problem solving problems in programming

Great article regarding problem solving skill, informative and motivating both.

Codility Tests

Outstanding post, I believe people should larn a lot from this website, its really user pleasant.

Technical Screening Tools

I was very happy to discover this great site. I need to thank you for your time just for this fantastic read!

Sharifa Ismail Yusuf

I learnt from this article that one of the key skills a developer need to have is the \"problem solving skills\". Developers also need dedication, time, create time to practice so they can improve their problem solving skills constantly. I do ask for help from others and learn from past solutions and apply them to new problems. From what I have learnt so far, I will try my best to start focusing on building and practicing Flexibility, critical thinking, communication and team work. Solve a lot of problems on a lot of different platforms. Solve problems on context other than work. To start carring out the above, I will schedule time in a week or everyday to conciously practice problem solving skills and other related problem solving skills.Thanks alot for this wonderful article!

dewayne sewell

Ive learnt the skill of problem solving is like a muscle, where it is important to keep exercising it to stay strong. It is important to be aware of the soft skills necessary for effective problem solving also, such as communication, critical thinking, team working that can leverage your technical hard skills to find a solution faster/more effective. Two things I will aim to do is; 1. To solve problems on different platforms so I don’t get too comfortable on only one and stagnate. This not only challenges the brain to see things from a new perspective, but to start the habit of continuous learning and skill building. 2. Reach out to others for help / discuss problems and my solutions for feedback and advice and sharing ideas.

Pakize Bozkurt

Problem solving skills is a crucial thing to make easier or better your life. In fact as a human being we do it in every day life. I mean, we have to do it for living. There are many ways to how to do it. The best way is we should ask right questions. First of all, we should ask some questions, such as; \' Are we aware of the problem?, Are we clarify the problem? Do we go into problem rational? Do we have reasons? or Do we have evidences? Do we do check them out? etc. I am from Philosophy teacher background. I like solving problem whatever in my work or daily life. Secondly, we should have more perspectives . Although our brain is lazy, it is always in a starvation for knowledge.For this there are many enjoyable things to do it. I highly recommend to read book every day which kind of you like it and playing game or solving puzzle. I love solving Sudoku, puzzle and reading book or article. Finally, solving problem is our invatiable needed. Having flexibility, critical thinking, communication and teamwork are easy way to improve us to how we can do our work better and good life. Massive thank for this amazing article!

I read this amazing article. Normally, everyone knows that but we dont use most of time this informations. Which one is the best way to use? Really it does not matter, every one is like a gold opinion. We can use this ideas for the daily life. I have already used that learn from past solution and ask to someone who knows very well. This is so helpful for me. Sometimes google is the best option for ask to someone. Google can be the best teacher for us as well. Soft skills like a team work or solving problem and critical thinking can be important than typing code. We can learn typing code but we can not learn critical thinking and solving problems from google very well. Thank you for this article.

Ipsa iure sed rerum

Excepturi quo volupt

Thanks for this !

Fahil kiima

Thanks a lot for the ideas on problem solving,I really had a problem with that and now going to use what you\'ve informed us about to better my problem solving skills. Thanks.

Alan Codinho

Nice overview

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Lesson 27 of 34 By Hemant Deshpande

Table of Contents

Coding and Programming skills hold a significant and critical role in implementing and developing various technologies and software. They add more value to the future and development. These programming and coding skills are essential for every person to improve problem solving skills. So, we brought you this article to help you learn and know the importance of these skills in the future. 

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Topics covered in this problem solving in programming article are:

• What is Problem Solving in Programming? 
• Problem Solving skills in Programming
• How does it impact your career ?
• Steps involved in Problem Solving
• Steps to improve Problem Solving in programming

What is Problem Solving in Programming?

Computers are used to solve various problems in day-to-day life. Problem Solving is an essential skill that helps to solve problems in programming. There are specific steps to be carried out to solve problems in computer programming, and the success depends on how correctly and precisely we define a problem. This involves designing, identifying and implementing problems using certain steps to develop a computer.

When we know what exactly problem solving in programming is, let us learn how it impacts your career growth.

How Does It Impact Your Career?

Many companies look for candidates with excellent problem solving skills. These skills help people manage the work and make candidates put more effort into the work, which results in finding solutions for complex problems in unexpected situations. These skills also help to identify quick solutions when they arise and are identified. 

People with great problem solving skills also possess more thinking and analytical skills, which makes them much more successful and confident in their career and able to work in any kind of environment. 

The above section gives you an idea of how problem solving in programming impacts your career and growth. Now, let's understand what problem solving skills mean.

Problem Solving Skills in Programming

Solving a question that is related to computers is more complicated than finding the solutions for other questions. It requires excellent knowledge and much thinking power. Problem solving in programming skills is much needed for a person and holds a major advantage. For every question, there are specific steps to be followed to get a perfect solution. By using those steps, it is possible to find a solution quickly.

The above section is covered with an explanation of problem solving in programming skills. Now let's learn some steps involved in problem solving.

Steps Involved in Problem Solving

Before being ready to solve a problem, there are some steps and procedures to be followed to find the solution. Let's have a look at them in this problem solving in programming article.

Basically, they are divided into four categories:

• Analysing the problem
• Developing the algorithm
• Testing and debugging

Analysing the Problem

Every problem has a perfect solution; before we are ready to solve a problem, we must look over the question and understand it. When we know the question, it is easy to find the solution for it. If we are not ready with what we have to solve, then we end up with the question and cannot find the answer as expected. By analysing it, we can figure out the outputs and inputs to be carried out. Thus, when we analyse and are ready with the list, it is easy and helps us find the solution easily. 

Developing the Algorithm

It is required to decide a solution before writing a program. The procedure of representing the solution  in a natural language called an algorithm. We must design, develop and decide the final approach after a number of trials and errors, before actually writing the final code on an algorithm before we write the code. It captures and refines all the aspects of the desired solution.

Once we finalise the algorithm, we must convert the decided algorithm into a code or program using a dedicated programming language that is understandable by the computer to find a desired solution. In this stage, a wide variety of programming languages are used to convert the algorithm into code. 

Testing and Debugging

The designed and developed program undergoes several rigorous tests based on various real-time parameters and the program undergoes various levels of simulations. It must meet the user's requirements, which have to respond with the required time. It should generate all expected outputs to all the possible inputs. The program should also undergo bug fixing and all possible exception handling. If it fails to show the possible results, it should be checked for logical errors.

Industries follow some testing methods like system testing, component testing and acceptance testing while developing complex applications. The errors identified while testing are debugged or rectified and tested again until all errors are removed from the program.

The steps mentioned above are involved in problem solving in programming. Now let's see some more detailed information about the steps to improve problem solving in programming.

Steps to Improve Problem Solving in Programming

Right mindset.

The way to approach problems is the key to improving the skills. To find a solution, a positive mindset helps to solve problems quickly. If you think something is impossible, then it is hard to achieve. When you feel free and focus with a positive attitude, even complex problems will have a perfect solution.

Making Right Decisions

When we need to solve a problem, we must be clear with the solution. The perfect solution helps to get success in a shorter period. Making the right decisions in the right situation helps to find the perfect solution quickly and efficiently. These skills also help to get more command over the subject.

Keeping Ideas on Track

Ideas always help much in improving the skills; they also help to gain more knowledge and more command over things. In problem solving situations, these ideas help much and help to develop more skills. Give opportunities for the mind and keep on noting the ideas.

Learning from Feedbacks

A crucial part of learning is from the feedback. Mistakes help you to gain more knowledge and have much growth. When you have a solution for a problem, go for the feedback from the experienced or the professionals. It helps you get success within a shorter period and enables you to find other solutions easily.

Asking Questions

Questions are an incredible part of life. While searching for solutions, there are a lot of questions that arise in our minds. Once you know the question correctly, then you are able to find answers quickly. In coding or programming, we must have a clear idea about the problem. Then, you can find the perfect solution for it. Raising questions can help to understand the problem.

These are a few reasons and tips to improve problem solving in programming skills. Now let's see some major benefits in this article.

• Problem solving in programming skills helps to gain more knowledge over coding and programming, which is a major benefit.
• These problem solving skills also help to develop more skills in a person and build a promising career.
• These skills also help to find the solutions for critical and complex problems in a perfect way.
• Learning and developing problem solving in programming helps in building a good foundation.
• Most of the companies are looking for people with good problem solving skills, and these play an important role when it comes to job opportunities 

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Problem solving in programming skills is important in this modern world; these skills build a great career and hold a great advantage. This article on problem solving in programming provides you with an idea of how it plays a massive role in the present world. In this problem solving in programming article, the skills and the ways to improve more command on problem solving in programming are mentioned and explained in a proper way.

If you are looking to advance in your career. Simplilearn provides training and certification courses on various programming languages - Python , Java , Javascript , and many more. Check out our Post Graduate Program in Full Stack Web Development course that will help you excel in your career.

If you have any questions for us on the problem solving in programming article. Do let us know in the comments section below; we have our experts answer it right away.

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About the author.

Hemant Deshpande, PMP has more than 17 years of experience working for various global MNC's. He has more than 10 years of experience in managing large transformation programs for Fortune 500 clients across verticals such as Banking, Finance, Insurance, Healthcare, Telecom and others. During his career he has worked across the geographies - North America, Europe, Middle East, and Asia Pacific. Hemant is an internationally Certified Executive Coach (CCA/ICF Approved) working with corporate leaders. He also provides Management Consulting and Training services. He is passionate about writing and regularly blogs and writes content for top websites. His motto in life - Making a positive difference.

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• PMP, PMI, PMBOK, CAPM, PgMP, PfMP, ACP, PBA, RMP, SP, and OPM3 are registered marks of the Project Management Institute, Inc.

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10 Steps to Solving a Programming Problem

Tips for new developers staring at a blank screen, unsure of where to start.

Valinda Chan

Some of the feedback I hear from new developers working on a programming problem revolves around uncertainty of where to start. You understand the problem, the logic, basics of the syntax, etc. If you see someone else’s code or have someone to guide you, you can follow along. But maybe you feel uncertain about doing it yourself and have trouble turning your thoughts into code at first even though you understand the syntax or logic. Here’s my process and some tips to tackling a sample problem that hopefully some of you may find helpful in your journey.

1. Read the problem at least three times (or however many makes you feel comfortable)

You can’t solve a problem you don’t understand. There is a difference between the problem and the problem you think you are solving. It’s easy to start reading the first few lines in a problem and assume the rest of it because it’s similar to something you’ve seen in the past. If you are making even a popular game like Hangman, be sure to read through any rules even if you’ve played it before. I once was asked to make a game like Hangman that I realized was “Evil Hangman” only after I read through the instructions (it was a trick!).

Sometimes I’ll even try explaining the problem to a friend and see if her understanding of my explanation matches the problem I am tasked with. You don’t want to find out halfway through that you misunderstood the problem. Taking extra time in the beginning is worth it. The better you understand the problem, the easier it will be to solve it.

Let’s pretend we are creating a simple function selectEvenNumbers that will take in an array of numbers and return an array evenNumbers of only even numbers. If there are no even numbers, return the empty array evenNumbers .

Here are some questions that run through my mind:

• How can a computer tell what is an even number? Divide that number by 2 and see if its remainder is 0.
• What am I passing into this function? An array
• What will that array contain? One or more numbers
• What are the data types of the elements in the array? Numbers
• What is the goal of this function? What am I returning at the end of this function? The goal is to take all the even numbers and return them in an array. If there are no even numbers, return an empty array.

2. Work through the problem manually with at least three sets of sample data

Take out a piece of paper and work through the problem manually. Think of at least three sets of sample data you can use. Consider corner and edge cases as well.

Corner case : a problem or situation that occurs outside of normal operating parameters, specifically when multiple environmental variables or conditions are simultaneously at extreme levels, even though each parameter is within the specified range for that parameter. Edge case : problem or situation that occurs only at an extreme (maximum or minimum) operating parameter

For example, below are some sets of sample data to use:

When you are first starting out, it is easy to gloss over the steps. Because your brain may already be familiar with even numbers, you may just look at a sample set of data and pull out numbers like 2 , 4 , 6 and so forth in the array without fully being aware of each and every step your brain is taking to solve it. If this is challenging, try using large sets of data as it will override your brain’s ability to naturally solve the problem just by looking at it. That helps you work through the real algorithm.

Let’s go through the first array [1]

• Look at the only element in the array [1]
• Decide if it is even. It is not
• Notice that there are no more elements in this array
• Determine there are no even numbers in this provided array
• Return an empty array

Let’s go through the array [1, 2]

• Look at the first element in array [1, 2]
• Look at the next element in the array
• Decide if it is even. It is even
• Make an array evenNumbers and add 2 to this array
• Return the array evenNumbers which is [2]

I go through this a few more times. Notice how the steps I wrote down for [1] varies slightly from [1, 2] . That is why I try to go through a couple of different sets. I have some sets with just one element, some with floats instead of just integers, some with multiple digits in an element, and some with negatives just to be safe.

3. Simplify and optimize your steps

Look for patterns and see if there’s anything you can generalize. See if you can reduce any steps or if you are repeating any steps.

• Create a function selectEvenNumbers
• Create a new empty array evenNumbers where I store even numbers, if any
• Go through each element in the array [1, 2]
• Find the first element
• Decide if it is even by seeing if it is divisible by 2. If it is even, I add that to evenNumbers
• Find the next element
• Repeat step #4
• Repeat step #5 and #4 until there are no more elements in this array
• Return the array evenNumbers , regardless of whether it has anything in it

This approach may remind you of Mathematical Induction in that you:

• Show it is true for n = 1 , n = 2 , ...
• Suppose it is true for n = k
• Prove it is true for n = k + 1

4. Write pseudocode

Even after you’ve worked out general steps, writing out pseudocode that you can translate into code will help with defining the structure of your code and make coding a lot easier. Write pseudocode line by line. You can do this either on paper or as comments in your code editor. If you’re starting out and find blank screens to be daunting or distracting, I recommend doing it on paper.

