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.

I was entering tens of millions of records per hour when I first published Slonik PostgreSQL client for Node.js. The data being entered was usually flat, making it straightforward to use INSERT INTO ... SELECT * FROM unnset() pattern. I advocated the unnest approach for inserting rows in groups (that was part I).

However, today I’ve found a better way: jsonb_to_recordset.

jsonb_to_recordset expands the top-level JSON array of objects to a set of rows having the composite type defined by an AS clause.

jsonb_to_recordset allows us to query and insert records from arbitrary JSON, like unnest. Since we're giving JSON to PostgreSQL instead of unnest, the final format is more expressive and powerful.

SELECT *
FROM json_to_recordset('[{"name":"John","tags":["foo","bar"]},{"name":"Jane","tags":["baz"]}]')
AS t1(name text, tags text[]);
 name |   tags
------+-----------
 John | {foo,bar}
 Jane | {baz}
(2 rows)

Let’s demonstrate how you would use it to insert data.

Inserting data using json_to_recordset

Say you need to insert a list of people with attributes into the database.

const persons = [
  {
    name: 'John',
    tags: ['foo', 'bar']
  },
  {
    name: 'Jane',
    tags: ['baz']
  }
];

You may be tempted to traverse through the array and insert each record separately, e.g.

for (const person of persons) {
  await pool.query(sql`
    INSERT INTO person (name, tags)
    VALUES (
      ${person.name},
      ${sql.array(person.tags, 'text[]')}
    )
  `);
}

It's easier to read and grasp when working with a few records. If you're like me and troubleshoot a 2M+ insert query per day, batching inserts may be beneficial.

What prompted the search for better alternatives.

Inserting using unnest pattern might look like this:

await pool.query(sql`
  INSERT INTO public.person (name, tags)
  SELECT t1.name, t1.tags::text[]
  FROM unnest(
    ${sql.array(['John', 'Jane'], 'text')},
    ${sql.array(['{foo,bar}', '{baz}'], 'text')}
  ) AS t1.(name, tags);
`);

You must convert arrays into PostgreSQL array strings and provide them as text arguments, which is unsightly. Iterating the array to create slices for each column is likewise unattractive.

However, with jsonb_to_recordset, we can:

await pool.query(sql`
  INSERT INTO person (name, tags)
  SELECT *
  FROM jsonb_to_recordset(${sql.jsonb(persons)}) AS t(name text, tags text[])
`);

In contrast to the unnest approach, using jsonb_to_recordset we can easily insert complex nested data structures, and we can pass the original JSON document to the query without needing to manipulate it.

In terms of performance they are also exactly the same. As such, my current recommendation is to prefer jsonb_to_recordset whenever inserting lots of rows or nested data structures.

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?

Three Arrows Capital's Google search volume rose over 5,000%.

Three Arrows Capital, a Singapore-based cryptocurrency hedge fund, filed for Chapter 15 bankruptcy last Friday to protect its U.S. assets from creditors.

• Three Arrows filed for bankruptcy on July 1 in New York.

• Three Arrows was ordered liquidated by a British Virgin Islands court last week after defaulting on a $670 million loan from Voyager Digital. Three days later, the Singaporean government reprimanded Three Arrows for spreading misleading information and exceeding asset limits.

• Three Arrows' troubles began with Terra's collapse in May, after it bought US$200 million worth of Terra's LUNA tokens in February, co-founder Kyle Davies told the Wall Street Journal. Three Arrows has failed to meet multiple margin calls since then, including from BlockFi and Genesis.

• Three Arrows Capital, founded by Kyle Davies and Su Zhu in 2012, manages $10 billion in crypto assets.

• Bitcoin's price fell from US$20,600 to below US$19,200 after Three Arrows' bankruptcy petition. According to CoinMarketCap, BTC is now above US$20,000.

What does it mean?

Every action causes an equal and opposite reaction, per Newton's third law. Newtonian physics won't comfort Three Arrows investors, but future investors will thank them for their overconfidence.

