Python Heatmap Technical Indicator

Heatmaps provide an instant overview. They can be used with correlations or to predict reactions or confirm the trend in trading. This article covers RSI heatmap creation.

The Market System

Market regime:

• Bullish trend: The market tends to make higher highs, which indicates that the overall trend is upward.

• Sideways: The market tends to fluctuate while staying within predetermined zones.

• Bearish trend: The market has the propensity to make lower lows, indicating that the overall trend is downward.

Most tools detect the trend, but we cannot predict the next state. The best way to solve this problem is to assume the current state will continue and trade any reactions, preferably in the trend.

If the EURUSD is above its moving average and making higher highs, a trend-following strategy would be to wait for dips before buying and assuming the bullish trend will continue.

Indicator of Relative Strength

J. Welles Wilder Jr. introduced the RSI, a popular and versatile technical indicator. Used as a contrarian indicator to exploit extreme reactions. Calculating the default RSI usually involves these steps:

• Determine the difference between the closing prices from the prior ones.

• Distinguish between the positive and negative net changes.

• Create a smoothed moving average for both the absolute values of the positive net changes and the negative net changes.

• Take the difference between the smoothed positive and negative changes. The Relative Strength RS will be the name we use to describe this calculation.

• To obtain the RSI, use the normalization formula shown below for each time step.

The 13-period RSI and black GBPUSD hourly values are shown above. RSI bounces near 25 and pauses around 75. Python requires a four-column OHLC array for RSI coding.

import numpy as np
def add_column(data, times):
    
    for i in range(1, times + 1):
    
        new = np.zeros((len(data), 1), dtype = float)
        
        data = np.append(data, new, axis = 1)
    return data
def delete_column(data, index, times):
    
    for i in range(1, times + 1):
    
        data = np.delete(data, index, axis = 1)
    return data
def delete_row(data, number):
    
    data = data[number:, ]
    
    return data
def ma(data, lookback, close, position): 
    
    data = add_column(data, 1)
    
    for i in range(len(data)):
           
            try:
                
                data[i, position] = (data[i - lookback + 1:i + 1, close].mean())
            
            except IndexError:
                
                pass
            
    data = delete_row(data, lookback)
    
    return data
def smoothed_ma(data, alpha, lookback, close, position):
    
    lookback = (2 * lookback) - 1
    
    alpha = alpha / (lookback + 1.0)
    
    beta  = 1 - alpha
    
    data = ma(data, lookback, close, position)
    data[lookback + 1, position] = (data[lookback + 1, close] * alpha) + (data[lookback, position] * beta)
    for i in range(lookback + 2, len(data)):
        
            try:
                
                data[i, position] = (data[i, close] * alpha) + (data[i - 1, position] * beta)
        
            except IndexError:
                
                pass
            
    return data
def rsi(data, lookback, close, position):
    
    data = add_column(data, 5)
    
    for i in range(len(data)):
        
        data[i, position] = data[i, close] - data[i - 1, close]
     
    for i in range(len(data)):
        
        if data[i, position] > 0:
            
            data[i, position + 1] = data[i, position]
            
        elif data[i, position] < 0:
            
            data[i, position + 2] = abs(data[i, position])
            
    data = smoothed_ma(data, 2, lookback, position + 1, position + 3)
    data = smoothed_ma(data, 2, lookback, position + 2, position + 4)
    data[:, position + 5] = data[:, position + 3] / data[:, position + 4]
    
    data[:, position + 6] = (100 - (100 / (1 + data[:, position + 5])))
    data = delete_column(data, position, 6)
    data = delete_row(data, lookback)
    return data

Make sure to focus on the concepts and not the code. You can find the codes of most of my strategies in my books. The most important thing is to comprehend the techniques and strategies.

My weekly market sentiment report uses complex and simple models to understand the current positioning and predict the future direction of several major markets. Check out the report here:

Using the Heatmap to Find the Trend

RSI trend detection is easy but useless. Bullish and bearish regimes are in effect when the RSI is above or below 50, respectively. Tracing a vertical colored line creates the conditions below. How:

• When the RSI is higher than 50, a green vertical line is drawn.

• When the RSI is lower than 50, a red vertical line is drawn.

Zooming out yields a basic heatmap, as shown below.

