More on Leadership

William Anderson
3 years ago
When My Remote Leadership Skills Took Off
4 Ways To Manage Remote Teams & Employees
The wheels hit the ground as I landed in Rochester.
Our six-person satellite office was now part of my team.
Their manager only reported to me the day before, but I had my ticket booked ahead of time.
I had managed remote employees before but this was different. Engineers dialed into headquarters for every meeting.
So when I learned about the org chart change, I knew a strong first impression would set the tone for everything else.
I was either their boss, or their boss's boss, and I needed them to know I was committed.
Managing a fleet of satellite freelancers or multiple offices requires treating others as more than just a face behind a screen.
You must comprehend each remote team member's perspective and daily interactions.
The good news is that you can start using these techniques right now to better understand and elevate virtual team members.
1. Make Visits To Other Offices
If budgeted, visit and work from offices where teams and employees report to you. Only by living alongside them can one truly comprehend their problems with communication and other aspects of modern life.
2. Have Others Come to You
• Having remote, distributed, or satellite employees and teams visit headquarters every quarter or semi-quarterly allows the main office culture to rub off on them.
When remote team members visit, more people get to meet them, which builds empathy.
If you can't afford to fly everyone, at least bring remote managers or leaders. Hopefully they can resurrect some culture.
3. Weekly Work From Home
No home office policy?
Make one.
WFH is a team-building, problem-solving, and office-viewing opportunity.
For dial-in meetings, I started working from home on occasion.
It also taught me which teams “forget” or “skip” calls.
As a remote team member, you experience all the issues first hand.
This isn't as accurate for understanding teams in other offices, but it can be done at any time.
4. Increase Contact Even If It’s Just To Chat
Don't underestimate office banter.
Sometimes it's about bonding and trust, other times it's about business.
If you get all this information in real-time, please forward it.
Even if nothing critical is happening, call remote team members to check in and chat.
I guarantee that building relationships and rapport will increase both their job satisfaction and yours.

Aniket
3 years ago
Yahoo could have purchased Google for $1 billion
Let's see this once-dominant IT corporation crumble.
What's the capital of Kazakhstan? If you don't know the answer, you can probably find it by Googling. Google Search returned results for Nur-Sultan in 0.66 seconds.
Google is the best search engine I've ever used. Did you know another search engine ruled the Internet? I'm sure you guessed Yahoo!
Google's friendly UI and wide selection of services make it my top choice. Let's explore Yahoo's decline.
Yahoo!
YAHOO stands for Yet Another Hierarchically Organized Oracle. Jerry Yang and David Filo established Yahoo.
Yahoo is primarily a search engine and email provider. It offers News and an advertising platform. It was a popular website in 1995 that let people search the Internet directly. Yahoo began offering free email in 1997 by acquiring RocketMail.
According to a study, Yahoo used Google Search Engine technology until 2000 and then developed its own in 2004.
Yahoo! rejected buying Google for $1 billion
Larry Page and Sergey Brin, Google's founders, approached Yahoo in 1998 to sell Google for $1 billion so they could focus on their studies. Yahoo denied the offer, thinking it was overvalued at the time.
Yahoo realized its error and offered Google $3 billion in 2002, but Google demanded $5 billion since it was more valuable. Yahoo thought $5 billion was overpriced for the existing market.
In 2022, Google is worth $1.56 Trillion.
What happened to Yahoo!
Yahoo refused to buy Google, and Google's valuation rose, making a purchase unfeasible.
Yahoo started losing users when Google launched Gmail. Google's UI was far cleaner than Yahoo's.
Yahoo offered $1 billion to buy Facebook in July 2006, but Zuckerberg and the board sought $1.1 billion. Yahoo rejected, and Facebook's valuation rose, making it difficult to buy.
Yahoo was losing users daily while Google and Facebook gained many. Google and Facebook's popularity soared. Yahoo lost value daily.
Microsoft offered $45 billion to buy Yahoo in February 2008, but Yahoo declined. Microsoft increased its bid to $47 billion after Yahoo said it was too low, but Yahoo rejected it. Then Microsoft rejected Yahoo’s 10% bid increase in May 2008.
In 2015, Verizon bought Yahoo for $4.5 billion, and Apollo Global Management bought 90% of Yahoo's shares for $5 billion in May 2021. Verizon kept 10%.
