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How to Solve Coding Problems: Step-by-Step Guide (2024)

May 20, 2024 · 13 min read

Coding challenges are a common obstacle for many programmers, whether they are just starting or have years of experience.

In this complete guide, we will provide expert tips and strategies for effectively solving coding problems.

By following these valuable tips, you can confidently enhance your problem-solving skills and conquer even the most challenging coding tasks.

Let's get started.

Read the Problem Statement Carefully

Identify key constraints

One imperative step in solving coding problems is identifying the key constraints in the problem statement. These constraints define the boundaries within which your solution must operate and can greatly influence your approach.

Note important variables

Carefully note down important variables mentioned in the problem statement as they often hold crucial information for solving the problem efficiently.

Understanding the significance of these variables can guide you toward the right solution approach.

Remember to consider any implicit variables that might affect your solution but are not explicitly mentioned in the problem statement.

Attention to all variables will ensure a more comprehensive understanding of the problem.

Tip:  Here, you can learn about key  programming definitions and terms

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Break Down Complexity

Divide into smaller Tasks

You'll find that breaking down a complex coding problem into smaller tasks makes it more manageable.

Start by identifying the different components of the problem and breaking them down into smaller subproblems. This approach will help you tackle each subproblem individually and eventually solve the larger problem.

Focus on one task

The key to successfully breaking down a complex coding problem is to focus on one task at a time.

Concentrating all your efforts on solving one specific subproblem can help you avoid feeling overwhelmed by the complexity of the overall task.

This focused approach will improve your problem-solving skills and allow you to make steady progress toward the final solution.

When focusing on one task, setting clear goals and objectives for that specific subproblem is vital. It will help you stay on track and prevent distractions derailing your problem-solving process.

By dedicating your full attention and energy to each task, you can efficiently work through the complexities of the coding problem and find an effective solution.

Tip:  The  Feynman learning technique  is the best solution for learning how to break down complex concepts.

Research and Learn

Study similar problems

Research shows that one of the best strategies to solve coding problems easily is to study similar problems.

By analyzing how others have approached and solved comparable issues, you can gain valuable insights and techniques to apply to your challenges.

Learn new concepts

Learning new concepts is imperative for continuous improvement in coding.

By staying updated with the latest technologies, algorithms, and best practices, you can enhance your problem-solving skills and broaden your understanding of different coding techniques.

Any aspiring coder should regularly explore new concepts through online courses, tutorials, and coding challenges.

This proactive approach helps solve current problems more effectively and prepares you for future challenges in the ever-evolving tech industry.

Tip:  The fastest way to learn any new concept is to share what you learn. For example, you can learn a piece of code and then use  code sharing tools  to share your knowledge with the audience.

Write Pseudocode First

Plan out Algorithm Steps

For effective problem-solving, it is crucial to plan out the steps of your algorithm before writing actual code.

Pseudocode helps break down the problem into smaller, manageable steps, making it easier to implement the solution in the chosen programming language.

Visualize solution flow

While writing pseudocode, visualize how the solution will flow from one step to another.

This visualization helps in understanding the logic of the algorithm and can highlight any potential issues or optimizations that can be made before writing actual code.

For instance, if you are working on a sorting algorithm, visualizing the flow can help you determine the most efficient way to arrange the elements and identify any redundant steps that you can eliminate to improve performance.

Start with Simple

Implement basic solution

Unlike complex problems, coding problems are best tackled with a straightforward approach.

Begin by implementing a basic solution that may not be the most efficient but solves the problem correctly.

This helps in understanding the problem better and getting a working solution.

Refine as needed

Implementing a basic solution is just the beginning.

As you progress, refine your code by optimizing it for performance, readability, and scalability.

Refactoring code to improve efficiency and incorporating best practices will boost your solution to the next level.

A key strategy for refining your code is to analyze its complexity and identify areas for optimization. This may involve revisiting your algorithm choices and data structures or breaking down the problem into smaller, manageable parts.

By continuously refining your solution, you improve your coding skills and enhance the quality of your code.

Use Online Resources

Leverage coding communities

Despite the various challenges of coding problems, the process becomes easier when you tap into the wealth of knowledge available in coding communities.

These online platforms, such as Stack Overflow and GitHub, offer a supportive environment where you can seek solutions, ask questions, and learn from experienced programmers.

