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.

Apple's search engine has long been rumored. Recent Google developments may confirm the rumor. Is Apple about to become Google's biggest rival?

Here's a video:

People noted Apple's changes in 2020. AppleBot, a web crawler that downloads and caches Internet content, was more active than in the last five years.

Apple hired search engine developers, including ex-Googlers, such as John Giannandrea, Google's former search chief.

Apple also changed the way iPhones search. With iOS 14, Apple's search results arrived before Google's.

These facts fueled rumors that Apple was developing a search engine.

Apple and Google Have a Contract

Many skeptics said Apple couldn't compete with Google. This didn't affect the company's competitiveness.

Apple is the only business with the resources and scale to be a Google rival, with 1.8 billion active devices and a $2 trillion market cap.

Still, people doubted that due to a license deal. Google pays Apple $8 to $12 billion annually to be the default iPhone and iPad search engine.

Apple can't build an independent search product under this arrangement.

Why would Apple enter search if it's being paid to stay out?

Ironically, this partnership has many people believing Apple is getting into search.

A New Default Search Engine May Be Needed

Google was sued for antitrust in 2020. It is accused of anticompetitive and exclusionary behavior. Justice wants to end Google's monopoly.

Authorities could restrict Apple and Google's licensing deal due to its likely effect on market competitiveness. Hence Apple needs a new default search engine.

Apple Already Has a Search Engine

The company already has a search engine, Spotlight.

Since 2004, Spotlight has aired. It was developed to help users find photos, documents, apps, music, and system preferences.

Apple's search engine could do more than organize files, texts, and apps.

Spotlight Search was updated in 2014 with iOS 8. Web, App Store, and iTunes searches became available. You could find nearby places, movie showtimes, and news.

This search engine has subsequently been updated and improved. Spotlight added rich search results last year.

If you search for a TV show, movie, or song, photos and carousels will appear at the top of the page.

This resembles Google's rich search results.

When Will the Apple Search Engine Be Available?

When will Apple's search launch? Robert Scoble says it's near.

Scoble tweeted a number of hints before this year's Worldwide Developer Conference.

Scoble bases his prediction on insider information and deductive reasoning. January 2023 is expected.

Will you use Apple's search engine?

TOP APPS

Who survives spring cleaning?

Relax. Notion is off-limits. This topic is popular.

(I wrote about it 2 years ago, before everyone else did.) So).

These apps are probably new to you. I hope you find a new phone app after reading this.

Outdooractive

ViewRanger is Google Maps for outdoor enthusiasts.

This app has been so important to me as a freedom-loving long-distance walker and hiker.

This app shows nearby trails and right-of-ways on top of an Open Street Map.

Helpful detail and data. Any route's distance,

You can download and follow tons of routes planned by app users.

This has helped me find new routes and places a fellow explorer has tried.

Free with non-intrusive ads. Years passed before I subscribed. Pro costs £2.23/month.

This app is for outdoor lovers.

Google Files

New phones come with bloatware. These rushed apps are frustrating.

We must replace these apps. 2017 was Google's year.

Files is a file manager. It's quick, innovative, and clean. They've given people what they want.

It's easy to organize files, clear space, and clear cache.

I recommend Gallery by Google as a gallery app alternative. It's quick and easy.

Trainline

App for trains, buses, and coaches.

I've used this app for years. It did the basics well when I first used it.

Since then, it's improved. It's constantly adding features to make traveling easier and less stressful.

Split-ticketing helps me save hundreds a year on train fares. This app is only available in the UK and Europe.

This service doesn't link to a third-party site. Their app handles everything.

Not all train and coach companies use this app. All the big names are there, though.

Here's more on the app.

Battlefield: Mobile

Play Store has 478,000 games. Few can turn my phone into a console.

Call of Duty Mobile and Asphalt 8/9 are examples.

Asphalt's loot boxes and ads make it unplayable. Call of Duty opens with a few ads. Close them to play without hassle.