Yahoo's opportunity to acquire Google and Facebook could have been a turning moment. It declined Microsoft's $45 billion deal in 2008 and was sold to Verizon for $4.5 billion in 2015. Poor decisions and lack of vision caused its downfall. Yahoo's aim wasn't obvious and it didn't stick to a single domain.
Hence, a corporation needs a clear vision and a leader who can see its future.
Liked this article? Join my tech and programming newsletter here.

Alison Randel
3 years ago
Raising the Bar on Your 1:1s
Managers spend much time in 1:1s. Most team members meet with supervisors regularly. 1:1s can help create relationships and tackle tough topics. Few appreciate the 1:1 format's potential. Most of the time, that potential is spent on small talk, surface-level updates, and ranting (Ugh, the marketing team isn’t stepping up the way I want them to).
What if you used that time to have deeper conversations and important insights? What if change was easy?
This post introduces a new 1:1 format to help you dive deeper, faster, and develop genuine relationships without losing impact.
A 1:1 is a chat, you would assume. Why use structure to talk to a coworker? Go! I know how to talk to people. I can write. I've always written. Also, This article was edited by Zoe.
Before you discard something, ask yourself if there's a good reason not to try anything new. Is the 1:1 only a talk, or do you want extra benefits? Try the steps below to discover more.
I. Reflection (5 minutes)
Context-free, broad comments waste time and are useless. Instead, give team members 5 minutes to write these 3 prompts.
What's effective?
What is decent but could be improved?
What is broken or missing?
Why these? They encourage people to be honest about all their experiences. Answering these questions helps people realize something isn't working. These prompts let people consider what's working.
Why take notes? Because you get more in less time. Will you feel awkward sitting quietly while your coworker writes? Probably. Persevere. Multi-task. Take a break from your afternoon meeting marathon. Any awkwardness will pay off.
What happens? After a few minutes of light conversation, create a template like the one given here and have team members fill in their replies. You can pre-share the template (with the caveat that this isn’t meant to take much prep time). Do this with your coworker: Answer the prompts. Everyone can benefit from pondering and obtaining guidance.
This step's output.
Part II: Talk (10-20 minutes)
Most individuals can explain what they see but not what's behind an answer. You don't like a meeting. Why not? Marketing partnership is difficult. What makes working with them difficult? I don't recommend slandering coworkers. Consider how your meetings, decisions, and priorities make work harder. The excellent stuff too. You want to know what's humming so you can reproduce the magic.
First, recognize some facts.
Real power dynamics exist. To encourage individuals to be honest, you must provide a safe environment and extend clear invites. Even then, it may take a few 1:1s for someone to feel secure enough to go there in person. It is part of your responsibility to admit that it is normal.
Curiosity and self-disclosure are crucial. Most leaders have received training to present themselves as the authorities. However, you will both benefit more from the dialogue if you can be open and honest about your personal experience, ask questions out of real curiosity, and acknowledge the pertinent sacrifices you're making as a leader.
Honesty without bias is difficult and important. Due to concern for the feelings of others, people frequently hold back. Or if they do point anything out, they do so in a critical manner. The key is to be open and unapologetic about what you observe while not presuming that your viewpoint is correct and that of the other person is incorrect.
Let's go into some prompts (based on genuine conversations):
“What do you notice across your answers?”
“What about the way you/we/they do X, Y, or Z is working well?”
“ Will you say more about item X in ‘What’s not working?’”
“I’m surprised there isn’t anything about Z. Why is that?”
“All of us tend to play some role in maintaining certain patterns. How might you/we be playing a role in this pattern persisting?”
“How might the way we meet, make decisions, or collaborate play a role in what’s currently happening?”
Consider the preceding example. What about the Monday meeting isn't working? Why? or What about the way we work with marketing makes collaboration harder? Remember to share your honest observations!
Third section: observe patterns (10-15 minutes)
Leaders desire to empower their people but don't know how. We also have many preconceptions about what empowerment means to us and how it works. The next phase in this 1:1 format will assist you and your team member comprehend team power and empowerment. This understanding can help you support and shift your team member's behavior, especially where you disagree.
How to? After discussing the stated responses, ask each team member what they can control, influence, and not control. Mark their replies. You can do the same, adding colors where you disagree.
This step's output.
Next, consider the color constellation. Discuss these questions:
Is one color much more prevalent than the other? Why, if so?
Are the colors for the "what's working," "what's fine," and "what's not working" categories clearly distinct? Why, if so?