Consult online tutorials

These resources provide step-by-step guidance on various programming concepts and problem-solving techniques, making grasping complex algorithms and data structures easier.

The abundance of online tutorials ranges from beginner to advanced, and they are fit for programmers of all proficiency levels.

By consulting these tutorials, you can enhance your understanding of coding principles and develop effective strategies for solving various coding problems.

Any aspiring coder should take advantage of the vast array of online resources that can facilitate the process of solving coding problems.

By leveraging coding communities, consulting online tutorials, and exploring other online platforms, you can quickly sharpen your problem-solving skills and become a more proficient programmer.

Tip:  Resources like YouTube and Udemy are great ways. But you can also read the  best development books  to enhance your coding skills further.

Debug Thoroughly

Identify common mistakes

Unlike overlooking small errors, identifying common mistakes is crucial in debugging code efficiently.

Any coder should be aware of recurring issues like:

• Syntax Errors
• Logical mistakes
• Incorrect variable usage

By recognizing these patterns, programmers can initiate debugging and write cleaner code.

Test edge cases

Any comprehensive debugging strategy should include testing edge cases to ensure code reliability and robustness.

By intentionally pushing the boundaries of input values or conditions, developers can uncover potential mistakes that might go unnoticed during regular testing.

This practice helps programmers anticipate and address unexpected scenarios, leading to more resilient code.

Testing edge cases involves evaluating the extremes of input data or conditions to verify the code's behavior under challenging circumstances.

By examining how the program handles unusual or extreme values, developers can identify vulnerabilities or inefficiencies that may occur in real-world usage.

Practice Regularly

Build problem-solving muscle

Your coding skills are like a muscle that needs regular exercise to strengthen. Make a habit of solving coding problems daily to enhance your problem-solving abilities.

Develop coding instincts

Build a strong intuition for coding by practicing regularly.

As you solve more problems, you'll notice patterns and common strategies that can help you tackle new problems more efficiently.

Developing coding instincts involves understanding different approaches to problem-solving and knowing when to apply them. This initiative will guide you in choosing the most effective solutions and optimizing your code for better performance.

Review and Refine

Analyze solution efficiency

Unlike simply finding a solution, it is imperative to analyze its efficiency.

Evaluate the time complexity, space complexity, and overall performance of the code.

This step will help you understand how the code will perform with larger inputs and whether there are any bottlenecks that need to be addressed.

Optimize code quality

Coding problems are not just about finding a solution but also about writing clean and efficient code.

Pay attention to coding standards, readability, and best practices.

Refactor the code to make it more concise, understandable, and maintainable. This step is crucial in ensuring that your code is not only functional but also of high quality.

You can use tools like linters and code formatters to check and improve your code's quality automatically.

These tools can help you catch potential errors, enforce coding standards, and enhance the overall readability of your codebase.

By optimizing your code quality, you can make it easier for yourself and others to understand and work with the code in the future.

Tip:  You can use a  code review checklist  to optimize code efficiency quickly.

Learn from Others

Study open-source code

Study open-source code to truly enhance your coding skills.

By studying the work of experienced developers, you can gain insight into different perspectives, problem-solving techniques, and coding styles.

This exposure can broaden your knowledge and inspire innovative solutions to coding problems.

Learn from mentors

Some of the most effective learning experiences come from mentors who can provide guidance, feedback, and real-world insights.

Connecting with experienced professionals in the field can offer valuable advice, help you navigate challenges, and accelerate your learning process.

Learn from mentors who have expertise in your specific area of interest.

Their guidance can help you grasp complex concepts, avoid common pitfalls, and stay updated on industry trends.

Building a strong mentorship relationship can significantly impact your coding journey and foster professional growth.

Stay Calm and Patient

Manage problem-solving stress

After encountering a challenging coding problem, managing the stress that comes with it is imperative.

Take deep breaths, step back, and remind yourself that feeling stuck is okay.

Keeping a clear mind will help you approach the problem more effectively.

Take breaks when needed

If you find yourself hitting a wall and getting frustrated, it's time to take a break.

Stepping away from the problem for a few minutes or even an hour can improve your mental clarity.

Some fresh air or a quick walk can help reset your mind and improve focus when you return to the task.

