graph theory questions, yet current software engineers don't practice algorithms. Graph theory challenges become obligatory in IT firm interviews.

Recognizing Applications of Recursion

A function in programming isolates input(s) and output(s) (s). Programming functions may have originated from mathematical function theories. Programming and math functions are different but similar. Both function types accept input and return value.

Recursion involves calling the same function inside another function. In its implementation, you'll call the Fibonacci sequence. Recursion solves divide-and-conquer software engineering difficulties and avoids code repetition. I recently built the following recursive Dart code to render a Flutter multi-depth expanding list UI:

Recursion is not the natural linear way to solve problems, hence thinking recursively is difficult. Everything becomes clear when a mathematical function definition includes a base case and recursive call.

Conclusion

Every codebase uses arithmetic operators, relational operators, and expressions. To build mathematical expressions, we typically employ log, ceil, floor, min, max, etc. Combinatorics, geometry, data structures, and recursion help implement algorithms. Unless you operate in a pure mathematical domain, you may not use calculus, limits, and other complex math in daily programming (i.e., a game engine). These principles are fundamental for daily programming activities.

Master the above math fundamentals to build clean, efficient code.