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.

They depend heavily on open source..

Discord users send billions of messages daily. Users wish to search these messages. How do we index these to search by message keywords?

Let’s find out.

1. Discord utilizes Elasticsearch. Elasticsearch is a free, open search engine for textual, numerical, geographical, structured, and unstructured data. Apache Lucene powers Elasticsearch.
   

2. How does elastic search store data? It stores it as numerous key-value pairs in JSON documents.
   

3. How does elastic search index? Elastic search's index is inverted. An inverted index lists every unique word in every page and where it appears.

4. Elasticsearch indexes documents and generates an inverted index to make data searchable in near real-time. The index API adds or updates JSON documents in a given index.

1. Let's examine how discord uses Elastic Search. Elasticsearch prefers bulk indexing. Discord couldn't index real-time messages. You can't search posted messages. You want outdated messages.

6. Let's check what bulk indexing requires.
1. A temporary queue for incoming communications.
2. Indexer workers that index messages into elastic search.

1. Discord's queue is Celery. The queue is open-source. Elastic search won't run on a single server. It's clustered. Where should a message go? Where?

8. A shard allocator decides where to put the message. Nevertheless. Shattered? A shard combines elastic search and index on. So, these two form a shard which is used as a unit by discord. The elastic search itself has some shards. But this is different, so don’t get confused.

1. Now, the final part is service discovery — to discover the elastic search clusters and the hosts within that cluster. This, they do with the help of etcd another open source tool.
   

A great thing to notice here is that discord relies heavily on open source systems and their base implementations which is very different from a lot of other products.

Apocodes helps entrepreneurs create SaaS products without writing code. This post introduces micro-SaaS and outlines its basic strategy.

Strategy

Vision and strategy differ when starting a startup.

• The company's long-term future state is outlined in the vision. It establishes the overarching objectives the organization aims to achieve while also justifying its existence. The company's future is outlined in the vision.

• The strategy consists of a collection of short- to mid-term objectives, the accomplishment of which will move the business closer to its vision. The company gets there through its strategy.

The vision should be stable, but the strategy must be adjusted based on customer input, market conditions, or previous experiments.

Begin modestly and aim high.

Be truthful. It's impossible to automate SaaS product creation from scratch. It's like climbing Everest without running a 5K. Physical rules don't prohibit it, but it would be suicide.

Apocodes 5K equivalent? Two options:

• (A) Create a feature that includes every setting option conceivable. then query potential clients “Would you choose us to build your SaaS solution if we offered 99 additional features of the same caliber?” After that, decide which major feature to implement next.

• (B) Build a few straightforward features with just one or two configuration options. Then query potential clients “Will this suffice to make your product?” What's missing if not? Finally, tweak the final result a bit before starting over.

(A) is an all-or-nothing approach. It's like training your left arm to climb Mount Everest. My right foot is next.

(B) is a better method because it's iterative and provides value to customers throughout.

Focus on a small market sector, meet its needs, and expand gradually. Micro-SaaS is Apocode's first market.

What is micro-SaaS.

Micro-SaaS enterprises have these characteristics:

• A limited range: They address a specific problem with a small number of features.

• A small group of one to five individuals.

• Low external funding: The majority of micro-SaaS companies have Total Addressable Markets (TAM) under $100 million. Investors find them unattractive as a result. As a result, the majority of micro-SaaS companies are self-funded or bootstrapped.

• Low competition: Because they solve problems that larger firms would rather not spend time on, micro-SaaS enterprises have little rivalry.

• Low upkeep: Because of their simplicity, they require little care.

• Huge profitability: Because providing more clients incurs such a small incremental cost, high profit margins are possible.

Micro-SaaS enterprises created with no-code are Apocode's ideal first market niche.

We'll create our own micro-SaaS solutions to better understand their needs. Although not required, we believe this will improve community discussions.

The challenge

In 100 days (September 12–December 20, 2022), we plan to build 10 micro-SaaS enterprises using Apocode.

They will be:

• Self-serve: Customers will be able to use the entire product experience without our manual assistance.

• Real: They'll deal with actual issues. They won't be isolated proofs of concept because we'll keep up with them after the challenge.

• Both free and paid options: including a free plan and a free trial period. Although financial success would be a good result, the challenge's stated objective is not financial success.

This will let us design Apocodes features, showcase them, and talk to customers.

(Edit: The first micro-SaaS was launched!)

Follow along

If you want to follow the story of Apocode or our progress in this challenge, you can subscribe here.

If you are interested in using Apocode, sign up here.

If you want to provide feedback, discuss the idea further or get involved, email me at nicolas.tresegnie@gmail.com

Yes, client meetings are difficult. Especially when I'm alone.

Clients must tell us their problems so we can help.

In-meeting challenges contribute nothing to our work. Consider this:

• Clients are unprepared.

• Clients are distracted.

• Clients are confused.

Introducing Jack Dorsey's Google Doc approach

I endorse his approach to meetings.

Not Google Doc-related. Jack uses it for meetings.

This is what his meetings look like.

• Prior to the meeting, the Chair creates the agenda, structure, and information using Google Doc.

• Participants in the meeting would have 5-10 minutes to read the Google Doc.

• They have 5-10 minutes to type their comments on the document.

• In-depth discussion begins

There is elegance in simplicity. Here's how Jack's approach is fantastic.

Unprepared clients are given time to read.

During the meeting, they think and work on it.

They can see real-time remarks from others.

Discussion ensues.

Three months ago, I fell for this strategy. After trying it with a client, I got good results.

I conducted social control experiments in a few client workshops.

Context matters.

I am sure Jack Dorsey’s method works well in meetings. What about client workshops?

So, I tested Enterprise of the Future with a consulting client.

I sent multiple emails to client stakeholders describing the new approach.

No PowerPoints that day. I spent the night setting up the Google Doc with conversation topics, critical thinking questions, and a Before and After section.

The client was shocked. First, a Google Doc was projected. Second surprise was a verbal feedback.

“No pre-meeting materials?”

“Don’t worry. I know you are not reading it before our meeting, anyway.”

We laughed. The experiment started.

Observations throughout a 90-minute engagement workshop from beginning to end

For 10 minutes, the workshop was silent.

People read the Google Doc. For some, the silence was unnerving.

“Are you not going to present anything to us?”

I said everything's in Google Doc. I asked them to read, remark, and add relevant paragraphs.

As they unlocked their laptops, they were annoyed.

Ten client stakeholders are typing on the Google Doc. My laptop displays comment bubbles, red lines, new paragraphs, and strikethroughs.

The first 10 minutes were productive. Everyone has seen and contributed to the document.

I was silent.

The move to a classical workshop was smooth. I didn't stimulate dialogue. They did.

Stephanie asked Joe why a blended workforce hinders company productivity. She questioned his comments and additional paragraphs.

That is when a light bulb hit my head. Yes, you want to speak to the right person to resolve issues!

Not only that was discussed. Others discussed their remark bubbles with neighbors. Debate circles sprung up one after the other.

The best part? I asked everyone to add their post-discussion thoughts on a Google Doc.

After the workshop, I have:

• An agreement-based working document

• A post-discussion minutes that are prepared for publication

• A record of the discussion points that were brought up, argued, and evaluated critically

It showed me how stakeholders viewed their Enterprise of the Future. It allowed me to align with them.

Finale Keynotes

Client meetings are a hit-or-miss. I know that.

Jack Dorsey's meeting strategy works for consulting. It promotes session alignment.

It relieves clients of preparation.

I get the necessary information to advance this consulting engagement.

It is brilliant.