This game uses all your phone's features to provide a high-quality, seamless experience. If my internet connection is good, I never experience lag or glitches.

The gameplay is energizing and intense, just like on consoles. Sometimes I'm too involved. I've thrown my phone in anger. I'm totally absorbed.

Customizability is my favorite. Since phones have limited screen space, we should only have the buttons we need, placed conveniently.

Size, opacity, and position are modifiable. Adjust audio, graphics, and textures. It's customizable.

This game has been on my phone for three years. It began well and has gotten better. When I think the creators can't do more, they do.

If you play, read my tips for winning a Battle Royale.

Lightroom

As a photographer, I believe your best camera is on you. The phone.

2017 was a big year for this app. I've tried many photo-editing apps since then. This always wins.

The app is dull. I've never seen better photo editing on a phone.

Adjusting settings and sliders doesn't damage or compress photos. It's detailed.

This is important for phone photos, which are lower quality than professional ones.

Some tools are behind a £4.49/month paywall. Adobe must charge a subscription fee instead of selling licenses. (I'm still bitter about Creative Cloud's price)

Snapseed is my pick. Lightroom is where I do basic editing before moving to Snapseed. Snapseed review:

These apps are great. They cover basic and complex editing needs while traveling.

Final Reflections

I hope you downloaded one of these. Share your favorite apps. These apps are scarce.

How a misplaced item may change your outlook

Losing your wallet means life stops. Money vanishes. No credit. Your identity is unverifiable. As you check your pockets for the missing object, you can't drive. You can't borrow a library book.

Last seen? intuitively. Every kid asks this, including yours. However, you know where you lost it: On the Providence River cycling trail. While pedaling vigorously, the wallet dropped out of your back pocket and onto the pavement.

A woman you know—your son's art teacher—says it will be returned. Faith.

You want that faith. Losing a wallet is all-consuming. You must presume it has been stolen and is being used to buy every diamond and non-fungible token on the market. Your identity may have been used to open bank accounts and fake passports. Because he used your license address, a ski mask-wearing man may be driving slowly past your house.

As you delete yourself by canceling cards, these images run through your head. You wait in limbo for replacements. Digital text on the DMV website promises your new license will come within 60 days and be approved by local and state law enforcement. In the following two months, your only defense is a screenshot.

Your wallet was ordinary. A worn, overstuffed leather rectangle. You understand how tenuous your existence has always been since you've never lost a wallet. You barely breathe without your documents.

Ironically, you wore a wallet-belt chain. You adored being a 1993 slacker for 15 years. Your wife just convinced you last year that your office job wasn't professional. You nodded and hid the chain.

Never lost your wallet. Until now.

Angry. Feeling stupid. How could you drop something vital? Why? Is the world cruel? No more dumb luck. You're always one pedal-stroke from death.

Then you get a call: We have your wallet.

Local post office, not cops.

The clerk said someone returned it. Due to trying to identify you, it's a chaos. It has your cards but no cash.

Your automobile screeches down the highway. You yell at the windshield, amazed. Submitted. Art teacher was right. Have some trust.

You thank the postmaster. You ramble through the story. The clerk doesn't know the customer, simply a neighborhood Good Samaritan. You wish you could thank that person for lifting your spirits.

You get home, beaming with gratitude. You thumb through your wallet, amazed that it’s all intact. Then you dig out your chain and reattach it.

Because even faith could use a little help.

Steve Jobs' initial mission at Apple in 1997 was to destroy. He killed the Newton PDA and Macintosh clones. Apple stopped trying to please everyone under Jobs.

Afterward, there were few highly targeted moves. First, the pink iMac. Modest success. The iPod, iPhone, and iPad made Apple the world's most valuable firm. Each maneuver changed the company's center of gravity and won.

That's the idea behind Schwerpunkt, a German military term meaning "focus." Jobs didn't need to win everywhere, just where it mattered, so he focused Apple's resources on a few key goods. Finding your Schwerpunkt is more important than charts and analysis for excellent strategy.