Plot code:

def indicator_plot(data, second_panel, window = 250):
    fig, ax = plt.subplots(2, figsize = (10, 5))
    sample = data[-window:, ]
    for i in range(len(sample)):
        ax[0].vlines(x = i, ymin = sample[i, 2], ymax = sample[i, 1], color = 'black', linewidth = 1)  
        if sample[i, 3] > sample[i, 0]:
            ax[0].vlines(x = i, ymin = sample[i, 0], ymax = sample[i, 3], color = 'black', linewidth = 1.5)  
        if sample[i, 3] < sample[i, 0]:
            ax[0].vlines(x = i, ymin = sample[i, 3], ymax = sample[i, 0], color = 'black', linewidth = 1.5)  
        if sample[i, 3] == sample[i, 0]:
            ax[0].vlines(x = i, ymin = sample[i, 3], ymax = sample[i, 0], color = 'black', linewidth = 1.5)  
    ax[0].grid() 
    for i in range(len(sample)):
        if sample[i, second_panel] > 50:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'green', linewidth = 1.5)  
        if sample[i, second_panel] < 50:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'red', linewidth = 1.5)  
    ax[1].grid()
indicator_plot(my_data, 4, window = 500)

Call RSI on your OHLC array's fifth column. 4. Adjusting lookback parameters reduces lag and false signals. Other indicators and conditions are possible.

Another suggestion is to develop an RSI Heatmap for Extreme Conditions.

Contrarian indicator RSI. The following rules apply:

• Whenever the RSI is approaching the upper values, the color approaches red.

• The color tends toward green whenever the RSI is getting close to the lower values.

Zooming out yields a basic heatmap, as shown below.

Plot code:

import matplotlib.pyplot as plt
def indicator_plot(data, second_panel, window = 250):
    fig, ax = plt.subplots(2, figsize = (10, 5))
    sample = data[-window:, ]
    for i in range(len(sample)):
        ax[0].vlines(x = i, ymin = sample[i, 2], ymax = sample[i, 1], color = 'black', linewidth = 1)  
        if sample[i, 3] > sample[i, 0]:
            ax[0].vlines(x = i, ymin = sample[i, 0], ymax = sample[i, 3], color = 'black', linewidth = 1.5)  
        if sample[i, 3] < sample[i, 0]:
            ax[0].vlines(x = i, ymin = sample[i, 3], ymax = sample[i, 0], color = 'black', linewidth = 1.5)  
        if sample[i, 3] == sample[i, 0]:
            ax[0].vlines(x = i, ymin = sample[i, 3], ymax = sample[i, 0], color = 'black', linewidth = 1.5)  
    ax[0].grid() 
    for i in range(len(sample)):
        if sample[i, second_panel] > 90:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'red', linewidth = 1.5)  
        if sample[i, second_panel] > 80 and sample[i, second_panel] < 90:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'darkred', linewidth = 1.5)  
        if sample[i, second_panel] > 70 and sample[i, second_panel] < 80:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'maroon', linewidth = 1.5)  
        if sample[i, second_panel] > 60 and sample[i, second_panel] < 70:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'firebrick', linewidth = 1.5) 
        if sample[i, second_panel] > 50 and sample[i, second_panel] < 60:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'grey', linewidth = 1.5) 
        if sample[i, second_panel] > 40 and sample[i, second_panel] < 50:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'grey', linewidth = 1.5) 
        if sample[i, second_panel] > 30 and sample[i, second_panel] < 40:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'lightgreen', linewidth = 1.5)
        if sample[i, second_panel] > 20 and sample[i, second_panel] < 30:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'limegreen', linewidth = 1.5) 
        if sample[i, second_panel] > 10 and sample[i, second_panel] < 20:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'seagreen', linewidth = 1.5)  
        if sample[i, second_panel] > 0 and sample[i, second_panel] < 10:
            ax[1].vlines(x = i, ymin = 0, ymax = 100, color = 'green', linewidth = 1.5)
    ax[1].grid()
indicator_plot(my_data, 4, window = 500)

Dark green and red areas indicate imminent bullish and bearish reactions, respectively. RSI around 50 is grey.

Summary

To conclude, my goal is to contribute to objective technical analysis, which promotes more transparent methods and strategies that must be back-tested before implementation.

Technical analysis will lose its reputation as subjective and unscientific.

When you find a trading strategy or technique, follow these steps:

• Put emotions aside and adopt a critical mindset.

• Test it in the past under conditions and simulations taken from real life.

• Try optimizing it and performing a forward test if you find any potential.

• Transaction costs and any slippage simulation should always be included in your tests.

• Risk management and position sizing should always be considered in your tests.