Do you have any disagreements? If yes, specifically where does your viewpoint differ? What activities do you object to? (Remember, there is no right or wrong in this. Give explicit details and ask questions with curiosity.)
Example: Based on the colors, you can ask, Is the marketing meeting's quality beyond your control? Were our marketing partners consulted? Are there any parts of team decisions we can control? We can't control people, but have we explored another decision-making method? How can we collaborate and generate governance-related information to reduce work, even if the requirement for prep can't be eliminated?
Consider the top one or two topics for this conversation. No 1:1 can cover everything, and that's OK. Focus on the present.
Part IV: Determine the next step (5 minutes)
Last, examine what this conversation means for you and your team member. It's easy to think we know the next moves when we don't.
Like what? You and your teammate answer these questions.
What does this signify moving ahead for me? What can I do to change this? Make requests, for instance, and see how people respond before thinking they won't be responsive.
What demands do I have on other people or my partners? What should I do first? E.g. Make a suggestion to marketing that we hold a monthly retrospective so we can address problems and exchange input more frequently. Include it on the meeting's agenda for next Monday.
Close the 1:1 by sharing what you noticed about the chat. Observations? Learn anything?
Yourself, you, and the 1:1
As a leader, you either reinforce or disrupt habits. Try this template if you desire greater ownership, empowerment, or creativity. Consider how you affect surrounding dynamics. How can you expect others to try something new in high-stakes scenarios, like meetings with cross-functional partners or senior stakeholders, if you won't? How can you expect deep thought and relationship if you don't encourage it in 1:1s? What pattern could this new format disrupt or reinforce?
Fight reluctance. First attempts won't be ideal, and that's OK. You'll only learn by trying.
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Emma Jade
3 years ago
6 hacks to create content faster
Content gurus' top time-saving hacks.
I'm a content strategist, writer, and graphic designer. Time is more valuable than money.
Money is always available. Even if you're poor. Ways exist.
Time is passing, and one day we'll run out.
Sorry to be morbid.
In today's digital age, you need to optimize how you create content for your organization. Here are six content creation hacks.
1. Use templates
Use templates to streamline your work whether generating video, images, or documents.
Setup can take hours. Using a free resource like Canva, you can create templates for any type of material.
This will save you hours each month.
2. Make a content calendar
You post without a plan? A content calendar solves 50% of these problems.
You can prepare, organize, and plan your material ahead of time so you're not scrambling when you remember, "Shit, it's Mother's Day!"
3. Content Batching
Batching content means creating a lot in one session. This is helpful for video content that requires a lot of setup time.
Batching monthly content saves hours. Time is a valuable resource.
When working on one type of task, it's easy to get into a flow state. This saves time.
4. Write Caption
On social media, we generally choose the image first and then the caption. Writing captions first sometimes work better, though.
Writing the captions first can allow you more creative flexibility and be easier if you're not excellent with language.
Say you want to tell your followers something interesting.
Writing a caption first is easier than choosing an image and then writing a caption to match.
Not everything works. You may have already-created content that needs captioning. When you don't know what to share, think of a concept, write the description, and then produce a video or graphic.
Cats can be skinned in several ways..
5. Repurpose
Reuse content when possible. You don't always require new stuff. In fact, you’re pretty stupid if you do #SorryNotSorry.
Repurpose old content. All those blog entries, videos, and unfinished content on your desk or hard drive.
This blog post can be turned into a social media infographic. Canva's motion graphic function can animate it. I can record a YouTube video regarding this issue for a podcast. I can make a post on each point in this blog post and turn it into an eBook or paid course.
And it doesn’t stop there.
My point is, to think outside the box and really dig deep into ways you can leverage the content you’ve already created.
6. Schedule Them
If you're still manually posting content, get help. When you batch your content, schedule it ahead of time.
Some scheduling apps are free or cheap. No excuses.
Don't publish and ghost.
Scheduling saves time by preventing you from doing it manually. But if you never engage with your audience, the algorithm won't reward your material.
Be online and engage your audience.
Content Machine
Use these six content creation hacks. They help you succeed and save time.

middlemarch.eth
3 years ago
ERC721R: A new ERC721 contract for random minting so people don’t snipe all the rares!
That is, how to snipe all the rares without using ERC721R!
Introduction: Blessed and Lucky
Mphers was the first mfers derivative, and as a Phunks derivative, I wanted one.
I wanted an alien. And there are only 8 in the 6,969 collection. I got one!