Pseudocode generally does not actually have specific rules in particular but sometimes, I might end up including some syntax from a language just because I am familiar enough with an aspect of the programming language. Don’t get caught up with the syntax. Focus on the logic and steps.

For our problem, there are many different ways to do this. For example, you can use filter but for the sake of keeping this example as easy to follow along as possible, we will use a basic for loop for now (but we will use filter later when we refactor our code).

Here is an example of pseudocode that has more words:

Here is an example of pseudocode that has fewer words:

Either way is fine as long as you are writing it out line-by-line and understand the logic on each line.

Refer back to the problem to make sure you are on track.

5. Translate pseudocode into code and debug

When you have your pseudocode ready, translate each line into real code in the language you are working on. We will use JavaScript for this example.

If you wrote it out on paper, type this up as comments in your code editor. Then replace each line in your pseudocode.

Then I call the function and give it some sample sets of data we used earlier. I use them to see if my code returns the results I want. You can also write tests to check if the actual output is equal to the expected output.

I generally use console.log() after each variable or line or so. This helps me check if the values and code are behaving as expected before I move on . By doing this, I catch any issues before I get too far. Below is an example of what values I would check when I am first starting out. I do this throughout my code as I type it out.

After working though each line of my pseudocode, below is what we end up with. // is what the line was in pseudocode. Text that is bolded is the actual code in JavaScript.

I get rid of the pseudocode to avoid confusion.

Sometimes new developers will get hung up with the syntax that it becomes difficult to move forward. Remember that syntax will come more naturally over time and there is no shame in referencing material for the correct syntax later on when coding.

6. Simplify and optimize your code

You’ve probably noticed by now that simplifying and optimizing are recurring themes.

“Simplicity is prerequisite for reliability.” — Edsger W. Dijkstra, Dutch computer scientist and early pioneer in many research areas of computing science

In this example, one way of optimizing it would be to filter out items from an array by returning a new array using filter . This way, we don’t have to define another variable evenNumbers because filter will return a new array with copies of elements that match the filter. This will not change the original array. We also don’t need to use a for loop with this approach. filter will go through each item, return either true , to have that element in the array, or false to skip it.

Simplifying and optimizing your code may require you to iterate a few times, identifying ways to further simplify and optimize code.

Here are some questions to keep in mind:

• What are your goals for simplifying and optimizing? The goals will depend on your team’s style or your personal preference. Are you trying to condense the code as much as possible? Is the goal to make it the code more readable? If that’s the case, you may prefer taking that extra line to define the variable or compute something rather than trying to define and compute all in one line.
• How else can you make the code more readable?
• Are there any more extra steps you can take out?
• Are there any variables or functions you ended up not even needing or using?
• Are you repeating some steps a lot? See if you can define in another function.
• Are there better ways to handle edge cases?

“Programs must be written for people to read, and only incidentally for machines to execute.” — Gerald Jay Sussman and Hal Abelson, Authors of “Structure and Interpretation of Computer Programs”

This step really should be throughout the process. Debugging throughout will help you catch any syntax errors or gaps in logic sooner rather than later. Take advantage of your Integrated Development Environment (IDE) and debugger. When I encounter bugs, I trace the code line-by-line to see if there was anything that did not go as expected. Here are some techniques I use:

• Check the console to see what the error message says. Sometimes it’ll point out a line number I need to check. This gives me a rough idea of where to start, although the issue sometimes may not be at this line at all.
• Comment out chunks or lines of code and output what I have so far to quickly see if the code is behaving how I expected. I can always uncomment the code as needed.
• Use other sample data if there are scenarios I did not think of and see if the code will still work.
• Save different versions of my file if I am trying out a completely different approach. I don’t want to lose any of my work if I end up wanting to revert back to it!

“The most effective debugging tool is still careful thought, coupled with judiciously placed print statements.” — Brian W. Kernighan, Computer Science Professor at Princeton University

8. Write useful comments

You may not always remember what every single line meant a month later. And someone else working on your code may not know either. That’s why it’s important to write useful comments to avoid problems and save time later on if you need to come back to it.

Stay away from comments such as:

// This is an array. Iterate through it.

// This is a variable

I try to write brief, high-level comments that help me understand what’s going on if it is not obvious. This comes in handy when I am working on more complex problems. It helps understand what a particular function is doing and why. Through the use of clear variable names, function names, and comments, you (and others) should be able to understand:

• What is this code for?
• What is it doing?

9. Get feedback through code reviews

Get feedback from your teammates, professors, and other developers. Check out Stack Overflow . See how others tackled the problem and learn from them. There are sometimes several ways to approach a problem. Find out what they are and you’ll get better and quicker at coming up with them yourself.

“No matter how slow you are writing clean code, you will always be slower if you make a mess.” — Uncle Bob Martin, Software Engineer and Co-author of the Agile Manifesto

10. Practice, practice, practice

Even experienced developers are always practicing and learning. If you get helpful feedback, implement it. Redo a problem or do similar problems. Keep pushing yourself. With each problem you solve, the better a developer you become. Celebrate each success and be sure to remember how far you’ve come. Remember that programming, like with anything, comes easier and more naturally with time.

“Take pride in how far you’ve come. Have faith in how far you can go. But don’t forget to enjoy the journey.” — Michael Josephson, Founder of Joseph and Edna Josephson Institute of Ethics

Thanks Gavin Stark

Written by Valinda Chan

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Problem Solving

Foundations course, introduction.

Before we start digging into some pretty nifty JavaScript, we need to begin talking about problem solving : the most important skill a developer needs.

Problem solving is the core thing software developers do. The programming languages and tools they use are secondary to this fundamental skill.

From his book, “Think Like a Programmer” , V. Anton Spraul defines problem solving in programming as:

Problem solving is writing an original program that performs a particular set of tasks and meets all stated constraints.

The set of tasks can range from solving small coding exercises all the way up to building a social network site like Facebook or a search engine like Google. Each problem has its own set of constraints, for example, high performance and scalability may not matter too much in a coding exercise but it will be vital in apps like Google that need to service billions of search queries each day.

New programmers often find problem solving the hardest skill to build. It’s not uncommon for budding programmers to breeze through learning syntax and programming concepts, yet when trying to code something on their own, they find themselves staring blankly at their text editor not knowing where to start.

The best way to improve your problem solving ability is by building experience by making lots and lots of programs. The more practice you have the better you’ll be prepared to solve real world problems.

In this lesson we will walk through a few techniques that can be used to help with the problem solving process.

Lesson overview

This section contains a general overview of topics that you will learn in this lesson.

• Explain the three steps in the problem solving process.
• Explain what pseudocode is and be able to use it to solve problems.
• Be able to break a problem down into subproblems.

Understand the problem

The first step to solving a problem is understanding exactly what the problem is. If you don’t understand the problem, you won’t know when you’ve successfully solved it and may waste a lot of time on a wrong solution .

To gain clarity and understanding of the problem, write it down on paper, reword it in plain English until it makes sense to you, and draw diagrams if that helps. When you can explain the problem to someone else in plain English, you understand it.

Now that you know what you’re aiming to solve, don’t jump into coding just yet. It’s time to plan out how you’re going to solve it first. Some of the questions you should answer at this stage of the process:

• Does your program have a user interface? What will it look like? What functionality will the interface have? Sketch this out on paper.
• What inputs will your program have? Will the user enter data or will you get input from somewhere else?
• What’s the desired output?
• Given your inputs, what are the steps necessary to return the desired output?

The last question is where you will write out an algorithm to solve the problem. You can think of an algorithm as a recipe for solving a particular problem. It defines the steps that need to be taken by the computer to solve a problem in pseudocode.

Pseudocode is writing out the logic for your program in natural language instead of code. It helps you slow down and think through the steps your program will have to go through to solve the problem.

Here’s an example of what the pseudocode for a program that prints all numbers up to an inputted number might look like:

This is a basic program to demonstrate how pseudocode looks. There will be more examples of pseudocode included in the assignments.

Divide and conquer

From your planning, you should have identified some subproblems of the big problem you’re solving. Each of the steps in the algorithm we wrote out in the last section are subproblems. Pick the smallest or simplest one and start there with coding.

It’s important to remember that you might not know all the steps that you might need up front, so your algorithm may be incomplete -— this is fine. Getting started with and solving one of the subproblems you have identified in the planning stage often reveals the next subproblem you can work on. Or, if you already know the next subproblem, it’s often simpler with the first subproblem solved.

Many beginners try to solve the big problem in one go. Don’t do this . If the problem is sufficiently complex, you’ll get yourself tied in knots and make life a lot harder for yourself. Decomposing problems into smaller and easier to solve subproblems is a much better approach. Decomposition is the main way to deal with complexity, making problems easier and more approachable to solve and understand.

In short, break the big problem down and solve each of the smaller problems until you’ve solved the big problem.

Solving Fizz Buzz

To demonstrate this workflow in action, let’s solve a common programming exercise: Fizz Buzz, explained in this wiki article .

Understanding the problem

Write a program that takes a user’s input and prints the numbers from one to the number the user entered. However, for multiples of three print Fizz instead of the number and for the multiples of five print Buzz . For numbers which are multiples of both three and five print FizzBuzz .

This is the big picture problem we will be solving. But we can always make it clearer by rewording it.

Write a program that allows the user to enter a number, print each number between one and the number the user entered, but for numbers that divide by 3 without a remainder print Fizz instead. For numbers that divide by 5 without a remainder print Buzz and finally for numbers that divide by both 3 and 5 without a remainder print FizzBuzz .

Does your program have an interface? What will it look like? Our FizzBuzz solution will be a browser console program, so we don’t need an interface. The only user interaction will be allowing users to enter a number.

What inputs will your program have? Will the user enter data or will you get input from somewhere else? The user will enter a number from a prompt (popup box).

What’s the desired output? The desired output is a list of numbers from 1 to the number the user entered. But each number that is divisible by 3 will output Fizz , each number that is divisible by 5 will output Buzz and each number that is divisible by both 3 and 5 will output FizzBuzz .

Writing the pseudocode

What are the steps necessary to return the desired output? Here is an algorithm in pseudocode for this problem:

Dividing and conquering

As we can see from the algorithm we developed, the first subproblem we can solve is getting input from the user. So let’s start there and verify it works by printing the entered number.

With JavaScript, we’ll use the “prompt” method.

The above code should create a little popup box that asks the user for a number. The input we get back will be stored in our variable answer .

We wrapped the prompt call in a parseInt function so that a number is returned from the user’s input.

With that done, let’s move on to the next subproblem: “Loop from 1 to the entered number”. There are many ways to do this in JavaScript. One of the common ways - that you actually see in many other languages like Java, C++, and Ruby - is with the for loop :

If you haven’t seen this before and it looks strange, it’s actually straightforward. We declare a variable i and assign it 1: the initial value of the variable i in our loop. The second clause, i <= answer is our condition. We want to loop until i is greater than answer . The third clause, i++ , tells our loop to increment i by 1 every iteration. As a result, if the user inputs 10, this loop would print numbers 1 - 10 to the console.

Most of the time, programmers find themselves looping from 0. Due to the needs of our program, we’re starting from 1

With that working, let’s move on to the next problem: If the current number is divisible by 3, then print Fizz .

We are using the modulus operator ( % ) here to divide the current number by three. If you recall from a previous lesson, the modulus operator returns the remainder of a division. So if a remainder of 0 is returned from the division, it means the current number is divisible by 3.

After this change the program will now output this when you run it and the user inputs 10:

The program is starting to take shape. The final few subproblems should be easy to solve as the basic structure is in place and they are just different variations of the condition we’ve already got in place. Let’s tackle the next one: If the current number is divisible by 5 then print Buzz .

When you run the program now, you should see this output if the user inputs 10:

We have one more subproblem to solve to complete the program: If the current number is divisible by 3 and 5 then print FizzBuzz .

We’ve had to move the conditionals around a little to get it to work. The first condition now checks if i is divisible by 3 and 5 instead of checking if i is just divisible by 3. We’ve had to do this because if we kept it the way it was, it would run the first condition if (i % 3 === 0) , so that if i was divisible by 3, it would print Fizz and then move on to the next number in the iteration, even if i was divisible by 5 as well.

With the condition if (i % 3 === 0 && i % 5 === 0) coming first, we check that i is divisible by both 3 and 5 before moving on to check if it is divisible by 3 or 5 individually in the else if conditions.

The program is now complete! If you run it now you should get this output when the user inputs 20:

• Read How to Think Like a Programmer - Lessons in Problem Solving by Richard Reis.
• Watch How to Begin Thinking Like a Programmer by Coding Tech. It’s an hour long but packed full of information and definitely worth your time watching.
• Read this Pseudocode: What It Is and How to Write It article from Built In.

Knowledge check

This section contains questions for you to check your understanding of this lesson on your own. If you’re having trouble answering a question, click it and review the material it links to.

• What are the three stages in the problem solving process?
• Why is it important to clearly understand the problem first?
• What can you do to help get a clearer understanding of the problem?
• What are some of the things you should do in the planning stage of the problem solving process?
• What is an algorithm?
• What is pseudocode?
• What are the advantages of breaking a problem down and solving the smaller problems?

Additional resources

This section contains helpful links to other content. It isn’t required, so consider it supplemental.