After checking the above, monitor the strategy because market dynamics may change and make it unprofitable.

New Stiglitz just dropped.

Here's the inflation story everyone believes (warning: it's false): America gave the poor too much money during the recession, and now the economy is awash with free money, which made them so rich they're refusing to work, meaning the economy isn't making anything. Prices are soaring due to increased cash and missing labor.

Lawrence Summers says there's only one answer. We must impoverish the poor: raise interest rates, cause a recession, and eliminate millions of jobs, until the poor are stripped of their underserved fortunes and return to work.

https://pluralistic.net/2021/11/20/quiet-part-out-loud/#profiteering

This is nonsense. Countries around the world suffered inflation during and after lockdowns, whether they gave out humanitarian money to keep people from starvation. America has slightly greater inflation than other OECD countries, but it's not due to big relief packages.

The Causes of and Responses to Today's Inflation, a Roosevelt Institute report by Nobel-winning economist Joseph Stiglitz and macroeconomist Regmi Ira, debunks this bogus inflation story and offers a more credible explanation for inflation.

https://rooseveltinstitute.org/wp-content/uploads/2022/12/RI CausesofandResponsestoTodaysInflation Report 202212.pdf

Sharp interest rate hikes exacerbate the slump and increase inflation, the authors argue. They compare monetary policy inflation cures to medieval bloodletting, where doctors repeated the same treatment until the patient recovered (for which they received credit) or died (which was more likely).

Let's discuss bloodletting. Inflation hawks warn of the wage price spiral, when inflation rises and powerful workers bargain for higher pay, driving up expenses, prices, and wages. This is the fairy-tale narrative of the 1970s, and it's true except that OPEC's embargo drove up oil prices, which produced inflation. Oh well.

Let's be generous to seventies-haunted inflation hawks and say we're worried about a wage-price spiral. Fantastic! No. Real wages are 2.3% lower than they were in Oct 2021 after peaking in June at 4.8%.

Why did America's powerful workers take a paycut rather than demand inflation-based pay? Weak unions, globalization, economic developments.

Workers don't expect inflation to rise, so they're not requesting inflationary hikes. Inflationary expectations have remained moderate, consistent with our data interpretation.

https://www.newyorkfed.org/microeconomics/sce#/

Neither are workers. Working people see surplus savings as wealth and spend it gradually over their lives, despite rising demand. People may have saved money by staying in during the lockdown, but they don't eat out every night to make up for it. Instead, they keep those savings as precautionary balances. This is why the economy is lagging.

People don't buy non-traded goods with pandemic savings (basically, imports). Imports don't multiply like domestic purchases. If you buy a loaf of bread from the corner baker for $1 and they spend it at the tavern across the street, that dollar generates $3 in economic activity. Spending a dollar on foreign goods leaves the country and any multiplier effect happens there, not in the US.

Only marginally higher wages. The ECI is up 1.6% from 2019. Almost all gains went to the 25% lowest-paid Americans. Contrary to the inflation worry about too much savings, these workers don't make enough to save, even post-pandemic.

Recreation and transit spending are at or below pre-pandemic levels. Higher food and hotel prices (which doesn’t mean we’re buying more food than we were in 2019, just that it costs more).

What causes inflation if not greedy workers, free money, and high demand? The most expensive domestic goods produce the biggest revenues for their manufacturers. They charge you more without paying their workers or suppliers more.

The largest price-gougers are funneling their earnings to rich people who store it offshore through stock buybacks and dividends. A $1 billion stock buyback doesn't buy $1 billion in bread.

Five factors influence US inflation today:

I. Price rises for energy and food

II. shifts in consumer tastes

III. supply interruptions (mainly autos);

IV. increased rents (due to telecommuting);

V. monopoly (AKA price-gouging).

None can be remedied by raising interest rates or laying off workers.

Russia's invasion of Ukraine, omicron, and China's Zero Covid policy all disrupted the flow of food, energy, and production inputs. The price went higher because we made less.

After Russia invaded Ukraine, oil prices spiked, and sanctions made it worse. But that was February. By October, oil prices had returned to pre-pandemic, 2015 levels attributable to global economic adjustments, including a shift to renewables. Every new renewable installation reduces oil consumption and affects oil prices.

High food prices have a simple solution. The US and EU have bribed farmers not to produce for 50 years. If the war continues, this program may end, and food prices may decline.