Regulators are taking notice of crypto's meteoric rise and subsequent fall. Historically, authorities labeled the industry "high risk" to warn traditional investors against entering it. That attitude is changing. Regulators are moving quickly to regulate crypto to protect investors and prevent broader asset market busts.

The EU has reached a landmark deal that will regulate crypto asset sales and crypto markets across the 27-member bloc. The U.S. is close behind with a similar ruling, and smaller markets are also looking to improve safeguards.

For many, regulation is the only way to ensure the crypto industry survives the current winter.

His story will inspire you.

“Google search went down for a few hours in 2002; Jeff Dean handled all the queries by hand and checked quality doubled.”- Jeff Dean Facts.

One of many Jeff Dean jokes, but you get the idea.

Google's top six engineers met in a war room in mid-2000. Google's crawling system, which indexed the Web, stopped working. Users could still enter queries, but results were five months old.

Google just signed a deal with Yahoo to power a ten-times-larger search engine. Tension rose. It was crucial. If they failed, the Yahoo agreement would likely fall through, risking bankruptcy for the firm. Their efforts could be lost.

A rangy, tall, energetic thirty-one-year-old man named Jeff dean was among those six brilliant engineers in the makeshift room. He had just left D. E. C. a couple of months ago and started his career in a relatively new firm Google, which was about to change the world. He rolled his chair over his colleague Sanjay and sat right next to him, cajoling his code like a movie director. The history started from there.

When you think of people who shaped the World Wide Web, you probably picture founders and CEOs like Larry Page and Sergey Brin, Marc Andreesen, Tim Berners-Lee, Bill Gates, and Mark Zuckerberg. They’re undoubtedly the brightest people on earth.

Under these giants, legions of anonymous coders work at keyboards to create the systems and products we use. These computer workers are irreplaceable.

Let's get to know him better.

It's possible you've never heard of Jeff Dean. He's American. Dean created many behind-the-scenes Google products. Jeff, co-founder and head of Google's deep learning research engineering team, is a popular technology, innovation, and AI keynote speaker.

While earning an MS and Ph.D. in computer science at the University of Washington, he was a teaching assistant, instructor, and research assistant. Dean joined the Compaq Computer Corporation Western Research Laboratory research team after graduating.

Jeff co-created ProfileMe and the Continuous Profiling Infrastructure for Digital at Compaq. He co-designed and implemented Swift, one of the fastest Java implementations. He was a senior technical staff member at mySimon Inc., retrieving and caching electronic commerce content.

Dean, a top young computer scientist, joined Google in mid-1999. He was always trying to maximize a computer's potential as a child.

An expert

His high school program for processing massive epidemiological data was 26 times faster than professionals'. Epi Info, in 13 languages, is used by the CDC. He worked on compilers as a computer science Ph.D. These apps make source code computer-readable.

Dean never wanted to work on compilers forever. He left Academia for Google, which had less than 20 employees. Dean helped found Google News and AdSense, which transformed the internet economy. He then addressed Google's biggest issue, scaling.

Growing Google faced a huge computing challenge. They developed PageRank in the late 1990s to return the most relevant search results. Google's popularity slowed machine deployment.

Dean solved problems, his specialty. He and fellow great programmer Sanjay Ghemawat created the Google File System, which distributed large data over thousands of cheap machines.

These two also created MapReduce, which let programmers handle massive data quantities on parallel machines. They could also add calculations to the search algorithm. A 2004 research article explained MapReduce, which became an industry sensation.

Several revolutionary inventions

Dean's other initiatives were also game-changers. BigTable, a petabyte-capable distributed data storage system, was based on Google File. The first global database, Spanner, stores data on millions of servers in dozens of data centers worldwide.

It underpins Gmail and AdWords. Google Translate co-founder Jeff Dean is surprising. He contributes heavily to Google News. Dean is Senior Fellow of Google Research and Health and leads Google AI.

Recognitions

The National Academy of Engineering elected Dean in 2009. He received the 2009 Association for Computing Machinery fellowship and the 2016 American Academy of Arts and Science fellowship. He received the 2007 ACM-SIGOPS Mark Weiser Award and the 2012 ACM-Infosys Foundation Award. Lists could continue.