• Read the first chapter in Think Like a Programmer: An Introduction to Creative Problem Solving ( not free ). This book’s examples are in C++, but you will understand everything since the main idea of the book is to teach programmers to better solve problems. It’s an amazing book and worth every penny. It will make you a better programmer.
• Watch this video on repetitive programming techniques .
• Watch Jonathan Blow on solving hard problems where he gives sage advice on how to approach problem solving in software projects.

Support us!

The odin project is funded by the community. join us in empowering learners around the globe by supporting the odin project.

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Challenge Walkthrough

Review the problem statement, choose a language, enter your code, test your code, submit to see results.

• Check your score

75 Basic Programming Problems and Tutorials for Practice

By Varun Saharawat | November 15, 2023

Solving Basic Programming Problems is the key to achieve success in coding challenges. Students must practice these basic programming problems!

Basic Programming Problems: Engaging in code challenges offers many benefits, serving as a dynamic tool to enhance problem-solving proficiency, deepen your comprehension of the programming language you work with, and acquaint yourself with diverse algorithms. If you aspire to elevate your programming skills, immersing yourself in coding is the most effective avenue.

The beauty of basic programming problems lies in their convenience—they provide a platform to hone your abilities through bite-sized problems, often eliminating the need to construct entire applications. This characteristic allows you to conquer these challenges swiftly, fostering a sense of accomplishment.

Moreover, code challenges are integral components of many coding interviews.

While your resume may showcase your skills and ability to articulate programming concepts, employers want to validate your practical coding capabilities. Tackling coding challenges during interviews becomes a testament to your proficiency and showcases your competence for the role.

Therefore, incorporating coding challenges into your routine sharpens your skills and is an invaluable preparation strategy for job interviews. To kickstart your coding journey, we have curated a collection of popular basic programming problems to pave the way for your continued growth.

Table of Contents

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• DSA Java Course

Basic Programming Problems Overview

Basic programming problems provide an essential foundation for individuals learning to code, offering a practical and hands-on approach to mastering fundamental concepts in programming.

These problems are designed to introduce beginners to the core coding principles, gradually building their problem-solving skills and comprehension of programming logic.

Whether you are a novice looking to embark on your coding journey or an experienced programmer aiming to reinforce your foundational knowledge, engaging with basic programming problems is a valuable practice.

These problems typically cover essential topics such as data types, loops, conditionals, functions, and basic algorithms, providing a well-rounded introduction to the key building blocks of programming.

The significance of basic programming problems extends beyond mere skill development; it serves as a stepping stone for individuals aspiring to pursue more advanced coding challenges and projects.

By grappling with these foundational problems, learners can cultivate a solid understanding of programming fundamentals, laying the groundwork for future exploration and mastery of more complex coding concepts. Basic programming problems are the cornerstone of a programmer’s educational journey, fostering a strong and resilient coding skill set.

Basic Programming Problems for Beginners

Starting your career in the programming field is  exciting and challenging. For beginners, mastering the basics is crucial, and what better way to do so than by solving basic programming problems ?

Basic Programming Problems Java

Here are some of the basic programming problems JAVA :

1) Hello World:

public class HelloWorld {

    public static void main(String[] args) {

        System.out.println(“Hello, World!”);

2) The sum of Two Numbers:

Add two numbers and print the result.

public class Sum {

        int num1 = 5, num2 = 10, sum;

        sum = num1 + num2;

        System.out.println(“Sum: ” + sum);

3) Factorial of a Number:

Calculate the factorial of a number.

public class Factorial {

        int num = 5;

        long factorial = 1;

        for (int i = 1; i <= num; ++i) {

            factorial *= i;

        System.out.println(“Factorial: ” + factorial);

4) Check Even or Odd:

Determine if a number is even or odd.

public class EvenOdd {

        int num = 8;

        if (num % 2 == 0) {

            System.out.println(num + ” is even.”);

        } else {

            System.out.println(num + ” is odd.”);

5) Reverse a String:

Reverse the characters in a given string.

public class ReverseString {

        String str = “Hello”;

        StringBuilder reversed = new StringBuilder(str).reverse();

        System.out.println(“Reversed String: ” + reversed);

Here are some theory-based basic programming problems Java:

1) Differences Between C++ and Java

• C++: Not platform-independent, follows “write once, compile anywhere.”
• Java: Platform-independent byte code allows programs to run on any machine.

Languages Compatibility:

• C++: Compatible with most high-level languages.
• Java: Incompatible with most languages, comparable to C and C++.

Interaction with the Library:

• C++: Direct access to native system libraries, suitable for system-level programming.
• Java: Requires Java Native Interface or library access, not direct call support.

Characteristics:

• C++: Combines features of procedural and object-oriented languages.
• Java: Known for automatic garbage collection, lacks support for destructors.

Semantics of the Type:

• C++: Consistent semantics for primitive and object types.
• Java: Inconsistent semantics between primitive and object types and classes.

Compiler and Interpreter:

• Java: Compiled and interpreted language, source code compiles into platform-independent bytecode.
• C++: Purely compiled language, source program compiles into object code, further executed.

2) Features of the Java Programming Language:

• Easy: Java is considered easy to learn, with fundamental Object-Oriented Programming (OOP) concepts.
• Secured Feature: Java provides a secured feature, ensuring the development of virus-free and tamper-free systems.
• OOP: Java follows Object-Oriented Programming, treating everything as an object.
• Independent Platform: Java compiles into platform-independent bytecode, interpreted by the Virtual Machine.

3) ClassLoader in Java:

• A ClassLoader in Java is a subsystem of the Java Virtual Machine responsible for loading class files during program execution.
• It is the first to load the executable file and includes Bootstrap, Extension, and Application classloaders.

4) Differences Between Heap and Stack Memory in Java:

• Stack Memory: Allocated to each individual program. Fixed memory space.
• Heap Memory: Not assigned to Java code initially but available during runtime. Used as needed by the Java code.

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Basic Programming Problems in C

The table below shows the basic programming problems in C :

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Basic Programming Problems in Python

In addition to introducing you to Python’s syntax and structure, tackling basic programming problems in Python helps you improve your problem-solving skills. With tasks ranging from basic logic puzzles to intricate algorithmic difficulties, these issues offer an interactive method of learning Python and put you on the route to becoming a skilled programmer.

Basic Programming Problems in Javascript

Whether you aim to enhance your web development skills or explore the vast world of JavaScript applications, these problems cater to beginners, guiding them through the foundational aspects of programming in this versatile language. Below table showcases the basic programming problems in Javascript :

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Basic Programming Problems and Solutions

Here are 10 basic programming problems along with their solutions:

• Hello World:

Problem: Write a program that prints “Hello, World!” to the console.

Solution (Python):

print(“Hello, World!”)

• Sum of Two Numbers:

Problem: Write a program that inputs two numbers and prints their sum.

Solution (Java):

import java.util.Scanner;

public class SumOfTwoNumbers {

        Scanner scanner = new Scanner(System.in);

        System.out.print(“Enter first number: “);

        int num1 = scanner.nextInt();

        System.out.print(“Enter second number: “);

        int num2 = scanner.nextInt();

        int sum = num1 + num2;

• Factorial of a Number:

Problem: Write a program to calculate the factorial of a given number.

Solution (C++):

#include <iostream>

using namespace std;

int factorial(int n) {

    if (n == 0 || n == 1)

        return 1;

        return n * factorial(n – 1);

int main() {

    int num;

    cout << “Enter a number: “;

    cin >> num;

    cout << “Factorial: ” << factorial(num) << endl;

    return 0;

• Check Even or Odd:

Problem: Write a program that checks if a given number is even or odd.

Solution (JavaScript):

let number = 7;

if (number % 2 === 0) {

    console.log(number + ” is even”);

    console.log(number + ” is odd”);

• Reverse a String:

Problem: Write a program to reverse a given string.

original_string = “Hello, World!”

reversed_string = original_string[::-1]

print(“Reversed String:”, reversed_string)

• Fibonacci Series:

Problem: Generate the Fibonacci series up to a specific limit.

public class FibonacciSeries {

        int limit = 10;

        int firstTerm = 0, secondTerm = 1;

        System.out.println(“Fibonacci Series up to ” + limit + ” terms:”);

        for (int i = 1; i <= limit; ++i) {

            System.out.print(firstTerm + “, “);

            int nextTerm = firstTerm + secondTerm;

            firstTerm = secondTerm;

            secondTerm = nextTerm;

• Check Prime Number:

Problem: Write a program to check if a given number is prime.

def is_prime(number):

    if number > 1:

        for i in range(2, int(number / 2) + 1):

            if (number % i) == 0:

                return False

        else:

            return True

        return False

if is_prime(num):

    print(num, “is a prime number.”)

    print(num, “is not a prime number.”)

• Find Maximum Element:

Problem: Write a program to find the maximum element in an array.

int findMax(int arr[], int size) {

    int max = arr[0];

    for (int i = 1; i < size; ++i) {

        if (arr[i] > max) {

            max = arr[i];

    return max;

    int numbers[] = {5, 8, 2, 10, 3};

    int size = sizeof(numbers) / sizeof(numbers[0]);

    cout << “Maximum Element: ” << findMax(numbers, size) << endl;

• Palindrome Check:

Problem: Write a program to check if a given string is a palindrome.

public class PalindromeCheck {

        String str = “level”;

        String reversedStr = new StringBuilder(str).reverse().toString();

        if (str.equals(reversedStr)) {

            System.out.println(str + ” is a palindrome.”);

            System.out.println(str + ” is not a palindrome.”);

• Count Vowels and Consonants:

Problem: Write a program to count the number of vowels and consonants in a given string.

text = “Hello, World!”

vowels = “AEIOU

Benefits of Solving Basic Programming Problems

Solving basic programming problems offers numerous benefits for individuals looking to enhance their programming skills. Here are some key advantages:

Skill Development:

• Coding Proficiency: Regular problem-solving helps improve your coding skills and fluency in programming languages.
• Algorithmic Thinking: It fosters the development of algorithmic thinking, enabling you to devise efficient solutions to various problems.

Logical Thinking:

• Problem Decomposition: Breaking down problems into smaller components and solving them enhances logical thinking and problem-solving abilities.
• Pattern Recognition: Regular problem-solving helps in recognizing patterns and similarities between different problems, leading to more efficient solutions.

Learning New Concepts:

• Exposure to Diverse Topics: Programming problems often cover a wide range of concepts, exposing you to different areas of computer science and software development.
• New Algorithms and Data Structures: Exploring various problems introduces you to new algorithms and data structures, expanding your knowledge base.

Preparation for Interviews:

• Technical Interviews: Many technical interviews for programming roles involve solving algorithmic and coding problems. Regular practice prepares you for such interviews and boosts your confidence.
• Coding Challenges: Familiarity with common coding challenges often encountered in interviews is an asset.

Building a Portfolio:

• Showcasing Skills: Solving problems allows you to build a portfolio of solutions that you can showcase to potential employers or on coding platforms.
• GitHub Contributions: Uploading your solutions to platforms like GitHub demonstrates your coding proficiency and problem-solving ability.

Enhanced Efficiency:

• Code Optimization: Regular practice encourages optimization, leading to more efficient and cleaner code.
• Time Complexity Awareness: Problem-solving helps in understanding and considering time complexity, contributing to the creation of scalable solutions.

Community Engagement:

• Online Communities: Engaging in online coding communities allows you to discuss problems, learn from others, and gain insights into alternative solutions.
• Peer Learning: Collaborating with peers on coding challenges can provide different perspectives and foster a collaborative learning environment.

Career Advancement:

• Competitive Edge: Building strong problem-solving skills sets you apart in a competitive job market, enhancing your employability.
• Adaptability: A wide range of problem-solving experiences makes you more adaptable to different tasks and projects.

Personal Satisfaction:

• Sense of Achievement: Successfully solving programming problems brings a sense of accomplishment, boosting confidence and motivation.
• Continuous Learning: It fosters a mindset of continuous learning, crucial in a rapidly evolving field like programming.

In summary, regular practice of solving basic programming problems contributes significantly to skill development, logical thinking, and overall proficiency in the field of programming.

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What is Programming? A Handbook for Beginners

Welcome to the amazing world of programming. This is one of the most useful and powerful skills that you can learn and use to make your visions come true.

In this handbook, we will dive into why programming is important, its applications, its basic concepts, and the skills you need to become a successful programmer.

You will learn:

• What programming is and why it is important .
• What a programming language is and why it is important .
• How programming is related to binary numbers .
• Real-world applications of programming .
• Skills you need to succeed as a programmer .
• Tips for learning how to code .
• Basic programming concepts .
• Types of programming languages .
• How to contribute to open source projects .
• And more...

Are you ready? Let's begin! ✨  

🔹 What is Programming?

Did you know that computer programming is already a fundamental part of your everyday lives? Let's see why. I'm sure that you will be greatly surprised.

Every time you turn on your smartphone, laptop, tablet, smart TV, or any other electronic device, you are running code that was planned, developed, and written by developers. This code creates the final and interactive result that you can see on your screen.

That is exactly what programming is all about. It is the process of writing code to solve a particular problem or to implement a particular task.

Programming is what allows your computer to run the programs you use every day and your smartphone to run the apps that you love. It is an essential part of our world as we know it.

Whenever you check your calendar, attend virtual conferences, browse the web, or edit a document, you are using code that has been written by developers.

"And what is code?" you may ask.

Code is a sequence of instructions that a programmer writes to tell a device (like a computer) what to do.

The device cannot know by itself how to handle a particular situation or how to perform a task. So developers are in charge of analyzing the situation and writing explicit instructions to implement what is needed.

To do this, they follow a particular syntax (a set of rules for writing the code).

A developer (or programmer) is the person who analyzes a problem and implements a solution in code.

Sounds amazing, right? It's very powerful and you can be part this wonderful world too by learning how to code. Let's see how.