In case it wasn't clear from the tweet, I meant that I was lucky to have figured out how to 100% guarantee I'd get an alien without any extra luck.
Read on to find out how I did it, how you can too, and how developers can avoid it!
How to make rare NFTs without luck.
# How to mint rare NFTs without needing luck
The key to minting a rare NFT is knowing the token's id ahead of time.
For example, once I knew my alien was #4002, I simply refreshed the mint page until #3992 was minted, and then mint 10 mphers.
How did I know #4002 was extraterrestrial? Let's go back.
First, go to the mpher contract's Etherscan page and look up the tokenURI of a previously issued token, token #1:
As you can see, mphers creates metadata URIs by combining the token id and an IPFS hash.
This method gives you the collection's provenance in every URI, and while that URI can be changed, it affects everyone and is public.
Consider a token URI without a provenance hash, like https://mphers.art/api?tokenId=1.
As a collector, you couldn't be sure the devs weren't changing #1's metadata at will.
The API allows you to specify “if #4002 has not been minted, do not show any information about it”, whereas IPFS does not allow this.
It's possible to look up the metadata of any token, whether or not it's been minted.
Simply replace the trailing “1” with your desired id.
Mpher #4002
These files contain all the information about the mpher with the specified id. For my alien, we simply search all metadata files for the string “alien mpher.”
Take a look at the 6,969 meta-data files I'm using OpenSea's IPFS gateway, but you could use ipfs.io or something else.
Use curl to download ten files at once. Downloading thousands of files quickly can lead to duplicates or errors. But with a little tweaking, you should be able to get everything (and dupes are fine for our purposes).
Now that you have everything in one place, grep for aliens:
The numbers are the file names that contain “alien mpher” and thus the aliens' ids.
The entire process takes under ten minutes. This technique works on many NFTs currently minting.
In practice, manually minting at the right time to get the alien is difficult, especially when tokens mint quickly. Then write a bot to poll totalSupply() every second and submit the mint transaction at the exact right time.
You could even look for the token you need in the mempool before it is minted, and get your mint into the same block!
However, in my experience, the “big” approach wins 95% of the time—but not 100%.
“Am I being set up all along?”
Is a question you might ask yourself if you're new to this.
It's disheartening to think you had no chance of minting anything that someone else wanted.
But, did you have no opportunity? You had an equal chance as everyone else!
Take me, for instance: I figured this out using open-source tools and free public information. Anyone can do this, and not understanding how a contract works before minting will lead to much worse issues.
The mpher mint was fair.
While a fair game, “snipe the alien” may not have been everyone's cup of tea.
People may have had more fun playing the “mint lottery” where tokens were distributed at random and no one could gain an advantage over someone simply clicking the “mint” button.
How might we proceed?
Minting For Fashion Hats Punks, I wanted to create a random minting experience without sacrificing fairness. In my opinion, a predictable mint beats an unfair one. Above all, participants must be equal.
Sadly, the most common method of creating a random experience—the post-mint “reveal”—is deeply unfair. It works as follows:
- During the mint, token metadata is unavailable. Instead, tokenURI() returns a blank JSON file for each id.
- An IPFS hash is updated once all tokens are minted.
- You can't tell how the contract owner chose which token ids got which metadata, so it appears random.
Because they alone decide who gets what, the person setting the metadata clearly has a huge unfair advantage over the people minting. Unlike the mpher mint, you have no chance of winning here.
But what if it's a well-known, trusted, doxxed dev team? Are reveals okay here?
No! No one should be trusted with such power. Even if someone isn't consciously trying to cheat, they have unconscious biases. They might also make a mistake and not realize it until it's too late, for example.
You should also not trust yourself. Imagine doing a reveal, thinking you did it correctly (nothing is 100%! ), and getting the rarest NFT. Isn't that a tad odd Do you think you deserve it? An NFT developer like myself would hate to be in this situation.
Reveals are bad*
UNLESS they are done without trust, meaning everyone can verify their fairness without relying on the developers (which you should never do).
An on-chain reveal powered by randomness that is verifiably outside of anyone's control is the most common way to achieve a trustless reveal (e.g., through Chainlink).
Tubby Cats did an excellent job on this reveal, and I highly recommend their contract and launch reflections. Their reveal was also cool because it was progressive—you didn't have to wait until the end of the mint to find out.
In his post-launch reflections, @DefiLlama stated that he made the contract as trustless as possible, removing as much trust as possible from the team.