When stress builds up, it can blur your thinking and make problem-solving even more challenging.

Taking breaks gives you a chance to relax and allows your brain to subconsciously work on the problem in the background, often leading to new insights and solutions.

Identify Patterns

Recognize common patterns

One vital skill in solving coding problems is recognizing common patterns.

By identifying recurring themes or structures in the problem you're trying to solve, you can apply similar solutions that have worked in the past. It can help simplify your problem-solving process and lead to more efficient coding.

Apply pattern-based solutions

To effectively apply pattern-based solutions, you need to understand different types of patterns commonly found in coding problems.

These patterns can include algorithms like sliding windows, two-pointers, or depth-first search.

By leveraging these patterns, you can quickly develop solutions that have been proven to work for similar problems.

Tip:  You can explore different  development frameworks  to identify common patterns.

Draw Diagrams

Visualize problem structure

When faced with a complex coding problem, start by visualizing its structure.

Use diagrams to represent different components, their relationships, and data flow. This visual representation can clarify the problem and help you identify key areas to focus on.

Illustrate solution flow

While solving coding problems, illustrating the solution flow through diagrams can facilitate the problem-solving process.

Create a step-by-step flowchart or sequence diagram to map the logic and algorithm.

This visual aid can guide you through the implementation phase and help you identify potential errors or optimizations in the solution.

Diagrams can also serve as documentation for your code, making it easier for others to understand your thought process and approach.

By incorporating visual elements into your problem-solving strategies, you can enhance your efficiency and accuracy in coding.

Collaborate with Peers

Work with coding partners

For an effective problem-solving strategy, consider working with coding partners.

Collaborating with peers can help you bounce ideas off each other, share different approaches, and collectively develop innovative solutions.

By leveraging your peers diverse skills and perspectives, you can tackle coding problems more efficiently and effectively.

Learn from peer feedback

Even the most experienced coders can benefit from constructive feedback from their peers.

Peer feedback can provide valuable insights into alternative solutions, code optimization techniques, and potential pitfalls to avoid.

You can continuously improve your problem-solving skills and expand your coding knowledge by actively seeking and incorporating feedback from your coding peers.

Work with your coding partners to brainstorm ideas, discuss different approaches, and troubleshoot any challenges you encounter.

Creating a collaborative environment with your peers can enhance your problem-solving abilities and accelerate your learning process.

Final Words

Mastering the key skills mentioned above will help you solve coding problems more easily and efficiently.

Buffing your problem-solving skills, staying organized, and utilizing various techniques such as pseudocoding and debugging can help you tackle coding challenges with confidence and precision.

Keep practicing and implementing these strategies to enhance your problem-solving abilities and become a more skilled coder.

Why is code optimization important in the problem-solving process?

Code optimization is important in the problem-solving process because it improves the code's performance and efficiency. Optimized code runs faster, requires less memory, and performs better with large input sizes. Optimization reduces the code's time and space complexity and ensures that it meets performance requirements.

Why is testing your code with different test cases important in coding problem-solving?

Testing your code with different test cases helps ensure your solution works correctly for various scenarios. It also helps identify edge cases, errors, and potential bugs in the code. Thorough testing enhances the reliability and accuracy of your code.

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20 Code Challenges To Put What You’re Learning to the Test

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Code challenges help you build problem-solving skills, better understand the programming language you use, and get to know algorithms you may not be familiar with. If you want to improve your skills in programming, there’s no better way than by writing code. In addition, coding challenges are convenient because they allow you to exercise your skills on a bite-sized problem and rarely require you to build a complete application, so you can usually complete them rather quickly.

Code challenges are also part of most coding interviews. Hiring managers may see the skills listed on your resume, and you may be able to talk like a programmer, but they also want to know that you can write code. By having you solve a coding challenge, they can assess your skills and be sure you can do the job. So working on coding challenges will also help you prepare for job interviews. We’ve collected 20 popular code challenges to get you started.

Learn something new for free

Intro to chatgpt, general programming challenges.

While most code challenges are small in scope, that doesn’t mean they won’t involve a complex solution, so it is best to choose a challenge that stretches your skills but isn’t completely out of your league. Below, we’ve ranked a few coding challenges by their complexity so you can find the best challenge for your skill level.