Comparison of Relative Strength and Relative Weakness

The iPod, Apple's first major hit after Jobs' return, didn't damage Microsoft and the PC, but instead focused Apple's emphasis on a fledgling, fragmented market that generated "sucky" products. Apple couldn't have taken on the computer titans at this stage, yet it beat them.

The move into music players used Apple's particular capabilities, especially its ability to build simple, easy-to-use interfaces. Jobs' charisma and stature, along his understanding of intellectual property rights from Pixar, helped him build up iTunes store, which was a quagmire at the time.

In Good Strategy | Bad Strategy, management researcher Richard Rumelt argues that good strategy uses relative strength to counter relative weakness. To discover your main point, determine your abilities and where to effectively use them.

Steve Jobs did that at Apple. Microsoft and Dell, who controlled the computer sector at the time, couldn't enter the music player business. Both sought to produce iPod competitors but failed. Apple's iPod was nobody else's focus.

Finding The Center of Attention

In a military engagement, leaders decide where to focus their efforts by assessing commanders intent, the situation on the ground, the topography, and the enemy's posture on that terrain. Officers spend their careers learning about schwerpunkt.

Business executives must assess internal strengths including personnel, technology, and information, market context, competitive environment, and external partner ecosystems. Steve Jobs was a master at analyzing forces when he returned to Apple.

He believed Apple could integrate technology and design for the iPod and that the digital music player industry sucked. By analyzing competitors' products, he was convinced he could produce a smash by putting 1000 tunes in my pocket.

The only difficulty was there wasn't the necessary technology. External ecosystems were needed. On a trip to Japan to meet with suppliers, a Toshiba engineer claimed the company had produced a tiny memory drive approximately the size of a silver dollar.

Jobs knew the memory drive was his focus. He wrote a $10 million cheque and acquired exclusive technical rights. For a time, none of his competitors would be able to recreate his iPod with the 1000 songs in my pocket.

How to Enter the OODA Loop

John Boyd invented the OODA loop as a pilot to better his own decision-making. First OBSERVE your surroundings, then ORIENT that information using previous knowledge and experiences. Then you DECIDE and ACT, which changes the circumstance you must observe, orient, decide, and act on.

Steve Jobs used the OODA loop to decide to give Toshiba $10 million for a technology it had no use for. He compared the new information with earlier observations about the digital music market.

Then something much more interesting happened. The iPod was an instant hit, changing competition. Other computer businesses that competed in laptops, desktops, and servers created digital music players. Microsoft's Zune came out in 2006, Dell's Digital Jukebox in 2004. Both flopped.

By then, Apple was poised to unveil the iPhone, which would cause its competitors to Observe, Orient, Decide, and Act. Boyd named this OODA Loop infiltration. They couldn't gain the initiative by constantly reacting to Apple.

Microsoft and Dell were titans back then, but it's hard to recall. Apple went from near bankruptcy to crushing its competition via Schwerpunkt.

Rather than a destination, it is a journey

Trying to win everywhere is a strategic blunder. Win significant fights, not trivial skirmishes. Identifying a focal point to direct resources and efforts is the essence of Schwerpunkt.

When Steve Jobs returned to Apple, PC firms were competing, but he focused on digital music players, and the iPod made Apple a player. He launched the iPhone when his competitors were still reacting. When Steve Jobs said, "One more thing," at the end of a product presentation, he had a new focus.

Schwerpunkt isn't static; it's dynamic. Jobs' ability to observe, refocus, and modify the competitive backdrop allowed Apple to innovate consistently. His strategy was tailored to Apple's capabilities, customers, and ecosystem. Microsoft or Dell, better suited for the enterprise sector, couldn't succeed with a comparable approach.

There is no optimal strategy, only ones suited to a given environment, when relative strength might be used against relative weakness. Discovering the center of gravity where you can break through is more of a journey than a destination; it will become evident after you reach.