Demand changes. We want different things than in 2019, not more. During the lockdown, people substituted goods. Half of the US toilet-paper supply in 2019 was on commercial-sized rolls. This is created from different mills and stock than our toilet paper.

Lockdown pushed toilet paper demand to residential rolls, causing shortages (the TP hoarding story was just another pandemic urban legend). Because supermarket stores don't have accounts with commercial paper distributors, ordering from languishing stores was difficult. Kleenex and paper towel substitutions caused greater shortages.

All that drove increased costs in numerous product categories, and there were more cases. These increases are transient, caused by supply chain inefficiencies that are resolving.

Demand for frontline staff saw a one-time repricing of pay, which is being recouped as we speak.

Illnesses. Brittle, hollowed-out global supply chains aggravated this. The constant pursuit of cheap labor and minimal regulation by monopolies that dominate most sectors means things are manufactured in far-flung locations. Financialization means any surplus capital assets were sold off years ago, leaving firms with little production slack. After the epidemic, several of these systems took years to restart.

Automobiles are to blame. Financialization and monopolization consolidated microchip and auto production in Taiwan and China. When the lockdowns came, these worldwide corporations cancelled their chip orders, and when they placed fresh orders, they were at the back of the line.

That drove up car prices, which is why the US has slightly higher inflation than other wealthy countries: the economy is car-centric. Automobile prices account for 9% of the CPI. France: 3.6%

Rent shocks and telecommuting. After the epidemic, many professionals moved to exurbs, small towns, and the countryside to work from home. As commercial properties were vacated, it was impractical to adapt them for residential use due to planning restrictions. Addressing these restrictions will cut rent prices more than raising inflation rates, which halts housing construction.

Statistical mirages cause some rent inflation. The CPI estimates what homeowners would pay to rent their properties. When rents rise in your neighborhood, the CPI believes you're spending more on rent even if you have a 30-year fixed-rate mortgage.

Market dominance. Almost every area of the US economy is dominated by monopolies, whose CEOs disclose on investor calls that they use inflation scares to jack up prices and make record profits.

https://pluralistic.net/2022/02/02/its-the-economy-stupid/#overinflated

Long-term profit margins are rising. Markups averaged 26% from 1960-1980. 2021: 72%. Market concentration explains 81% of markup increases (e.g. monopolization). Profit margins reach a 70-year high in 2022. These elements interact. Monopolies thin out their sectors, making them brittle and sensitive to shocks.

If we're worried about a shrinking workforce, there are more humanitarian and sensible solutions than causing a recession and mass unemployment. Instead, we may boost US production capacity by easing workers' entry into the workforce.

https://pluralistic.net/2022/06/01/factories-to-condos-pipeline/#stuff-not-money

US female workforce participation ranks towards the bottom of developed countries. Many women can't afford to work due to America's lack of daycare, low earnings, and bad working conditions in female-dominated fields. If America doesn't have enough workers, childcare subsidies and minimum wages can help.

By contrast, driving the country into recession with interest-rate hikes will reduce employment, and the last recruited (women, minorities) are the first fired and the last to be rehired. Forcing America into recession won't enhance its capacity to create what its people want; it will degrade it permanently.

Nothing the Fed does can stop price hikes from international markets, lack of supply chain investment, COVID-19 disruptions, climate change, the Ukraine war, or market power. They can worsen it. When supply problems generate inflation, raising interest rates decreases investments that can remedy shortages.

Increasing interest rates won't cut rents since landlords pass on the expenses and high rates restrict investment in new dwellings where tenants could escape the costs.

Fixing the supply fixes supply-side inflation. Increase renewables investment (as the Inflation Reduction Act does). Monopolies can be busted (as the IRA does). Reshore key goods (as the CHIPS Act does). Better pay and child care attract employees.

Windfall taxes can claw back price-gouging corporations' monopoly earnings.

https://pluralistic.net/2022/03/15/sanctions-financing/#soak-the-rich

In 2008, we ruled out fiscal solutions (bailouts for debtors) and turned to monetary policy (bank bailouts). This preserved the economy but increased inequality and eroded public trust.

Monetary policy won't help. Even monetary policy enthusiasts recognize an 18-month lag between action and result. That suggests monetary tightening is unnecessary. Like the medieval bloodletter, central bankers whose interest rate hikes don't work swiftly may do more of the same, bringing the economy to its knees.

Interest rates must rise. Zero-percent interest fueled foolish speculation and financialization. Increasing rates will stop this. Increasing interest rates will destroy the economy and dampen inflation.