Basic code challenges

These are good beginner challenges. They may not actually show up in a coding interview, but everyone has to start somewhere. These challenges are good for practicing your skills at using a programming language.

• Build a binary search tree .
• Write a program that prints the numbers from 1 to 100. But for multiples of three, print Fizz instead of the number, and multiples of five, print Buzz. For numbers that are multiples of both three and five, print FizzBuzz .
• Print Hello World in several different ways in a programming language .
• Code in a new language .
• Write a function that will take a given string and reverse the order of the words .
• Write a function that will find the 50th number in the Fibonacci Sequence .
• Write a function that tests if a number, n, is a prime number .

Intermediate code challenges

These code challenges are examples of what might be asked in interviews. There may be a big difference in difficulty compared to the basic challenges. If you get stuck on these, go back to the basics, practice more, and you will get there.

• Write a function to check that a binary search tree is balanced .
• Write a function to reverse the order of words that have punctuation and keep the punctuation in place .
• Given two words (beginWord and endWord) and a dictionary’s word list, find the length of the shortest transformation sequence from beginWord to endWord .
• Write a function that will find the nth number in the Fibonacci Sequence .
• Write a function that will print out all prime numbers in a given string .

Hard code challenges

The point of these challenges is to challenge you, which will help you learn more. These will be similar to the type of work you’ll do on the job. Most of these challenges will be hard but use Big O notation and expect a certain type of performance. If you are struggling with these, search StackOverflow or Google for direction. Many developers have run into these types of problems and will help you find the solution. Just don’t cheat and copy the answer. What good would that do?

• Write a function that inserts a list of n numbers into a binary search tree that runs at O(n log n) time .
• Write a function to reverse the order of words with punctuation and keep the punctuation in place that runs at 0(n) time .
• Write a function that will find the nth number in the Fibonacci Sequence and runs at O(n) time .
• Write a function that tests if a number, n, is a prime number and a function that will print out all prime numbers in a given string as efficiently as possible .

Technology specific challenges

If you want to try some coding challenges that will test your skills on specific technologies, we have a few of those challenges.

Web development code challenges

• Build a web page for your favorite band . A fun challenge can be creating a webpage for your favorite musical artist. Start by using only static HTML , and if you want to challenge yourself, even more, add CSS and JavaScript . Then, for extra credit, build it in a front-end framework like React and make it an interactive experience.
• Recreate a magazine layout using Semantic HTML and CSS Flexbox . It is not always that easy to recreate a design. This code challenge will really test your skills with HTML and CSS by having you recreate a design from scratch on your own. Once you are a working web developer, you will be doing this daily.
• Build a static portfolio site . Once you finish the first two web development challenges listed here, you will have demonstrated your skills in web development. So why not take it a step further and show off those skills to the world or a potential employer by building a portfolio site? With this challenge, you will do just that. You can use HTML and CSS and, if you want, JavaScript. If you need help creating a portfolio, watch the video below for a step-by-step tutorial. And if you want to learn how to use JavaScript to make it interactive, check out Part 2 .

Financial data analysis code challenges

Maximize stock trading profit . This is reportedly a question asked in a Google interview and will test your skills in analyzing financial data . There are three levels to this challenge:

• Basic: Given the daily values of a stock, write a program that will find how you can gain the most with a single buy-sell-trade.
• Intermediate: Given the daily values of a stock over several days n , write a program that will find how you can gain the most with a combination of buy-sell trades.
• Hard: Complete both the basic and intermediate algorithms in the most efficient way possible.

Code challenges are a great way to practice your coding skills or keep yourself from getting rusty. Building complete applications will also teach you a lot, but they can take time to finish. On the other hand, a coding challenge can be completed in an evening and will expose you to new algorithms and programming concepts. They are also part of many coding interviews, so completing a few can help you prepare for a job interview. For more details on the code challenges we have, check out Essential Information on Code Challenges .

Whether you’re looking to break into a new career, build your technical skills, or just code for fun, we’re here to help every step of the way. Check out our blog post about how to choose the best Codecademy plan for you to learn about our structured courses, professional certifications, interview prep resources, career services, and more.

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How to think like a programmer — lessons in problem solving

by Richard Reis

If you’re interested in programming, you may well have seen this quote before:

“Everyone in this country should learn to program a computer, because it teaches you to think.” — Steve Jobs

You probably also wondered what does it mean, exactly, to think like a programmer? And how do you do it??