You, as a developer.

Let's put you in a developer's shoes for a moment. Imagine that you are developing a mobile app, like the ones that you probably have installed on your smartphone right now.

What is the first thing that you would do?

Think about this for a moment.

The answer is...

Analyzing the problem. What are you trying to build?

As a developer, you would start by designing the layout of the app, how it will work, its different screens and functionality, and all the small details that will make your app an awesome tool for users around the world.

Only after you have everything carefully planned out, you can start to write your code. To do that, you will need to choose a programming language to work with. Let's see what a programming language is and why they are super important.

🔸 What is a Programing Language?

A programming language is a language that computers can understand.

We cannot just write English words in our program like this:

"Computer, solve this task!"

and hope that our computer can understand what we mean. We need to follow certain rules to write the instructions.

Every programming language has its own set of rules that determine if a line of code is valid or not. Because of this, the code you write in one programming language will be slightly different from others.

💡 Tip: Some programming languages are more complex than others but most of them share core concepts and functionality. If you learn how to code in one programming language, you will likely be able to learn another one faster.

Before you can start writing awesome programs and apps, you need to learn the basic rules of the programming language you chose for the task.

💡 Tip: a program is a set of instructions written in a programming language for the computer to execute. We usually write the code for our program in one or multiple files.

For example, this is a line of code in Python (a very popular programming language) that shows the message "Hello, World!" :

But if we write the same line of code in JavaScript (a programming language mainly used for web development), we will get an error because it will not be valid.

To do something very similar in JavaScript, we would write this line of code instead:

Visually, they look very different, right? This is because Python and JavaScript have a different syntax and a different set of built-in functions .

💡 Tip : built-in functions are basically tasks that are already defined in the programming language. This lets us use them directly in our code by writing their names and by specifying the values they need.  

In our examples, print() is a built-in function in Python while console.log() is a function that we can use in JavaScript to see the message in the console (an interactive tool) if we run our code in the browser.

Examples of programming languages include Python, JavaScript, TypeScript, Java, C, C#, C++, PHP, Go, Swift, SQL, and R. There are many programming languages and most of them can be used for many different purposes.

💡 Tip: These were the most popular programming languages on the Stack Overflow Developer Survey 2022 :

There are many other programming languages (hundreds or even thousands!) but usually, you will learn and work with some of the most popular ones. Some of them have broader applications like Python and JavaScript while others (like R) have more specific (and even scientific) purposes.

This sounds very interesting, right? And we are only starting to talk about programming languages. There is a lot to learn about them and I promise you that if you dive deeper into programming, your time and effort will be totally worth it.

Awesome! Now that you know what programming is and what programming languages are all about, let's see how programming is related to binary numbers.

🔹 Programming and Binary Numbers

When you think about programming, perhaps the first thing that comes to your mind is something like the below image, right? A sequence of 0 s and 1 s on your computer.

Programming is indeed related to binary numbers ( 0 and 1 ) but in an indirect way. Developers do not actually write their code using zeros and ones.

We usually write programs in a high-level programming language, a programming language with a syntax that recognizes specific words (called keywords), symbols, and values of different data types.

Basically, we write code in a way that humans can understand.

For example, these are the keywords that we can use in Python:

Every programming language has its own set of keywords (words written in English). These keywords are part of the syntax and core functionality of the programming language.

But keywords are just common words in English, almost like the ones that we would find in a book.

That leads us to two very important questions:

• How does the computer understand and interpret what we are trying to say?
• Where does the binary number system come into play here?

The computer does not understand these words, symbols, or values directly.

When a program runs, the code that we write in a high-level programming language that humans can understand is automatically transformed into binary code that the computer can understand.

This transformation of source code that humans can understand into binary code that the computer can understand is called compilation .

According to Britannica , a compiler is defined as:

Computer software that translates (compiles) source code written in a high-level language (e.g., C++) into a set of machine-language instructions that can be understood by a digital computer’s CPU.

Britannica also mentions that:

The term compiler was coined by American computer scientist Grace Hopper , who designed one of the first compilers in the early 1950s.

Some programming languages can be classified as compiled programming languages while others can be classified as interpreted programming languages based on how to they are transformed into machine-language instructions.

However, they all have to go through a process that converts them into instructions that the computer can understand.

Awesome. Now you know why binary code is so important for computer science. Without it, basically programming would not exist because computers would not be able to understand our instructions.

Now let's dive into the applications of programming and the different areas that you can explore.

🔸 Real-World Applications of Programming

Programming has many different applications in many different industries. This is truly amazing because you can apply your knowledge in virtually any industry that you are interested in.

From engineering to farming, from game development to physics, the possibilities are endless if you learn how to code.  

Let's see some of them. (I promise you. They are amazing! ⭐) .

Front-End Web Development

If you learn how to code, you can use your programming skills to design and develop websites and online platforms. Front-End Web Developers create the parts of the websites that users can see and interact with directly.

For example, right now you are reading an article on freeCodeCamp 's publication. The publication looks like this and it works like this thanks to code that front-end web developers wrote line by line.

💡 Tip: If you learn front-end web development, you can do this too.

Front-End Web Developers use HTML and CSS to create the structure of the website (these are markup languages, which are used to present information) and they write JavaScript code to add functionality and interactivity.

If you are interested in learning front-end web development, you can learn HTML and CSS with these free courses on freeCodeCamp's YouTube Channel:

• Learn HTML5 and CSS3 From Scratch - Full Course
• Learn HTML & CSS – Full Course for Beginners
• Frontend Web Development Bootcamp Course (JavaScript, HTML, CSS)
• Introduction To Responsive Web Design - HTML & CSS Tutorial

You can also learn JavaScript for free with these free online courses:

• Learn JavaScript - Full Course for Beginners
• JavaScript Programming - Full Course
• JavaScript DOM Manipulation – Full Course for Beginners
• Learn JavaScript by Building 7 Games - Full Course

💡 Tip: You can also earn a Responsive Web Design Certification while you learn with interactive exercises on freeCodeCamp.

Back-End Web Development

More complex and dynamic web applications that work with user data also require a server . This is a computer program that receives requests and sends appropriate responses. They also need a database , a collection of values stored in a structured way.

Back-End Web Developers are in charge of developing the code for these servers. They decide how to handle the different requests, how to send appropriate resources, how to store the information, and basically how to make everything that runs behind the scenes work smoothly and efficiently.

A real-world example of back-end web development is what happens when you create an account on freeCodeCamp and complete a challenge. Your information is stored on a database and you can access it later when you sign in with your email and password.

This amazing interactive functionality was implemented by back-end web developers.

💡 Tip: Full-stack Web Developers are in charge of both Front-End and Back-End Web Development. They have specialized knowledge on both areas.

All the complex platforms that you use every day, like social media platforms, online shopping platforms, and educational platforms, use servers and back-end web development to power their amazing functionality.

Python is an example of a powerful programming language used for this purpose. This is one of the most popular programming languages out there, and its popularity continues to rise every year. This is partly because it is simple and easy to learn and yet powerful and versatile enough to be used in real-world applications.

💡 Tip: if you are curious about the specific applications of Python, this is an article I wrote on this topic .

JavaScript can also be used for back-end web development thanks to Node.js.

Other programming languages used to develop web servers are PHP, Ruby, C#, and Java.

If you would like to learn Back-End Web Development, these are free courses on freeCodeCamp's YouTube channel:

• Python Backend Web Development Course (with Django)
• Node.js and Express.js - Full Course
• Full Stack Web Development for Beginners (Full Course on HTML, CSS, JavaScript, Node.js, MongoDB)
• Node.js / Express Course - Build 4 Projects

💡 Tip: freeCodeCamp also has a free Back End Development and APIs certification.

Mobile App Development

Mobile apps have become part of our everyday lives. I'm sure that you could not imagine life without them.

Think about your favorite mobile app. What do you love about it?

Our favorite apps help us with our daily tasks, they entertain us, they solve a problem, and they help us to achieve our goals. They are always there for us.

That is the power of mobile apps and you can be part of this amazing world too if you learn mobile app development.

Developers focused on mobile app development are in charge of planning, designing, and developing the user interface and functionality of these apps. They identify a gap in the existing apps and they try to create a working product to make people's lives better.

💡 Tip: regardless of the field you choose, your goal as a developer should always be making people's lives better. Apps are not just apps, they have the potential to change our lives. You should always remember this when you are planning your projects. Your code can make someone's life better and that is a very important responsibility.

Mobile app developers use programming languages like JavaScript, Java, Swift, Kotlin, and Dart. Frameworks like Flutter and React Native are super helpful to build cross-platform mobile apps (that is, apps that run smoothly on multiple different operating systems like Android and iOS).

According to Flutter 's official documentation:

Flutter is an open source framework by Google for building beautiful, natively compiled, multi-platform applications from a single codebase.

If you would like to learn mobile app development, these are free courses that you can take on freeCodeCamp's YouTube channel:

• Flutter Course for Beginners – 37-hour Cross Platform App Development Tutorial
• Flutter Course - Full Tutorial for Beginners (Build iOS and Android Apps)
• React Native - Intro Course for Beginners
• Learn React Native Gestures and Animations - Tutorial

Game Development

Games create long-lasting memories. I'm sure that you still remember your favorite games and why you love (or loved) them so much. Being a game developer means having the opportunity of bringing joy and entertainment to players around the world.

Game developers envision, design, plan, and implement the functionality of a game. They also need to find or create assets such as characters, obstacles, backgrounds, music, sound effects, and more.

💡 Tip: if you learn how to code, you can create your own games. Imagine creating an awesome and engaging game that users around the world will love. That is what I personally love about programming. You only need your computer, your knowledge, and some basic tools to create something amazing.

Popular programming languages used for game development include JavaScript, C++, Python, and C#.

If you are interested in learning game development, you can take these free courses on freeCodeCamp's YouTube channel:

• JavaScript Game Development Course for Beginners
• Learn Unity - Beginner's Game Development Tutorial
• Learn Python by Building Five Games - Full Course
• Code a 2D Game Using JavaScript, HTML, and CSS (w/ Free Game Assets) – Tutorial
• 2D Game Development with GDevelop - Crash Course
• Pokémon Coding Tutorial - CS50's Intro to Game Development

Biology, Physics, and Chemistry

Programming can be applied in every scientific field that you can imagine, including biology, physics, chemistry, and even astronomy. Yes! Scientists use programming all the time to collect and analyze data. They can even run simulations to test hypotheses.

In biology, computer programs can simulate population genetics and population dynamics. There is even an entire field called bioinformatics .

According to this article "Bioinformatics" by Ardeshir Bayat, member of the Centre for Integrated Genomic Medical Research at the University of Manchester:

Bioinformatics is defined as the application of tools of computation and analysis to the capture and interpretation of biological data.

Dr. Bayat mentions that bioinformatics can be used for genome sequencing. He also mentions that its discoveries may lead to drug discoveries and individualized therapies.

Frequently used programming languages for bioinformatics include Python, R, PHP, PERL, and Java.

💡 Tip: R is a programming "language and environment for statistical computing and graphics" ( source ).

An example of a great tool that scientists can use for biology is Biopython . This is a Python framework with "freely available tools for biological computation."

If you would like to learn more about how you can apply your programming skills in science, these are free courses that you can take on freeCodeCamp's YouTube channel:

• Python for Bioinformatics - Drug Discovery Using Machine Learning and Data Analysis
• R Programming Tutorial - Learn the Basics of Statistical Computing
• Learn Python - Full Course for Beginners [Tutorial]

Physics requires running many simulations and programming is perfect for doing exactly that. With programming, scientists can program and run simulations based on specific scenarios that would be hard to replicate in real life. This is much more efficient.

Programming languages that are commonly used for physics simulations include C, Java, Python, MATLAB, and JavaScript.  

Chemistry also relies on simulations and data analysis, so it's a field where programming can be a very helpful tool.

In this scientific article by Dr. Ivar Ugi and his colleagues from Organisch-chemisches Institut der Technischen Universität München, they mention that:

The design of entirely new syntheses, and the classification and documentation of structures, substructures, and reactons are examples of new applications of computers to chemistry.

Scientific experiments also generate detailed data and results that can be analyzed with computer programs developed by scientists.  

Think about it: writing a program to generate a box plot or a scatter plot or any other type of plot to visualize trends in thousands of measurements can save researchers a lot of time and effort. This lets them focus on the most important part of their work: analyzing the results.

💡 Tips: if you are interested in diving deeper into this, this is a list of chemistry simulations by the American Chemical Society. These simulations were programmed by developers and they are helping thousands of students and teachers around the world.

Think about it...You could build the next great simulation. If you are interested in a scientific field, I totally recommend learning how to code. Your work will be much more productive and your results will be easier to analyze.

If you are interested in learning programming for scientific applications, these are free courses on freeCodeCamp's YouTube channel:

• Python for Data Science - Course for Beginners (Learn Python, Pandas, NumPy, Matplotlib)

Data Science and Engineering

Talking about data...programming is also essential for a field called Data Science . If you are interested in answering questions through data and statistics, this field might be exactly what you are looking for and having programming skills will help you to achieve your goals.

Data scientists collect and analyze data in order to answer questions in many different fields. According to UC Berkeley in the article " What is Data Science? ":

Effective data scientists are able to identify relevant questions, collect data from a multitude of different data sources, organize the information, translate results into solutions, and communicate their findings in a way that positively affects business decisions.

There are many powerful programming languages for analyzing and visualizing data, but perhaps one of the most frequently used ones for this purpose is Python.

This is an example of the type of data visualizations that you can create with Python. They are very helpful to analyze data visually and you can customize them to your fit needs.