Then what? All recent evidence indicate to inflation decreasing on its own, as the authors argue. Supply side difficulties are finally being overcome, evidence shows. Energy and food prices are showing considerable mean reversion, which is disinflationary.

The authors don't recommend doing nothing. Best case scenario, they argue, is that the Fed won't keep raising interest rates until morale improves.

Ali's $1,054,053.74 YouTube Adsense haul.

YouTuber, entrepreneur, and former doctor Ali Abdaal. He began filming productivity and financial videos in 2017. Ali Abdaal has 3 million YouTube subscribers and has crossed $1 million in AdSense revenue. Crazy, no?

Ali will share the revenue of his top 5 youtube videos, things he's learned that you can apply to your side hustle, and how many views it takes to make a livelihood off youtube.

First, "The Long Game."

All good things take time to bear fruit. Compounding improves everything. Long-term work yields better returns. Ali made his first dollar after nine months and 85 videos.

Second, "One piece of content can transform your life, but you never know which one."

Had he abandoned YouTube at 84 videos without making any money, he wouldn't have filmed the 85th video that altered everything.

Third Lesson: Your Industry Choice Can Multiply.

The industry or niche you target as a business owner or side hustler can have a major impact on how much money you make.

Here are the top 5 videos.

1) 9.8m views: $191,258.16 for 9 passive income ideas

Ali made 2 points.

We should consider YouTube videos digital assets. They're investments, which make us money. His investments are yielding passive income.

Investing extra time and effort in your films can pay off.

2) How to Invest for Beginners — 5.2m Views: $87,200.08.

This video did poorly in the first several weeks after it was published; it was his tenth poorest performer. Don't worry about things you can't control. This applies to life, not just YouTube videos.

He stated we constantly have anxieties, fears, and concerns about things outside our control, but if we can find that line, life is easier and more pleasurable.

3) How to Build a Website in 2022— 866.3k views: $42,132.72.

The RPM was $48.86 per thousand views, making it his highest-earning video. Squarespace, Wix, and other website builders are trying to put ads on it and competing against one other, so ad rates go up.

Because it was beyond his niche, Ali almost didn't make the video. He made the video because he wanted to help at least one person.

4) How I take notes on my iPad in medical school — 5.9m views: $24,479.80

85th video. It's the video that affected Ali's YouTube channel and his life the most. The video's success wasn't certain.

5) How I Type Fast 156 Words Per Minute — 8.2M views: $25,143.17

Ali didn't know this video would perform well; he made it because he can type fast and has been practicing for 10 years. So he made a video with his best advice.

How many views to different wealth levels?

It depends on geography, niche, and other monetization sources. To keep things simple, he would solely utilize AdSense.

How many views to generate money?

To generate money on Youtube, you need 1,000 subscribers and 4,000 hours of view time. How much work do you need to make pocket money?

Ali's first 1,000 subscribers took 52 videos and 6 months. The typical channel with 1,000 subscribers contains 152 videos, according to Tubebuddy. It's time-consuming.

After monetizing, you'll need 15,000 views/month to make $5-$10/day.

How many views to go part-time?

Say you make $35,000/year at your day job. If you work 5 days/week, you make $7,000/year each day. If you want to drop down from 5 days to 4 days/week, you need to make an extra $7,000/year from YouTube, or $600/month.

What's the quit-your-job budget?

Silicon Valley Girl is in a highly successful niche targeting tech-focused folks in the west. When her channel had 500k views/month, she made roughly $3,000/month or $47,000/year, enough to quit your work.

Marina has another 1.5m subscriber channel in Russia, which has a lower rpm because fewer corporations advertise there than in the west. 2.3 million views/month is $4,000/month or $50,000/year, enough to quit your employment.

Marina is an intriguing example because she has three YouTube channels with the same skills, but one is 16x more profitable due to the niche she chose.

In Ali's case, he made 100+ videos when his channel was producing enough money to quit his job, roughly $4,000/month.

How many views make you rich?

Depending on how you define rich. Ali felt prosperous with over $100,000/year and 3–5m views/month.

Conclusion

YouTubers and artists don't treat their work like a company, which is a mistake. Businesses have been attempting to figure this out for decades, if not centuries.

We can learn from the business world how to monetize YouTube, Instagram, and Tiktok and make them into sustainable enterprises where we can hire people and delegate tasks.

Bonus

Watch Ali's video explaining all this:

This post is a summary. Read the full article here

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.