Essentially, it’s all about a more effective way for problem solving .

In this post, my goal is to teach you that way.

By the end of it, you’ll know exactly what steps to take to be a better problem-solver.

Why is this important?

Problem solving is the meta-skill.

We all have problems. Big and small. How we deal with them is sometimes, well…pretty random.

Unless you have a system, this is probably how you “solve” problems (which is what I did when I started coding):

• Try a solution.
• If that doesn’t work, try another one.
• If that doesn’t work, repeat step 2 until you luck out.

Look, sometimes you luck out. But that is the worst way to solve problems! And it’s a huge, huge waste of time.

The best way involves a) having a framework and b) practicing it.

“Almost all employers prioritize problem-solving skills first.

Problem-solving skills are almost unanimously the most important qualification that employers look for….more than programming languages proficiency, debugging, and system design.

Demonstrating computational thinking or the ability to break down large, complex problems is just as valuable (if not more so) than the baseline technical skills required for a job.” — Hacker Rank ( 2018 Developer Skills Report )

Have a framework

To find the right framework, I followed the advice in Tim Ferriss’ book on learning, “ The 4-Hour Chef ”.

It led me to interview two really impressive people: C. Jordan Ball (ranked 1st or 2nd out of 65,000+ users on Coderbyte ), and V. Anton Spraul (author of the book “ Think Like a Programmer: An Introduction to Creative Problem Solving ”).

I asked them the same questions, and guess what? Their answers were pretty similar!

Soon, you too will know them.

Sidenote: this doesn’t mean they did everything the same way. Everyone is different. You’ll be different. But if you start with principles we all agree are good, you’ll get a lot further a lot quicker.

“The biggest mistake I see new programmers make is focusing on learning syntax instead of learning how to solve problems.” — V. Anton Spraul

So, what should you do when you encounter a new problem?

Here are the steps:

1. Understand

Know exactly what is being asked. Most hard problems are hard because you don’t understand them (hence why this is the first step).

How to know when you understand a problem? When you can explain it in plain English.

Do you remember being stuck on a problem, you start explaining it, and you instantly see holes in the logic you didn’t see before?

Most programmers know this feeling.

This is why you should write down your problem, doodle a diagram, or tell someone else about it (or thing… some people use a rubber duck ).

“If you can’t explain something in simple terms, you don’t understand it.” — Richard Feynman

Don’t dive right into solving without a plan (and somehow hope you can muddle your way through). Plan your solution!

Nothing can help you if you can’t write down the exact steps.

In programming, this means don’t start hacking straight away. Give your brain time to analyze the problem and process the information.

To get a good plan, answer this question:

“Given input X, what are the steps necessary to return output Y?”

Sidenote: Programmers have a great tool to help them with this… Comments!

Pay attention. This is the most important step of all.

Do not try to solve one big problem. You will cry.

Instead, break it into sub-problems. These sub-problems are much easier to solve.

Then, solve each sub-problem one by one. Begin with the simplest. Simplest means you know the answer (or are closer to that answer).

After that, simplest means this sub-problem being solved doesn’t depend on others being solved.

Once you solved every sub-problem, connect the dots.

Connecting all your “sub-solutions” will give you the solution to the original problem. Congratulations!

This technique is a cornerstone of problem-solving. Remember it (read this step again, if you must).

“If I could teach every beginning programmer one problem-solving skill, it would be the ‘reduce the problem technique.’

For example, suppose you’re a new programmer and you’re asked to write a program that reads ten numbers and figures out which number is the third highest. For a brand-new programmer, that can be a tough assignment, even though it only requires basic programming syntax.

If you’re stuck, you should reduce the problem to something simpler. Instead of the third-highest number, what about finding the highest overall? Still too tough? What about finding the largest of just three numbers? Or the larger of two?

Reduce the problem to the point where you know how to solve it and write the solution. Then expand the problem slightly and rewrite the solution to match, and keep going until you are back where you started.” — V. Anton Spraul

By now, you’re probably sitting there thinking “Hey Richard... That’s cool and all, but what if I’m stuck and can’t even solve a sub-problem??”

First off, take a deep breath. Second, that’s fair.