If you are interested in learning programming for data science, these are free courses on freeCodeCamp's YouTube channel:

• Learn Data Science Tutorial - Full Course for Beginners
• Intro to Data Science - Crash Course for Beginners
• Build 12 Data Science Apps with Python and Streamlit - Full Course
• Data Analysis with Python - Full Course for Beginners (Numpy, Pandas, Matplotlib, Seaborn)

💡 Tip: you can also earn these free certifications on freeCodeCamp:

• Data Visualization
• Data Analysis with Python

Engineering

Engineering is another field where programming can help you to succeed. Being able to write your own computer programs can make your work much more efficient.

There are many tools created specifically for engineers. For example, the R programming language is specialized in statistical applications and Python is very popular in this field too.

Another great tool for programming in engineering is MATLAB . According to its official website:

MATLAB is a programming and numeric computing platform used by millions of engineers and scientists to analyze data, develop algorithms, and create models.

Really, the possibilities are endless.

You can learn MATLAB with this crash course on the freeCodeCamp YouTube channel .

If you are interested in learning engineering tools related to programming, this is a free course on freeCodeCamp's YouTube channel that covers AutoCAD, a 2D and 3D computer-aided design software used by engineers:

• AutoCAD for Beginners - Full University Course

Medicine and Pharmacology

Medicine and pharmacology are constantly evolving by finding new treatments and procedures. Let's see how you can apply your programming skills in these fields.

Programming is really everywhere. If you are interested in the field of medicine, learning how to code can be very helpful for you too. Even if you would like to focus on computer science and software development, you can apply your knowledge in both fields.

Specialized developers are in charge of developing and writing the code that powers and controls the devices and machines that are used by modern medicine.

Think about it...all these machines and devices are controlled by software and someone has to write that software. Medical records are also stored and tracked by specialized systems created by developers. That could be you if you decide to follow this path. Sounds exciting, right?

According to the scientific article Application of Computer Techniques in Medicine :

Major uses of computers in medicine include hospital information system, data analysis in medicine, medical imaging laboratory computing, computer assisted medical decision making, care of critically ill patients, computer assisted therapy and so on.

Pharmacology

Programming and computer science can also be applied to develop new drugs in the field of pharmacology.

A remarkable example of what you can achieve in this field by learning how to code is presented in this article by MIT News. It describes how an MIT senior, Kristy Carpenter, was using computer science in 2019 to develop "new, more affordable drugs." Kristy mentions that:

Artificial intelligence, which can help compute the combinations of compounds that would be better for a particular drug, can reduce trial-and-error time and ideally quicken the process of designing new medicines.

Another example of a real-world application of programming in pharmacology is related to Python (yes, Python has many applications!). Among its success stories , we find that Python was selected by AstraZeneca to develop techniques and programs that can help scientists to discover new drugs faster and more efficiently.

The documentation explains that:

To save time and money on laboratory work, experimental chemists use computational models to narrow the field of good drug candidates, while also verifying that the candidates to be tested are not simple variations of each other's basic chemical structure.

If you are interested in learning programming for medicine or health-related fields, this is a free course on freeCodeCamp's YouTube channel on programming for healthcare imaging:

• PyTorch and Monai for AI Healthcare Imaging - Python Machine Learning Course

Have you ever thought that programming could be helpful for education? Well, let me tell you that it is and it is very important. Why? Because the digital learning tools that students and teachers use nowadays are programmed by developers.

Every time a student opens an educational app, browses an educational platform like freeCodeCamp, writes on a digital whiteboard, or attends a class through an online meeting platform, programming is making that possible.

As a programmer or as a teacher who knows how to code, you can create the next great app that will enhance the learning experience of students around the world.

Perhaps it will be a note-taking app, an online learning platform, a presentation app, an educational game, or any other app that could be helpful for students.

The important thing is to create it with students in mind if your goal is to make something amazing that will create long-lasting memories.

If you envision it, then you can create it with code.  

Teachers can also teach their students how to code to develop their problem-solving skills and to teach them important skills for their future.

💡 Tip: if you are teaching students how to code, Scratch is a great programming language to teach the basics of programming. It is particularly focused on teaching children how to code in an interactive way.

According to the official Scratch website:

Scratch is the world’s largest coding community for children and a coding language with a simple visual interface that allows young people to create digital stories, games, and animations.

If you are interested in learning how to code for educational purposes, these are courses that you may find helpful on freeCodeCamp's YouTube channel:

• Scratch Tutorial for Beginners - Make a Flappy Bird Game
• Computational Thinking & Scratch - Intro to Computer Science - Harvard's CS50 (2018)
• Android Development for Beginners - Full Course

Machine Learning, Artificial Intelligence, and Robotics

Some of the most amazing fields that are directly related to programming are Machine Learning, Artificial Intelligence, and Robotics. Let's see why.

Artificial Intelligence is defined by Britannica as:

The project of developing systems endowed with the intellectual processes characteristic of humans, such as the ability to reason, discover meaning, generalize, or learn from past experience.

Machine learning is a branch or a subset of the field of Artificial Intelligence in which systems can learn on their own based on data. The goal of this learning process is to predict the expected output. These models continuously learn how to "think" and how to analyze situations based on their previous training.

The most commonly used programming languages in these fields are Python, C, C#, C++, and MATLAB.

Artificial intelligence and Machine Learning have amazing applications in various industries, such as:

• Image and object detection.
• Making predictions based on patterns.
• Text recognition.
• Recommendation engines (like when an online shopping platform shows you products that you may like or when YouTube shows you videos that you may like).
• Spam detection for emails.
• Fraud detection.
• Social media features like personalized feeds.
• Many more... there are literally millions of applications in virtually every industry.

If you are interested in learning how to code for Artificial Intelligence and Machine Learning, these are free courses on freeCodeCamp's YouTube channel:

• Machine Learning for Everybody – Full Course
• Machine Learning Course for Beginners
• PyTorch for Deep Learning & Machine Learning – Full Course
• TensorFlow 2.0 Complete Course - Python Neural Networks for Beginners Tutorial
• Self-Driving Car with JavaScript Course – Neural Networks and Machine Learning
• Python TensorFlow for Machine Learning – Neural Network Text Classification Tutorial
• Practical Deep Learning for Coders - Full Course from fast.ai and Jeremy Howard
• Deep Learning Crash Course for Beginners
• Advanced Computer Vision with Python - Full Course

💡 Tip: you can also earn a Machine Learning with Python Certification on freeCodeCamp.

Programming is also very important for robotics. Yes, robots are programmed too!

Robotics is defined by Britannica as the:

Design, construction, and use of machines (robots) to perform tasks done traditionally by human beings.

Robots are just like computers. They do not know what to do until you tell them what to do by writing instructions in your programs. If you learn how to code, you can program robots and industrial machinery found in manufacturing facilities.

If you are interested in learning how to code for robotics, electronics, and related fields, this is a free course on Arduino on freeCodeCamp's YouTube channel:

• Arduino Course for Beginners - Open-Source Electronics Platform

Other Applications

There are many other fascinating applications of programming in almost every field. These are some highlights:

• Agriculture: in this article by MIT News, a farmer developed an autonomous tractor app after learning how to code.
• Self-driving cars: autonomous cars rely on software to analyze their surroundings and to make quick and accurate decisions on the road. If you are interested in this area, this is a course on this topic on freeCodeCamp's YouTube channel.
• Finance: programming can also be helpful to develop programs and models that predict financial indicators and trends. For example, this is a course on algorithmic trading on freeCodeCamp's YouTube channel.

The possibilities are endless. I hope that this section will give you a notion of why learning how to code is so important for your present and for your future. It will be a valuable skill to have in any field you choose.

Awesome. Now let's dive into the soft skills that you need to become a successful programmer.

🔹 Skills of a Successful Programmer

After going through the diverse range of applications of programming, you must be curious to know what skills are needed to succeed in this field.

A programmer should be curious. Whether you are just starting to learn how to code or you already have 20 years of experience, coding projects will always present you with new challenges and learning opportunities. If you take these opportunities, you will continously improve your skills and succeed.

Enthusiasm is a key trait of a successful programmer but this applies in general to any field if you want to succeed. Enthusiasm will keep you happy and curious about what you are creating and learning.

💡 Tip: If you ever feel like you are not as enthusiastic as you used to be, it's time to find or learn something new that can light the spark in you again and fill you with hope and dreams.

A programmer must be patient because transforming an initial idea into a working product can take time, effort, and many different steps. Patience will keep you focused on your final goal.  

Programming can be challenging. That is true. But what defines you is not how many challenges you face, it's how you face them. If you thrive despite these challenges, you will become a better programmer and you could create something that could change the world.

Programmers must be creative because even though every programming language has a particular set of rules for writing the code, coding is like using LEGOs. You have the building-blocks but you need to decide what to create and how to create it. The process of writing the code requires creativity while following the established best practices.

Problem-solving and Analysis

Programming is basically analyzing and solving problems with code. Depending on your field of choice, those problems will be simpler or more complex but they will all require some level of problem-solving skills and a thorough analysis of the situation.

Questions like:

• What should I build?
• How can I build it?
• What is the best way to build this?

Are part of the everyday routine of a programmer.

Ability to Focus for Long Periods of Time

When you are working on a coding project, you will need to focus on a task for long periods of time. From creating the design, to planning and writing the code, to testing the result, and to fixing bugs (issues with the code), you will dedicate many hours to a particular task. This is why it's essential to be able to focus and to keep your final goal in mind.

Taking Detailed Notes

This skill is very important for programmers, particularly when you are learning how to code. Taking detailed notes can be help you to understand and remember the concepts and tools you learn. This also applies for experienced programmers, since being a programmer involves life-long learning.

Communication

Initially, you might think that programming is a solitary activity and imagine that a programmer spends hundreds of hours alone sitting on a desk.

But the reality is that when you find your first job, you will see that communication is super important to coordinate tasks with other team members and to exchange ideas and feedback.

Open to Feedback

In programming, there is usually more than one way to implement the same functionality. Different alternatives may work similarly, but some may be easier to read or more efficient in terms of time or resource consumption.

When you are learning how to code, you should always take constructive feedback as a tool for learning. Similarly, when you are working on a team, take your colleagues' feedback positively and always try to improve.

Life-long Learning

Programming equals life-long learning. If you are interested in learning how to code, you must know that you will always need to be learning new things as new technologies emerge and existing technologies are updated. Think about it... that is great because there is always something interesting and new to learn!

Open to Trying New Things

Finally, an essential skill to be a successful programmer is to be open to trying new things. Step out of your comfort zone and be open to new technologies and products. In the technology industry, things evolve very quickly and adapting to change is essential.

🔸 Tips for Learning How to Code

Now that you know more about programming, programming languages, and the skills you need to be a successful programmer, let's see some tips for learning how to code.

💡 Tip: these tips are based on my personal experience and opinions.

• Choose one programming language to learn first. When you are learning how to code, it's easy to feel overwhelmed with the number of options and entry paths. My advice would be to focus on understanding the essential computer science concepts and one programming language first. Python and JavaScript are great options to start learning the fundamentals.
• Take detailed notes. Note-taking skills are essential to record and to analyze the topics you are learning. You can add custom comments and annotations to explain what you are learning.
• Practice constantly. You can only improve your problem-solving skills by practicing and by learning new techniques and tools. Try to practice every day.

💡 Tip: There is a challenge called the #100DaysOfCode challenge that you can join to practice every day.  

• Always try again. If you can't solve a problem on your first try, take a break and come back again and again until you solve it. That is the only way to learn. Learn from your mistakes and learn new approaches.
• Learn how to research and how to find answers. Programming languages, libraries, and frameworks usually have official documentations that explain their built-in elements and tools and how you can use them. This is a precious resource that you should definitely refer to.
• Browse Stack Overflow . This is an amazing platform. It is like an online encyclopedia of answers to common programming questions. You can find answers to existing questions and ask new questions to get help from the community.
• Set goals. Motivation is one of the most important factors for success. Setting goals is very important to keep you focused, motivated, and enthusiastic. Once you reach your goals, set new ones that you find challenging and exciting.
• Create projects. When you are learning how to code, applying your skills will help you to expand your knowledge and remember things better. Creating projects is the perfect way to practice and to create a portfolio that you can show to potential employers.

🔹 Basic Programming Concepts

Great. If reading this article has helped you confirm that you want to learn programming, let's take your first steps.

These are some basic programming concepts that you should know:

• Variable: a variable is a name that we assign to a value in a computer program. When we define a variable, we assign a value to a name and we allocate a space in memory to store that value. The value of a variable can be updated during the program.
• Constant: a constant is similar to a variable. It stores a value but it cannot be modified. Once you assign a value to a constant, you cannot change it during the entire program.
• Conditional: a conditional is a programming structure that lets developers choose what the computer should do based on a condition. If the condition is True, something will happen but if the condition is False, something different can happen.
• Loop: a loop is a programming structure that let us run a code block (a sequence of instructions) multiple times. They are super helpful to avoid code repetition and to implement more complex functionality.
• Function: a function helps us to avoid code repetition and to reuse our code. It is like a code block to which we assign a name but it also has some special characteristics. We can write the name of the function to run that sequence of instructions without writing them again.

💡 Tip: Functions can communicate with main programs and main programs can communicate with functions through parameters , arguments , and return statements.

• Class: a class is used as a blueprint to define the characteristics and functionality of a type of object. Just like we have objects in our real world, we can represent objects in our programs.
• Bug: a bug is an error in the logic or implementation of a program that results in an unexpected or incorrect output.
• Debugging: debugging is the process of finding and fixing bugs in a program.
• IDE: this acronym stands for Integrated Development Environment. It is a software development environment that has the most helpful tools that you will need to write computer programs such as a file editor, an explorer, a terminal, and helpful menu options.