A sneaky question may arrive in your mind: How much does this big brain earn? Well, most believe he is one of the highest-paid employees at Google. According to a survey, he is paid $3 million a year.

He makes espresso and chats with a small group of Googlers most mornings. Dean steams milk, another grinds, and another brews espresso. They discuss families and technology while making coffee. He thinks this little collaboration and idea-sharing keeps Google going.

“Some of us have been working together for more than 15 years,” Dean said. “We estimate that we’ve collectively made more than 20,000 cappuccinos together.”

We all know great developers and software engineers. It may inspire many.

What does Ukraine's murderous craziness mean?

Vladimir Putin expressed his patience to Israeli Prime Minister Naftali Bennet. Thousands, even hundreds of thousands of young and middle-aged males in his country have no meaning to him.

During a meeting in March with Prime Minister Naftali Bennett of Israel, Mr. Putin admitted that the Ukrainians were tougher “than I was told,” according to two people familiar with the exchange. “This will probably be much more difficult than we thought. But the war is on their territory, not ours. We are a big country and we have patience (The Inside Story of a Catastrophe).”

Putin should explain to Russian mothers how patient he is with his invasion of Ukraine.

Putin is rich. Even while sanctions have certainly limited Putin's access to his fortune, he has access to everything in Russia. Unlimited wealth.

The Russian leader's infrastructure was designed with his whims in mind. Vladimir Putin is one of the wealthiest and most catered-to people alive. He's also all-powerful, as his lack of opposition shows. His incredible wealth and power have isolated him from average people so much that he doesn't mind turning lives upside down to prove a point.

For many, losing a Russian spouse or son is painful. Whether the soldier was a big breadwinner or unemployed, the loss of a male figure leaves many families bewildered and anxious. Putin, Russia's revered president, seems unfazed.

People who know Mr. Putin say he is ready to sacrifice untold lives and treasure for as long as it takes, and in a rare face-to-face meeting with the Americans last month the Russians wanted to deliver a stark message to President Biden: No matter how many Russian soldiers are killed or wounded on the battlefield, Russia will not give up (The Inside Story of a Catastrophe).

Imagine a country's leader publicly admitting a mistake he's made. Imagine getting Putin's undivided attention.

So, I underestimated Ukrainians. I can't allow them make me appear terrible, so I'll utilize as many drunken dopes as possible to cover up my error. They'll die fulfilled and heroic.

Russia's human resources are limited, but its willingness to cause suffering is not. How many Russian families must die before the curse is broken? If mass protests started tomorrow, Russia's authorities couldn't stop them.

When Moscovites faced down tanks in August 1991, the Gorbachev coup ended in three days. Even though few city residents showed up, everything collapsed. This wicked disaster won't require many Russians.

One NATO member is warning allies that Mr. Putin is ready to accept the deaths or injuries of as many as 300,000 Russian troops — roughly three times his estimated losses so far.

If 100,000 Russians have died in Ukraine and Putin doesn't mind another 200,000 dying, why don't these 200,000 ghosts stand up and save themselves? Putin plays the role of concerned and benevolent leader effectively, but things aren't going well for Russia.

What would 300,000 or more missing men signify for Russia's future? How many kids will have broken homes? How many families won't form, and what will the economy do?

Putin reportedly cared about his legacy. His place in Russian history Putin's invasion of Ukraine settled his legacy. He has single-handedly weakened and despaired Russia since the 1980s.

Putin will be viewed by sensible people as one of Russia's worst adversaries, but Russians will think he was fantastic despite Ukraine.

The more setbacks Mr. Putin endures on the battlefield, the more fears grow over how far he is willing to go. He has killed tens of thousands in Ukraine, leveled cities, and targeted civilians for maximum pain — obliterating hospitals, schools, and apartment buildings while cutting off power and water to millions before winter. Each time Ukrainian forces score a major blow against Russia, the bombing of their country intensifies. And Mr. Putin has repeatedly reminded the world that he can use anything at his disposal, including nuclear arms, to pursue his notion of victory.

How much death and damage will there be in Ukraine if Putin sends 200,000 more Russians to the front? It's scary, sad, and sick.

Monster.