Don’t worry though, friend. This happens to everyone!

The difference is the best programmers/problem-solvers are more curious about bugs/errors than irritated.

In fact, here are three things to try when facing a whammy:

• Debug: Go step by step through your solution trying to find where you went wrong. Programmers call this debugging (in fact, this is all a debugger does).

“The art of debugging is figuring out what you really told your program to do rather than what you thought you told it to do.”” — Andrew Singer

• Reassess: Take a step back. Look at the problem from another perspective. Is there anything that can be abstracted to a more general approach?

“Sometimes we get so lost in the details of a problem that we overlook general principles that would solve the problem at a more general level. […]

The classic example of this, of course, is the summation of a long list of consecutive integers, 1 + 2 + 3 + … + n, which a very young Gauss quickly recognized was simply n(n+1)/2, thus avoiding the effort of having to do the addition.” — C. Jordan Ball

Sidenote: Another way of reassessing is starting anew. Delete everything and begin again with fresh eyes. I’m serious. You’ll be dumbfounded at how effective this is.

• Research: Ahh, good ol’ Google. You read that right. No matter what problem you have, someone has probably solved it. Find that person/ solution. In fact, do this even if you solved the problem! (You can learn a lot from other people’s solutions).

Caveat: Don’t look for a solution to the big problem. Only look for solutions to sub-problems. Why? Because unless you struggle (even a little bit), you won’t learn anything. If you don’t learn anything, you wasted your time.

Don’t expect to be great after just one week. If you want to be a good problem-solver, solve a lot of problems!

Practice. Practice. Practice. It’ll only be a matter of time before you recognize that “this problem could easily be solved with <insert concept here>.”

How to practice? There are options out the wazoo!

Chess puzzles, math problems, Sudoku, Go, Monopoly, video-games, cryptokitties, bla… bla… bla….

In fact, a common pattern amongst successful people is their habit of practicing “micro problem-solving.” For example, Peter Thiel plays chess, and Elon Musk plays video-games.

“Byron Reeves said ‘If you want to see what business leadership may look like in three to five years, look at what’s happening in online games.’

Fast-forward to today. Elon [Musk], Reid [Hoffman], Mark Zuckerberg and many others say that games have been foundational to their success in building their companies.” — Mary Meeker ( 2017 internet trends report )

Does this mean you should just play video-games? Not at all.

But what are video-games all about? That’s right, problem-solving!

So, what you should do is find an outlet to practice. Something that allows you to solve many micro-problems (ideally, something you enjoy).

For example, I enjoy coding challenges. Every day, I try to solve at least one challenge (usually on Coderbyte ).

Like I said, all problems share similar patterns.

That’s all folks!

Now, you know better what it means to “think like a programmer.”

You also know that problem-solving is an incredible skill to cultivate (the meta-skill).

As if that wasn’t enough, notice how you also know what to do to practice your problem-solving skills!

Phew… Pretty cool right?

Finally, I wish you encounter many problems.

You read that right. At least now you know how to solve them! (also, you’ll learn that with every solution, you improve).

“Just when you think you’ve successfully navigated one obstacle, another emerges. But that’s what keeps life interesting.[…]

Life is a process of breaking through these impediments — a series of fortified lines that we must break through.

Each time, you’ll learn something.

Each time, you’ll develop strength, wisdom, and perspective.

Each time, a little more of the competition falls away. Until all that is left is you: the best version of you.” — Ryan Holiday ( The Obstacle is the Way )

Now, go solve some problems!

And best of luck ?

Special thanks to C. Jordan Ball and V. Anton Spraul . All the good advice here came from them.

Thanks for reading! If you enjoyed it, test how many times can you hit in 5 seconds. It’s great cardio for your fingers AND will help other people see the story.

If this article was helpful, share it .