💡 Tip: a commonly used and free IDE is Visual Studio Code , created by Microsoft.

Awesome! Now you know some of the fundamental concepts in programming. Like you learned, each programming language has a different syntax, but they all share most of these programming structures and concepts.  

🔸 Types of Programming Languages

Programming languages can be classified based on different criteria. If you want to learn how to code, it's important for you to learn these basic classifications:

• High-level programming languages: they are designed to be understood by humans and they have to be converted into machine code before the computer can understand them. They are the programming languages that we commonly use. For example: JavaScript, Python, Java, C#, C++, and Kotlin.
• Low-level programming languages: they are more difficult to understand because they are not designed for humans. They are designed to be understood and processed efficiently by machines.

Conversion into Machine Code

• Compiled programming languages: programs written with this type of programming language are converted directly into machine code by a compiler. Examples include C, C++, Haskell, and Go.
• Interpreted programming languages: programs written with this type of programming language rely on another program called the interpreter, which is in charge of running the code line by line. Examples include Python, JavaScript, PHP, and Ruby.

💡 Tip: according to this article on freeCodeCamp's publication:

Most programming languages can have both compiled and interpreted implementations – the language itself is not necessarily compiled or interpreted. However, for simplicity’s sake, they’re typically referred to as such.

There are other types of programming languages based on different criteria, such as:

• Procedural programming languages
• Functional programming languages
• Object-oriented programming languages
• Scripting languages
• Logic programming languages

And the list of types of programming languages continues. This is very interesting because you can analyze the characteristics of a programming language to help you choose the right one for your project.

🔹 How to Contribute to Open Source Projects

Finally, you might think that coding implies sitting at a desk for many hours looking at your code without any human interaction. But let me tell you that this does not have to be true at all. You can be part of a learning community or a developer community.

Initially, when you are learning how to code, you can participate in a learning community like freeCodeCamp. This way, you will share your journey with others who are learning how to code, just like you.

Then, when you have enough skills and confidence in your knowledge, you can practice by contributing to open source projects and join developer communities.

Open source software is defined by Opensource.com as:

Software with source code that anyone can inspect, modify, and enhance.

GitHub is an online platform for hosting projects with version control. There, you can find many open source projects (like freeCodeCamp ) that you can contribute to and practice your skills.

💡 Tip: many open source projects welcome first-time contributions and contributions from all skill levels. These are great opportunities to practice your skills and to contribute to real-world projects.  

Contributing to open source projects on GitHub is great to acquire new experience working and communicating with other developers. This is another important skill for finding a job in this field.

Working on a team is a great experience. I totally recommend it once you feel comfortable enough with your skills and knowledge.

You did it! You reached the end of this article. Great work. Now you know what programming is all about. Let's see a brief summary.

🔸 In Summary

• Programming is a very powerful skill. If you learn how to code, you can make your vision come true.
• Programming has many different applications in many different fields. You can find an application for programming in basically any field you choose.
• Programming languages can be classified based on different criteria and they share basic concepts such as variables, conditionals, loops, and functions.
• Always set goals and take detailed notes. To succeed as a programmer, you need to be enthusiastic and consistent.

Thank you very much for reading my article. I hope you liked it and found it helpful. Now you know why you should learn how to code.

🔅 I invite you to follow me on Twitter ( @EstefaniaCassN ) and YouTube ( Coding with Estefania ) to find coding tutorials.

Developer, technical writer, and content creator @freeCodeCamp. I run the freeCodeCamp.org Español YouTube channel.

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Dynamic Programming: Strategies for Solving Complex Problems Efficiently

Dynamic Programming Demystified 🚀

Hey there, fellow tech enthusiasts! 🤖 Today, let’s delve into the fascinating world of Dynamic Programming 🌟. Don’t be scared off by the jargon; I’m here to break it down with a sprinkle of humor and a dollop of enthusiasm! So, grab your virtual seat and let’s dive right in! 💻

Understanding Dynamic Programming

So, what in the world is Dynamic Programming ? 🤔 Imagine you have this colossal problem to solve, and it’s so complex that you feel like pulling your hair out! Dynamic Programming swoops in like a superhero, offering you a strategy to break down this mammoth task into bite-sized, manageable chunks. Voila! Problem solved! 💪

Definition of Dynamic Programming

Dynamic Programming is like the master chef in the kitchen of algorithms . It’s a methodical way of solving complex problems by breaking them down into simpler subproblems. 🍳 Each subproblem’s solution is stored to avoid redundant calculations, making the overall process more efficient. Efficiency for the win! 🎉

Importance of Dynamic Programming

Picture this: You’re at a buffet, and you want to sample every dish. Dynamic Programming allows you to do just that in the realm of algorithms – optimize your solutions and tackle even the most intricate problems with finesse. It’s like having a secret recipe book for cracking challenging puzzles in record time! 🍽️

Basic Principles of Dynamic Programming

Let’s talk about the fundamental rules that make Dynamic Programming the rockstar of problem-solving techniques! 🌟

• Overlapping Subproblems : It’s like finding money in the pockets of your old jeans. Dynamic Programming identifies these recurring subproblems and saves their solutions for later use, eliminating unnecessary work. It’s all about efficiency, baby! 💸
• Optimal Substructure : This principle is like building a sturdy LEGO tower. Each piece (subproblem) fits perfectly to create the optimal solution . Dynamic Programming ensures that each subproblem’s solution contributes to the overall best answer. It’s all about that solid foundation! 🏗️

Strategies for Applying Dynamic Programming

Now that we’ve got the basics under our belt, let’s explore the two dynamic strategies that make the magic happen! 🎩✨

• Top-down Approach : Imagine you’re skydiving from the top. This approach starts with the main problem and recursively breaks it down into subproblems. It’s adventurous, exhilarating, and definitely keeps you on your toes! 🪂
• Bottom-up Approach : Ever built a tower from the ground up? That’s the bottom-up approach. You start with the smallest subproblems, gradually solving larger ones until you conquer the main problem like a champ. It’s a steady climb to success! 🗼

Applications of Dynamic Programming

Dynamic Programming isn’t just a fancy term; it’s the powerhouse behind some incredible real-world applications! 🌐 Let’s take a peek at a couple of them:

• Fibonacci Sequence : Ah, the Fibonacci sequence, nature’s favorite mathematical marvel ! Dynamic Programming nimbly calculates Fibonacci numbers faster than you can say “Golden Ratio.” It’s all about those efficient number-crunching skills! 🔢
• Shortest Path Algorithms : Navigating through a maze? Dynamic Programming has your back! It’s the GPS guiding you through the shortest route with speed and precision. Say goodbye to taking the long, scenic route! 🗺️

Challenges and Tips for Mastering Dynamic Programming

Ah, every hero has their kryptonite, right? Let’s uncover some challenges in mastering Dynamic Programming and how to conquer them like a pro! 🦸‍♂️

• Identifying Optimal Substructure : Sometimes the forest (complex problem) is so dense that you can’t see the trees (optimal substructure). Mastering Dynamic Programming involves honing your detective skills to spot these crucial patterns. Sherlock, who? 🕵️
• Handling State Transitions efficiently : It’s like switching gears in a Formula 1 race. Efficiently transitioning between states is key to zipping through problems with ease. Rev up those mental engines and zoom past any hurdles! 🏎️

Overall, Mastering Dynamic Programming Like a Pro! 🚀

So, there you have it, folks! Dynamic Programming, the unsung hero of problem-solving, ready to tackle any challenge with finesse. Remember, practice makes perfect, and with a dash of determination and a sprinkle of creativity, you’ll be mastering Dynamic Programming like a seasoned pro in no time! 💪

Thanks for tuning in, and remember: Keep coding, keep smiling, and embrace the dynamic journey ahead! 🌟

Stay Dynamically Awesome, Techies! 🚀👩‍💻

In closing, thanks a ton for joining me on this Dynamic Programming rollercoaster! 🎢 Keep shining bright and solving those tech puzzles like a boss! See you in the next coding adventure! ✨

Program Code – Dynamic Programming: Strategies for Solving Complex Problems Efficiently

Code Output: The 10th Fibonacci number is: 55

Code Explanation:

In the given dynamic programming example , we solve for the nth Fibonacci number, a popular problem showcasing the elegance and efficiency of the dynamic programming approach. The recursive nature of the Fibonacci sequence, where each number is the sum of the two preceding ones (excluding the first two numbers which are both considered as 1), makes it an ideal candidate for dynamic programming, particularly memoization.

The code defines a fibonacci function that takes two arguments: n , the position in the Fibonacci sequence whose value we want to find, and memo , a dictionary used as a cache to store the results of the Fibonacci numbers we’ve already computed.

At the function’s core, we employ a base case for when n is less than or equal to 2. For these cases, we simply return 1, as the first two Fibonacci numbers by definition are 1.

The true power and efficiency lie in the subsequent lines. Before plunging headlong into a recursive frenzy, we first check if our current n is in the memo . If it’s not, this means we haven’t computed it yet, and then we proceed to perform the recursive operations to calculate fibonacci(n-1) and fibonacci(n-2) . Crucially, we then store this computed value in memo[n] . This storage step is what saves us from the redundant work if we encounter the same n value again in our computations.

In essence, any subsequent calls for the same Fibonacci number won’t have to go through the recursion again; instead, they’ll directly fetch the result from our memo , dramatically reducing the time complexity from what would have been exponential in a naive recursive approach (O(2^n)) to O(n) in our dynamic programming approach.

Let’s not forget—the function concludes by returning the memoized or newly computed value of the nth Fibonacci number, giving us our desired result efficiently and elegantly. Dynamic programming, with its memoization strategy, thus transforms an otherwise computationally intensive problem into a tractable one, showcasing its power in optimizing the performance of algorithms dealing with overlapping subproblems.

Frequently Asked Questions (F&Q) on Dynamic Programming

What is dynamic programming and how does it work.

Dynamic programming is a method for solving complex problems by breaking them down into simpler subproblems. It involves solving each subproblem only once and storing the solution to avoid redundant calculations. This approach can significantly improve the efficiency of solving problems with overlapping subproblems.

When should I use dynamic programming to solve a problem?

Dynamic programming is most useful when a problem can be broken down into overlapping subproblems, and the optimal solution to the problem can be constructed from optimal solutions to its subproblems. It is commonly used in optimization problems, such as finding the shortest path or maximizing profit.

What are the key characteristics of problems that are suitable for dynamic programming?

Problems suitable for dynamic programming usually exhibit two key characteristics: optimal substructure and overlapping subproblems. Optimal substructure means that the optimal solution to the problem can be constructed from the optimal solutions to its subproblems. Overlapping subproblems refer to the fact that the same subproblems are solved multiple times in a recursive algorithm .

Can you provide an example of a problem that can be solved using dynamic programming?

One classic example of a problem solved using dynamic programming is the Fibonacci sequence. By storing the results of subproblems (calculating Fibonacci numbers for smaller indices), we can avoid redundant calculations and compute the nth Fibonacci number efficiently.

Are there different strategies or approaches to dynamic programming?

Yes, there are several strategies for approaching dynamic programming problems, such as top-down with memoization and bottom-up with tabulation. Top-down with memoization involves solving the problem recursively while storing the results of subproblems to avoid redundant calculations. Bottom-up with tabulation involves solving the problem iteratively, starting from the smallest subproblems and building up to the desired solution.

What are some common pitfalls to avoid when using dynamic programming?

One common pitfall when using dynamic programming is not recognizing the overlapping subproblems and failing to store and reuse intermediate results. It is essential to identify the repeating subproblems to benefit from the efficiency of dynamic programming . Additionally, starting with a brute-force approach before optimizing with dynamic programming can help in understanding the problem better.

How can I improve my skills in dynamic programming?

To improve your skills in dynamic programming, practice solving a variety of problems that can be optimized using dynamic programming techniques . Online coding platforms, coding contests, and algorithmic problem-solving websites offer a wide range of problems to help you sharpen your skills. Additionally, studying different dynamic programming patterns and approaches can enhance your problem-solving abilities.

What are some resources to learn more about dynamic programming?

There are plenty of resources available to deepen your understanding of dynamic programming, including online courses, textbooks, and tutorials. Websites like LeetCode, GeeksforGeeks, and CodeSignal offer practice problems and explanations related to dynamic programming. Additionally, joining online coding communities and forums can provide valuable insights and tips from experienced programmers in the field.

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Programming for Problem Solving

This book provides an introduction to computer programming using Python as a way to solve problems. It focuses on programming concepts and fundamentals within the context of solving real world problems.

Table of Contents

• Attributions
• Acknowledgments
• Learning Objectives
• Introduction
• Computational Thinking
• An Example Algorithm
• Verifying your Algorithm
• The Process of Computational Problem Solving
• Values and Variables
• What is a Program?
• Computational Problem Design Using the Basic Programming Constructs
• The Role of Programming in the Field of Informatics
• Unit Summary
• Practice Problems
• Computer Hardware Architecture
• Digital Computing: It’s All about 0’s and 1’s
• Operating Systems—Bridging Software and Hardware
• Software Development Tools
• Learning Programming with Python
• Writing a Python Program
• The Python Interactive Shell
• The Basics of Python Programming
• Example: Using Variables and Literal Constants
• Operators and Expressions
• Practice with Operators & Expressions
• Evaluation Order
• Input/Process/Output Pattern
• Type Converter Functions
• Python’s Standard Library
• More on Strings
• Object Oriented Programming
• Simple Graphics Programming
• Graphics Windows: Coordinate Systems
• GraphWin Objects
• Text Methods
• Entry Objects
• Displaying Images
• Generating Colors
• Interactive Graphics
• Boolean Expressions
• Logical Operators
• Conditional Execution
• Exception Handling
• Practice with Handling Exceptions in our Programs
• The for…in Statement
• Nested Loops
• Basic File Processing
• Installing Python 3 and IDLE
• Using Python and its IDE 
• Appendix B: Python Cheat Sheet

This courseware includes resources copyrighted and openly licensed by multiple individuals and organizations. Click the words "Licenses and Attributions" at the bottom of each page for copyright and licensing information specific to the material on that page. If you believe that this courseware violates your copyright, please contact us .