In my opinion, everyone should know the rules of the game and trust that they will not be changed mid-stream, while trust minimization is critical because smart contracts were designed to reduce trust (and it makes it impossible to hack even if the team is compromised). This was a huge mistake because it limited our flexibility and our ability to correct mistakes.
And @DefiLlama is a superstar developer. Imagine how much stress maximizing trustlessness will cause you!
That leaves me with a bad solution that works in 99 percent of cases and is much easier to implement: random token assignments.
Introducing ERC721R: A fully compliant IERC721 implementation that picks token ids at random.
ERC721R implements the opposite of a reveal: we mint token ids randomly and assign metadata deterministically.
This allows us to reveal all metadata prior to minting while reducing snipe chances.
Then import the contract and use this code:
What is ERC721R and how does it work
First, a disclaimer: ERC721R isn't truly random. In this sense, it creates the same “game” as the mpher situation, where minters compete to exploit the mint. However, ERC721R is a much more difficult game.
To game ERC721R, you need to be able to predict a hash value using these inputs:
This is impossible for a normal person because it requires knowledge of the block timestamp of your mint, which you do not have.
To do this, a miner must set the timestamp to a value in the future, and whatever they do is dependent on the previous block's hash, which expires in about ten seconds when the next block is mined.
This pseudo-randomness is “good enough,” but if big money is involved, it will be gamed. Of course, the system it replaces—predictable minting—can be manipulated.
The token id is chosen in a clever implementation of the Fisher–Yates shuffle algorithm that I copied from CryptoPhunksV2.
Consider first the naive solution: (a 10,000 item collection is assumed):
- Make an array with 0–9999.
- To create a token, pick a random item from the array and use that as the token's id.
- Remove that value from the array and shorten it by one so that every index corresponds to an available token id.
This works, but it uses too much gas because changing an array's length and storing a large array of non-zero values is expensive.
How do we avoid them both? What if we started with a cheap 10,000-zero array? Let's assign an id to each index in that array.
Assume we pick index #6500 at random—#6500 is our token id, and we replace the 0 with a 1.
But what if we chose #6500 again? A 1 would indicate #6500 was taken, but then what? We can't just "roll again" because gas will be unpredictable and high, especially later mints.
This allows us to pick a token id 100% of the time without having to keep a separate list. Here's how it works:
- Make a 10,000 0 array.
- Create a 10,000 uint numAvailableTokens.
- Pick a number between 0 and numAvailableTokens. -1
- Think of #6500—look at index #6500. If it's 0, the next token id is #6500. If not, the value at index #6500 is your next token id (weird!)
- Examine the array's last value, numAvailableTokens — 1. If it's 0, move the value at #6500 to the end of the array (#9999 if it's the first token). If the array's last value is not zero, update index #6500 to store it.
- numAvailableTokens is decreased by 1.
- Repeat 3–6 for the next token id.
So there you go! The array stays the same size, but we can choose an available id reliably. The Solidity code is as follows:
Unfortunately, this algorithm uses more gas than the leading sequential mint solution, ERC721A.
This is most noticeable when minting multiple tokens in one transaction—a 10 token mint on ERC721R costs 5x more than on ERC721A. That said, ERC721A has been optimized much further than ERC721R so there is probably room for improvement.
Conclusion
Listed below are your options:
- ERC721A: Minters pay lower gas but must spend time and energy devising and executing a competitive minting strategy or be comfortable with worse minting results.
- ERC721R: Higher gas, but the easy minting strategy of just clicking the button is optimal in all but the most extreme cases. If miners game ERC721R it’s the worst of both worlds: higher gas and a ton of work to compete.
- ERC721A + standard reveal: Low gas, but not verifiably fair. Please do not do this!
- ERC721A + trustless reveal: The best solution if done correctly, highly-challenging for dev, potential for difficult-to-correct errors.
Did I miss something? Comment or tweet me @dumbnamenumbers.
Check out the code on GitHub to learn more! Pull requests are welcome—I'm sure I've missed many gas-saving opportunities.
Thanks!
Read the original post here

Shalitha Suranga
3 years ago
The Top 5 Mathematical Concepts Every Programmer Needs to Know
Using math to write efficient code in any language
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.
Inbuilt max and min functions can minimize verbose if statements.
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.
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):
Logarithms aid with programming math. Metas Watchman uses a logarithmic utility function to find the next power of two.
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.