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• Basics of Input/Output
• Time and Space Complexity
• Basics of Implementation
• Basics of Operators
• Basics of Bit Manipulation
• Recursion and Backtracking
• Multi-dimensional
• Basics of Stacks
• Basics of Queues
• Basics of Hash Tables
• Singly Linked List
• Binary/ N-ary Trees
• Binary Search Tree
• Heaps/Priority Queues
• Trie (Keyword Tree)
• Segment Trees
• Fenwick (Binary Indexed) Trees
• Suffix Trees
• Suffix Arrays
• Basics of Disjoint Data Structures
• Linear Search
• Binary Search
• Ternary Search
• Bubble Sort
• Selection Sort
• Insertion Sort
• Counting Sort
• Bucket Sort
• Basics of Greedy Algorithms
• Graph Representation
• Breadth First Search
• Depth First Search
• Minimum Spanning Tree
• Shortest Path Algorithms
• Flood-fill Algorithm
• Articulation Points and Bridges
• Biconnected Components
• Strongly Connected Components
• Topological Sort
• Hamiltonian Path
• Maximum flow
• Minimum Cost Maximum Flow
• Basics of String Manipulation
• String Searching
• Z Algorithm
• Manachar’s Algorithm
• Introduction to Dynamic Programming 1
• 2 Dimensional
• State space reduction
• Dynamic Programming and Bit Masking
• Basic Number Theory-1
• Basic Number Theory-2
• Primality Tests
• Totient Function
• Basics of Combinatorics
• Inclusion-Exclusion
• Line Sweep Technique
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Problem Solving Strategies

Breaking down coding challenges and solving them step by step is an essential skill for any programmer. In this article, we will discuss some problem-solving strategies that can help you tackle coding problems more effectively.

Understand the Problem

Before diving into writing code, it's crucial to have a clear understanding of the problem. Read the problem statement carefully and try to identify the following:

• What are the inputs?
• What are the expected outputs?
• Are there any constraints or limitations?

Once you have a good understanding of the problem, it's helpful to write down a brief summary in your own words. This will help solidify your understanding and make it easier to explain the problem to others if you need assistance.

Break the Problem into Smaller Parts

Divide the problem into smaller, manageable parts. This will help you focus on individual aspects of the problem and make it easier to solve. For example, if you're building a web application, break the problem down into smaller tasks such as creating the user interface, handling user input, and processing data.

Write Pseudocode

Before writing actual code, it's helpful to write pseudocode, a high-level description of your solution using plain English. Pseudocode helps you focus on the logic of your solution without getting bogged down in syntax.

Here's an example of pseudocode for a function that calculates the factorial of a number:

Write Code and Test

Now that you have a clear understanding of the problem and a plan for your solution, it's time to write the code. Start by writing code for each smaller part you identified earlier. Test each part individually to ensure it works as expected. This will help you catch errors early and make it easier to debug your code.

Review and Optimize

Once your code is working, take some time to review it for readability and efficiency. Are there any parts of your code that could be written more clearly or more efficiently? Are there any edge cases you haven't considered? Make any necessary changes to optimize your code and ensure it's easy to understand and maintain.

Practice Regularly

The more you practice problem-solving, the better you'll become at it. Regularly tackle coding challenges and problems to sharpen your skills and become a more effective problem solver.

By following these strategies, you'll be better equipped to break down coding challenges and solve them step by step. Remember to understand the problem, break it into smaller parts, write pseudocode, write and test your code, and review and optimize your solution. And most importantly, practice regularly to hone your problem-solving skills.

What are some common problem-solving strategies in coding?

Some common problem-solving strategies in coding include:

• Understanding the problem: Read the problem statement carefully and identify the inputs, outputs, and constraints.
• Breaking the problem down: Divide the problem into smaller, manageable tasks or subproblems.
• Designing an algorithm: Create a step by step process to solve the problem, keeping in mind the language and data structures you'll be using.
• Implementing the solution: Write clean, efficient, and well-documented code to implement your algorithm.
• Testing and debugging: Test your code with various input cases, and debug any issues that arise.

How can I effectively break down a coding problem into smaller tasks?

To break down a coding problem into smaller tasks, first identify the main components of the problem, like input processing, calculations, and output formatting. Next, tackle each component one by one, focusing on the logic and data structures needed for each task. This approach not only helps you understand the problem better but also simplifies the implementation process.

What should I keep in mind while designing an algorithm for a coding problem?

When designing an algorithm for a coding problem, consider the following:

• Understand the problem requirements and constraints.
• Choose appropriate data structures and algorithms that fit the problem.
• Think about the time and space complexity of your solution.
• Ensure your algorithm covers edge cases and handles invalid inputs.

How can I improve my problem-solving skills in coding?