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Pave the Way for Self-regulation and Problem-solving With Social-emotional Learning

Posted: April 3, 2024

Problem-solving is a social-emotional learning (SEL) skill children need for lifelong success. Effective problem-solving skills support children's ability to self-regulate, focus on tasks, think flexibly and creatively, work with others, and generate multiple ways to solve problems. When young children develop and build these skills, it positively impacts their interactions with others, grows their capacity to manage challenges, and boosts a sense of competence.

A group of school-age children are stacking plastic blocks with an educator.

The foundation for effective social problem-solving is grounded in self-regulation, or the ability to regulate emotions when interacting with others. It is easier to focus on one's feelings and the feelings and perspectives of others and to work cooperatively toward solutions when a child can self-regulate and calm down. Children develop self-regulation skills over time, with practice and with adult guidance. Equally important is how an adult models emotion regulation and co-regulation. 

"Caregivers play a key role in cultivating the development of emotion regulation through co-regulation, or the processes by which they provide external support or scaffolding as children navigate their emotional experiences" (Paley & Hajal, 2022, p. 1).

When adults model calm and self-regulated approaches to problem-solving, it shows children how to approach problems constructively. For example, an educator says, "I'm going to take a breath and calm down so I can think better." This model helps children see and hear a strategy to support self-regulation.

Problem-solving skills help children resolve conflicts and interact with others as partners and collaborators. Developing problem-solving skills helps children learn and grow empathy for others, stand up for themselves, and build resilience and competence to work through challenges in their world. 

Eight strategies to support problem-solving 

• Teach about emotions and use feeling words throughout the day. When children have more words to express themselves and their feelings, it is easier to address and talk about challenges when they arise. 
• Recognize and acknowledge children's feelings throughout the day. For example, when children enter the classroom during circle time, mealtime, and outside time, ask them how they feel. Always acknowledge children's feelings, both comfortable and uncomfortable, to support an understanding that all feelings are OK to experience.  
• Differentiate between feelings and behaviors. By differentiating feelings from behaviors, educators contribute to children’s understanding that all feelings are OK, but not all behaviors are OK. For example, an educator says, "It looks like you may be feeling mad because you want the red blocks, and Nila is playing with them. It's OK to feel mad but not OK to knock over your friend’s blocks."
• Support children's efforts to calm down. When children are self-regulated, they can think more clearly. For example, practice taking a breath with children as a self-regulation technique during calm moments. Then, when challenges arise, children have a strategy they have practiced many times and can use to calm down before problem-solving begins.  
• Encourage children's efforts to voice the problem and their feelings after they are calm. For example, when a challenge arises, encourage children to use the phrase, "The problem is_______, and I feel______." This process sets the stage to begin problem-solving.
• Acknowledge children's efforts to think about varied ways to solve problems. For example, an educator says, "It looks like you and Nila are trying to work out how to share the blocks. What do you think might work so you can both play with them? Do you have some other ideas about how you could share?"
• Champion children's efforts as they problem-solve. For example, "You and Nila thought about two ways you could share. One way is to divide the red blocks so you can each build, and the other is to build a tower together. Great thinking, friends!"
• Create opportunities for activities and play that offer problem-solving practice. For example, when children play together in the block area, it provides opportunities to negotiate plans for play and role-play, build perspective, talk about feelings, and share. The skills children learn during play, along with adult support, enhance children’s ability to solve more complex and challenging social problems and conflicts when they occur in and out of the early learning setting.

References: 

Paley, B., & Hajal, N. J. (2022). Conceptualizing emotion regulation and coregulation as family-level phenomena. Clinical Child and Family Psychology Review ,  25 (1), 19-43.

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The Eclipse Chaser

As millions of americans prepare to see a total solar eclipse, a retired astrophysicist known as “mr. eclipse,” discusses the celestial phenomenon..

This transcript was created using speech recognition software. While it has been reviewed by human transcribers, it may contain errors. Please review the episode audio before quoting from this transcript and email [email protected] with any questions.

Can you hear — Fred, can you hear me?

[DISTORTED SPEECH]:

The internet is a little wonky.

OK. Well, [DISTORTED SPEECH]: Arizona. So the internet speed here isn’t really fast.

I think we’re going to call — yeah, I think we’re going to call you back on a — for the first time in a really long time — a landline.

[PHONE RINGING]

Hey, Fred, it’s Michael Barbaro.

You can hear me OK?

I can hear you.

Perfect. So, Fred, where exactly am I reaching you?

I’m in Portal, Arizona, in a little community called Arizona Sky Village. And it’s a very rural community. So our internet and phone lines are not very good. And the nearest grocery store is 60 miles away.

Wow. And why would you choose to live in such a remote place with such bad internet?

Because the sky is dark. It’s like the sky was a hundred years ago before cities encroached on all of the country. I guess you’d call it an astronomy development. Mainly, amateur astronomers who have built homes here far from city lights for the express purpose of studying the sky.

[MUSIC PLAYING]

So it’s literally a community where once the sun goes down, it’s pitch black. And some, perhaps all of you, are stargazing?

Yes, exactly.

Well, I think I’m beginning to understand why you might have the nickname that you do. Can you just tell our listeners what that nickname is?

My nickname is Mr. Eclipse.

From “The New York Times,” I’m Michael Barbaro. This is “The Daily.” Today’s total solar eclipse will be watched by millions of people across North America, none of them as closely as Fred Espenak, a longtime NASA scientist who’s devoted his entire life to studying, chasing, and popularizing the wonder that is an eclipse.

It’s Monday, April 8.

Fred, help me understand how you become Mr. Eclipse, how you go from being Fred to this seemingly very hard-earned nickname of Mr. Eclipse.

Well, I was visiting my grandparents at their summer home. And it was a partial eclipse of the sun back in the early 1960s. And I was a 10 - or 12-year-old kid. I got my parents to get me a small telescope. And I watched some of the partial phases. And it was really interesting.

And I started reading about eclipses. And I found out that as interesting as a partial eclipse is, a total eclipse is far more interesting. The moon is only 1/400 the diameter of the sun. It’s tiny compared to the sun. But it’s 400 times closer to the Earth. So it’s just this incredible coincidence that the moon and sun appear to be the same size in the sky. And once in a while, the moon passes directly between the Earth and the sun. And you’re plunged into this very strange midday twilight.

But they’re limited to a very small geographic areas to see a total eclipse. And this little book I was studying had a map of the world, showing upcoming paths of total solar eclipses. And I realized that one was passing through North America about 600 miles from where I lived. And that eclipse was in 1970.

And I was reading about this in 1963, 1964. And I made a promise to myself that I was going to get to that eclipse in 1970 to see it because I thought it was a one chance in a lifetime to see a total eclipse of the sun.

So just to be very clear, you see a partial eclipse, and you immediately think to yourself, that was fine. But I need the real thing. I need a full eclipse. And you happen to find out, around this time, that a real eclipse is coming but in seven years.

Right. I mean, there were other eclipses between that time and seven years in the future. But they were in other parts of the world. And I couldn’t buy an airplane ticket and fly to Europe or Australia.

And by 1970, I’d been waiting for this. And by this point, I had just gotten a driver’s license. And I convinced my parents to let me drive the car 600 miles to get down into the path of totality to see this great event.

Wow. Wait, from where to where?

From Staten Island, New York, down to a little town in North Carolina.

How did you convince your parents to let you do that? I mean, that’s —

Well, I had seven years to work on it.

[LAUGHS]: Right.

And I was just a nerdy kid. I didn’t get into trouble. I was interested in science. I was out in the woods, studying frogs and wildlife and stuff. So this was just a natural progression of the type of things I would normally do.

Right. OK. So I wonder if you can describe this journey you end up taking from Staten Island. How does the trip unfold as you’re headed on this 600 mile?

So, I think, on March 6, 1970, it was a Friday. My friend and I left to drive to the eclipse path. We probably got on the road probably at 5:00 AM because it was going to be a very long day.

And we’ve got a detailed map in the car, which I’ve plotted the eclipse path on. And we’re just trying to get far enough south to get into the path of the eclipse, which for us is easternmost Virginia or Eastern North Carolina. And I drive and drive and drive all day long. Very long day.

We get down to North Carolina right about maybe 6:00 PM. And we just see this little town in North Carolina that we’re driving through. And it happens to have a convenient motel right in the center of the path. And that was good enough. Got a room available. And we check in. And that’s where we’re going to watch the eclipse from.

And the next morning was eclipse day. It was a bright, crisp, sunny morning. There weren’t any clouds at all in the sky. And I was amazed that outside the back of the motel, in this grassy field, there were dozens and dozens of people with telescopes out there, specifically there for the eclipse that morning.

We were really excited about this. We set up our — my telescope. And we had another camera set up to watch it. And we walked around and marveled at some of the other people and their telescopes and discussed the eclipse with them. And the eclipse started probably around noon or 1:00 in the afternoon.

Describe the actual event itself, the eclipse. How did it begin?

Well, all solar eclipses begin as a partial eclipse. And the sun is gradually covered by the moon as the moon takes larger and larger pieces out of the sun, as it slowly crawls across the sun’s surface. And you don’t really notice much going on with a naked eye.

It’s really only in the last 10 minutes or so that you start to notice changes in the environment because now enough of the sun has been covered, upwards of maybe 90 percent of the sun. And you start to notice the temperature falling. There’s a chill in the air.

Also, since so much of the sun is covered, the daylight starts to take on an anemic quality. It’s weak. The sun is still too bright to look at. But the surroundings, the environment is not as bright as it was a half hour earlier.

You start to notice animals reacting to the dwindling sunlight. They start acting like it’s sunset. And they start performing some of their evening rituals, like birds roosting, perhaps calling their evening songs. And plants start closing up and the dropping sunlight. And then the dropping temperatures.

And there’s an acceleration now of all these effects. The temperature drop, the drop in the sunlight, it starts happening faster and faster and getting darker and darker. And maybe about a minute before the total eclipse began, we noticed strange patterns on the ground beneath us, on the grassy field that we were on — these ripples racing across the field. And these are something called shadow bands.

They look a lot like the rippling patterns that you would see on the bottom of a swimming pool, bands of light and dark, and moving very quickly across the ground. The sky is — it’s a dark blue. And it’s getting darker rapidly in this dwindling sunlight. And you go from daylight to twilight in just 10 or 20 seconds. It’s almost like someone has the hand on the rheostat and turns the house lights down in the theater.

You just see the light just go right down.

And the sky gets dark enough that the corona, the outer atmosphere of the sun, starts emerging from the background sky. This ring or halo of gas that surrounds the sun, and it’s visible around the moon, which is in silhouette against the sun. And along one edge of the moon is this bright bead of sunlight because that’s the last remaining piece of the sun before it becomes total.

And this is the diamond ring effect because you’ve got the ring of the corona and this dazzling jewel along one edge of it. You only get to see this for 10 or 15 seconds — it’s very fleeting — before the moon completely covers the sun’s disk. And totality begins. Suddenly, you’re in this twilight of the moon’s shadow.

And you look around the horizon. And you’re seeing the colors of sunrise or sunset 360 degrees around the horizon because you’re looking out the edge of the moon’s shadow. And looking back up into the sky, the sun is gone now. And you see this black disk of the moon in silhouette surrounded by the sun’s corona.

Maybe this says more about my nature than anything else, but what you’re describing, a little bit, feels like the end of the world.

Well, I think, when you see this all transpire, you can easily understand how people thought this was the end of the world because it seems far outside of the realms of nature. It seems supernatural. So you can see how people panicked that didn’t understand what was going on.

That was not your reaction?

No. I think it’s a sense of belonging — belonging to this incredible universe, both belonging and a humbleness that how minuscule we are. And yet we’re a part of this fantastic cosmic wheel of motion in the solar system. You almost get a three-dimensional sense of the motions of the Earth and the moon around the sun when you see this clockwork displayed right in front of you, this mechanics of the eclipse taking place.

It almost lifts you up off the planet, and you can look back down at the solar system and see how it’s all put together. And you’ve only got to, in that case — in that particular eclipse, it was only 2 and 1/2 minutes to look at this.

Wow. It’s kind of a clock in your head, saying, you don’t have much of this.

You don’t have much of it. And it almost seems like time stops.

And at the same time, all of a sudden, the eclipse is over. Those 2 minutes just raced by. And it’s over. All of a sudden, the diamond ring forms again on the opposite side of the moon, as the sun starts to become uncovered at the end of totality. And the diamond ring appears. It grows incredibly bright in just a few seconds. And you can’t look at it anymore. It’s too bright. You’ve got to put your filters back on and cover your telescope with a solar filter so it doesn’t get damaged. And you’re trembling because of this event.

Everybody was cheering and shouting and yelling. I mean, you would have thought you were at a sports game, and the home team just scored a touchdown. Just everybody screaming at the top of their lungs. And I immediately started thinking that this can’t be a once in a lifetime experience. I’ve got to see this again.

We’ll be right back.

OK. So, Fred, it’s the early 1970s. And you are not Mr. Eclipse yet. You’re just a kid who felt something very big when you watched an eclipse. So how did you end up becoming the premier authority that you now are on eclipses?

Well, after that 1970 eclipse, I started looking into upcoming solar eclipses so I could get a chance to see the sun’s corona again. And the next total eclipse was in Eastern Canada in July of 1972. And I started thinking about that eclipse. And by then, I was going to be in college.

And I started planning because that one was still something I could drive to. It was 1,200 miles instead of 600 miles.

So the summer of 1972 rolls around. And I drove up to the eclipse in Quebec to see totality and was unfortunately clouded out of the eclipse. I saw some of the partial phases. But clouds moved in and obscured the sun for that view of the sun’s corona.

You were robbed.

I was robbed. And I realized, well, I’ve got to expand my outlook on what’s an acceptable distance to travel to see a total eclipse because the next total eclipse then, in 1973, was through the Sahara Desert in Northern Africa. So I traveled to the Sahara desert for the eclipse, where we had decent weather, not perfect but decent weather. And we got to see totality there.

You saw totality in the desert?

In the desert. In the Sahara Desert. After that, it was just trying to get to every total eclipse I possibly could get to.

At this point, you’re clearly starting to become an eclipse chaser. And I don’t even know if such a thing existed at that moment.

Yeah. I don’t know if it was called that then, but certainly, yeah.

And if you’ll permit me a question that might seem maybe dopey to someone in your field, after you’ve seen one or two or three of these, do they start to blend in together and become a little bit the same?

Not at all. Each one is distinctly different. The sun itself is dramatically different. The sun’s corona is different at each eclipse because the corona is a product of the sun’s magnetic field. And that magnetic field is changing every day. So the details, the fine structure in the sun’s corona is always different. So every eclipse is dramatically different. The appearance of the sun’s corona.

Right. If you look at one Renoir, it’s not the same as the next one. You’re describing the corona of each eclipse as its own work of art, basically.

Exactly. Yeah.

So as you’re chasing these eclipses around the world, what is the place of an eclipse in your day-to-day academic studies and, soon enough, your professional work?

So I went to grad school at University of Toledo and did some work at Kitt Peak National Observatory, learning the ins and outs of photometric photometry — that is, measuring the brightness of stars. And eventually, this led to a job opening at the NASA Goddard Space Flight Center.

And I got interested in the idea of predicting eclipses and started studying the mathematics of how to do this. And I took it over unofficially and started publishing these technical maps and details. And we published about a dozen books through NASA on upcoming eclipses. People would just write me a letter and say they wanted a copy of the eclipse bulletin for such and such an eclipse. And I would stuff it in an envelope and mail it to them.

So you take it upon yourself to make sure that everyone is going to know when the next eclipse is coming?

And no doubt, during this period, you keep going to each and every eclipse. And I wonder which of them stand out to you.

Well, I’ve seen total eclipses from Australia, from Africa, from the Altiplanos in Bolivia, from the ice sheet on the coast of Antarctica, and even from Northern China, on the edge of the Gobi Desert. But one of the most notable eclipses for me was I traveled to India to see a 41-second eclipse, which was very short. And besides seeing a great eclipse in India, I also met my future wife there. She was on the same trip.

I have to hear that story.

Well, she had been trying to see a total eclipse for about 25 years.

She tried to see the 1970 eclipse. But her friends who were going to drive down from Pennsylvania down to North Carolina talked her out of it at the 11th hour.

They talked her out of seeing the same eclipse that was your first total eclipse that was so important to you?

Yes. And they talked her out of it because from Pennsylvania, they were going to have maybe a 90 percent eclipse. They didn’t know any better. They thought that was good enough. And she regretted that decision.

So then she said, OK, well, I’ve got to get to the next total eclipse, which was in Quebec in 1972, the same one that was my second eclipse. And we were probably within five miles of each other in Quebec. And we were both clouded out. Then she was married. She was raising kids. She got busy with domestic life for 20 years. She became a widow.

So now, 1995, there’s this 41-second eclipse in India that is very difficult to get to. It’s halfway around the world. But she’s still itching to see a total eclipse. And we joined the same expedition, a travel group, of 30 eclipse chasers and end up in India for the eclipse. And we have fantastic weather. It’s perfect.

She was in tears after totality. She had been waiting so long to see it. And we struck up a friendship on that trip. By the time the 1998 eclipse was taking place in the Caribbean, at that point, we were together. That was our first eclipse to observe as a couple. I think our wedding cake had a big eclipse on the top of the cake.

[LAUGHS]: Perfect.

We made a music CD for the wedding that we played during the reception. And of course, all the music on the CD had sun and moon themes to it.

Nothing I can say, a total eclipse of the heart

Of course, we had “Total Eclipse of the Heart.” It was a must-have.

Had to. Had to.

It strikes me, Fred, that eclipses are such an organizing principle in your life. Your life seems to literally orbit around them. When you were a kid, you started planning for them years in advance. This work becomes central to your career. It’s how you meet your wife.

And you said, when I asked you, about each eclipse that they’re all different. And obviously, you’re different at each eclipse because time has passed. Your life has changed. And it just feels like your life is being lived in a kind of ongoing conversation with this phenomenon of the sun and the moon overlapping.

Well, the eclipses are like benchmarks that I can use to figure out what else was going on in my life during these times, because I remember the dates of every single eclipse I’ve been to. And if I see a photograph of the solar corona shot during any particular eclipse, I know what eclipse that was. I can recognize the pattern of the corona like a fingerprint.

That’s amazing.

And I the year of the eclipse. It reminds me of when Pat and I got married and between which eclipse we were getting married and had to plan our wedding so it didn’t interfere with any kind of eclipse trips.

And they just serve as benchmarks or markers for the rest of my life of when various eclipses take place. So they’re easy for marking the passage of time.

So we are, of course, talking to you a few days before this year’s eclipse, which I cannot fathom you missing. So where are you planning to watch this total eclipse?

Pat and I are leaving for Mazatlán, Mexico, actually tomorrow. And we’ve got about 80 people joining us down in Mazatlán for this eclipse in our tour group.

And for you, of course, this year’s eclipse is just the latest in a very long line of eclipses. But I think, for the rest of us — and here, I’m thinking about myself — this is really going to be my first total eclipse, at least that I can remember. And for my two little kids, it’s absolutely going to be their first.

And given the hard-earned wisdom that you’ve accumulated in all your decades of chasing eclipses around the world, I wonder if you can give us just a little bit of advice for how to best live inside this very brief window of a total solar eclipse, to make sure, not to be cliche, but that we make it count.

Well, I think one mistake that people tend to make is getting preoccupied with recording everything in their lives, what they had for lunch, what they had for dinner. And seeing the eclipse is something that you want to witness firsthand. Try to be present in seeing the eclipse in the moment of it. So don’t get preoccupied with recording every instant of it.

Sit back and try to take in the entire experience because those several minutes pass by so rapidly. But you’ll replay them in your mind over and over and over again. And you don’t want technology getting between you and that experience. And remember to take your eclipse glasses off when totality begins. Note how dark it gets during totality.

Take the glasses off because?

Well, the glasses protect your eyes from the sun’s bright disk. But when totality begins, the sun’s bright disk is gone. So if you use your solar eclipse glasses to try to look at the corona, you won’t see anything. You’ll just see blackness. You’ve got to remove the eclipse glasses in order to see the corona. And it’s completely safe.

And it’s an incredible sight to behold. But during totality, you just want to look around without the glasses on. And take in the sights. Take in the horizon, 360 degrees, surrounding you with these twilight colors and sunset colors.

You’ll easily be able to see Jupiter and Venus shining on either side of the sun during totality. And look at the details in the sun’s corona, fine, wispy textures, and any possible red prominences hugging against the moon’s disk during totality.

And let’s say it’s now the moment of totality, and you, Mr. Eclipse, can whisper one thing into someone’s ear as they’re watching. What would you say to them?

Enjoy. Just take it all in.

Well, Fred, thank you very much. We really appreciate it.

No, thank you. I hope everybody has some clear sky.

After today, the next total solar eclipse to be visible from the continental United States will occur 20 years from now, in 2044. In other words, you might as well watch today’s.

Here’s what else you need to know today. Israel has fired two officers in connection with the deadly airstrike on aid workers from the World Central Kitchen who were killed last week while delivering food to civilians in Gaza. In a report released on Friday, Israel blamed their deaths on a string of errors made by the military. The airstrike, Israel said, was based on insufficient and incorrect evidence that a passenger traveling with the workers was armed.

Meanwhile, Israel said it withdrew a division of ground troops from Southern Gaza on Sunday, leaving no soldiers actively patrolling the area. The move raises questions about Israel’s strategy as the war drags into its sixth month. In particular, it casts doubt on Israel’s plans to invade Rafah, Gaza’s southernmost city, an invasion that the United States has asked Israel not to carry out for fear of large-scale civilian casualties.

Today’s episode was produced by Alex Stern and Sydney Harper, with help from Will Reid and Jessica Cheung. It was edited by Devon Taylor; fact-checked by Susan Lee; contains original music by Dan Powell, Marion Lozano, Elisheba Ittoop, and Corey Schreppel; and sound design by Elisheba Ittoop and Dan Powell. It was engineered by Chris Wood. Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly. Special thanks to Anthony Wallace.

[THEME MUSIC]

That’s it for “The Daily.” I’m Michael Barbaro. See you tomorrow.

• April 9, 2024   •   30:48 How Tesla Planted the Seeds for Its Own Potential Downfall
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• April 5, 2024   •   29:11 An Engineering Experiment to Cool the Earth
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• April 1, 2024   •   36:14 Ronna McDaniel, TV News and the Trump Problem
• March 29, 2024   •   48:42 Hamas Took Her, and Still Has Her Husband
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• March 27, 2024   •   28:06 Democrats’ Plan to Save the Republican House Speaker
• March 26, 2024   •   29:13 The United States vs. the iPhone

Hosted by Michael Barbaro

Produced by Sydney Harper and Alex Stern

With Will Reid and Jessica Cheung

Edited by Devon Taylor

Original music by Dan Powell ,  Marion Lozano ,  Elisheba Ittoop and Corey Schreppel

Sound Design by Elisheba Ittoop and Dan Powell

Engineered by Chris Wood

Listen and follow The Daily Apple Podcasts | Spotify | Amazon Music

Today, millions of Americans will have the opportunity to see a rare total solar eclipse.

Fred Espenak, a retired astrophysicist known as Mr. Eclipse, was so blown away by an eclipse he saw as a teenager that he dedicated his life to traveling the world and seeing as many as he could.

Mr. Espenak discusses the eclipses that have punctuated and defined the most important moments in his life, and explains why these celestial phenomena are such a wonder to experience.

On today’s episode

Fred Espenak, a.k.a. “Mr. Eclipse,” a former NASA astrophysicist and lifelong eclipse chaser.

Background reading

A total solar eclipse is coming. Here’s what you need to know.

Millions of people making plans to be in the path of the solar eclipse on Monday are expecting an awe-inspiring. What is that feeling?

The eclipse that ended a war and shook the gods forever.

There are a lot of ways to listen to The Daily. Here’s how.

We aim to make transcripts available the next workday after an episode’s publication. You can find them at the top of the page.

Fact-checking by Susan Lee .

Special thanks to Anthony Wallace.

The Daily is made by Rachel Quester, Lynsea Garrison, Clare Toeniskoetter, Paige Cowett, Michael Simon Johnson, Brad Fisher, Chris Wood, Jessica Cheung, Stella Tan, Alexandra Leigh Young, Lisa Chow, Eric Krupke, Marc Georges, Luke Vander Ploeg, M.J. Davis Lin, Dan Powell, Sydney Harper, Mike Benoist, Liz O. Baylen, Asthaa Chaturvedi, Rachelle Bonja, Diana Nguyen, Marion Lozano, Corey Schreppel, Rob Szypko, Elisheba Ittoop, Mooj Zadie, Patricia Willens, Rowan Niemisto, Jody Becker, Rikki Novetsky, John Ketchum, Nina Feldman, Will Reid, Carlos Prieto, Ben Calhoun, Susan Lee, Lexie Diao, Mary Wilson, Alex Stern, Dan Farrell, Sophia Lanman, Shannon Lin, Diane Wong, Devon Taylor, Alyssa Moxley, Summer Thomad, Olivia Natt, Daniel Ramirez and Brendan Klinkenberg.

Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly. Special thanks to Sam Dolnick, Paula Szuchman, Lisa Tobin, Larissa Anderson, Julia Simon, Sofia Milan, Mahima Chablani, Elizabeth Davis-Moorer, Jeffrey Miranda, Renan Borelli, Maddy Masiello, Isabella Anderson and Nina Lassam.

Corey Schreppel leads the technical team that supports all Times audio shows, including “The Daily,” “Hard Fork,” “The Run-Up,” and “Modern Love.” More about Corey Schreppel

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Welcome to the daily solving of our PROBLEM OF THE DAY with Yash Dwivedi . We will discuss the entire problem step-by-step and work towards developing an optimized solution. This will not only help you brush up on your concepts of DP but also build up problem-solving skills. In this problem, we are given, there are n stairs, and a person standing at the bottom wants to reach the top. The person can climb either 1 stair or 2 stairs at a time. Count the number of ways, the person can reach the top (order does not matter).

Input: n = 4 Output:  3 Explanation:  You can reach 4th stair in 3 ways. 3 possible ways are: 1, 1, 1, 1 1, 1, 2 2, 2 Here, note that {1, 1, 2}, {1, 2, 1} and {2, 1, 1} are considered same as their order does not matter.  Give the problem a try before going through the video. All the best!!! Problem Link: https://www.geeksforgeeks.org/problems/count-ways-to-nth-stairorder-does-not-matter1322/1 Solution IDE Link: https://ide.geeksforgeeks.org/online-cpp14-compiler/2fd77a44-ecda-43e5-8eef-856f5a1cded5