To improve your problem-solving skills in coding:

• Practice regularly by solving coding challenges on platforms like LeetCode, HackerRank, or Codecademy.
• Read and analyze other people's code to learn different approaches and techniques.
• Participate in coding competitions or hackathons to challenge yourself.
• Learn new programming languages, data structures, and algorithms to expand your knowledge base.

How do I know if my code is efficient and optimized?

To determine if your code is efficient and optimized, analyze the time and space complexity of your solution. An optimized solution should have a relatively low complexity, meaning it can handle large input sizes without significant performance degradation. Additionally, review your code for any repetitive or unnecessary calculations, and consider alternative data structures or algorithms that could improve the efficiency of your solution.

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Solving a DSA (Data Structures and Algorithms) Problem is quite tough. In This article, we help you not only solve the problem but actually understand it, It’s not about just solving a problem it’s about understanding the problem. we will help to solve DSA problems on websites like Leetcode, CodeChef, Codeforces, and Geeksforgeeks. the importance of solving a problem is not just limited to job interviews or solve problems on online platform, its about develop a problem solving abilities which is make your prefrontal cortex strong, sharp and prepared it to solve complex problem in future, not only DSA problems also in life.

These steps you need to follow while solving a problem:

– Understand the question, read it 2-3 times. – Take an estimate of the required complexity. – find, edge cases based on the constraints. – find a brute-force solution. ensure it will pass. – Optimize code, ensure, and repeat this step. – Dry-run your solution(pen& paper) on the test cases and edge cases. – Code it and test it with the test cases and edge cases. – Submit solution. Debug it and fix it, if the solution does not work.

Understand The Question

firstly read it 2-3 times, It doesn’t matter if you have seen the question in the past or not, read the question several times and understand it completely. Now, think about the question and analyze it carefully. Sometimes we read a few lines and assume the rest of the things on our own but a slight change in your question can change a lot of things in your code so be careful about that. Now take a paper and write down everything. What is given (input) and what you need to find out (output)? While going through the problem you need to ask a few questions yourself…

• Did you understand the problem fully?
• Would you be able to explain this question to someone else?
• What and how many inputs are required?
• What would be the output for those inputs
• Do you need to separate out some modules or parts from the problem?
• Do you have enough information to solve that question? If not then read the question again or clear it to the interviewer.

                Estimate of the required complexity

Look at the constraints and time limit. This should give you a rough idea of the expected time and space complexity. Use this step to reject the solutions that will not pass the limits. With some practice, you will be able to get an estimate within seconds of glancing at the constraints and limits.

              Find, edge cases 

In most problems, you would be provided with sample input and output with which you can test your solution. These tests would most likely not contain the edge cases. Edge cases are the boundary cases that might need additional handling. Before jumping on to any solution, write down the edge cases that your solution should work on. When you try to understand the problem take some sample inputs and try to analyze the output. Taking some sample inputs will help you to understand the problem in a better way. You will also get clarity that how many cases your code can handle and what all can be the possible output or output range.

Constraints 

0 <= T <= 100

1 <= N <= 1000

-1000 <= value of element <= 1000

Find a brute-force Solution

A brute-force solution for a DSA (Data Structure and Algorithm) problem involves exhaustively checking all possible solutions until the correct one is found. This method is typically very time-consuming and not efficient, but can be useful for small-scale problems or as a way to verify the correctness of a more optimized solution. One example of a problem that could be solved using a brute-force approach is finding the shortest path in a graph. The algorithm would check every possible path until the shortest one is found.

Break Down The Problem

When you see a coding question that is complex or big, instead of being afraid and getting confused that how to solve that question, break down the problem into smaller chunks and then try to solve each part of the problem. Below are some steps you should follow in order to solve the complex coding questions… 

• Make a flow chart or a UML for the problem at hand.
• Divide the problem into sub-problems or smaller chunks.
• Solve the subproblems. Make independent functions for each subproblem.
• Connect the solutions of each subproblem by calling them in the required order, or as necessary.
• Wherever it’s required use classes and objects while handling questions (for real-world problems like management systems, etc.)

Optimize your Code

Always try to improve your code. Look back, analyze it once again and try to find a better or alternate solution. We have mentioned earlier that you should always try to write the right amount of good code so always look for the alternate solution which is more efficient than the previous one. Writing the correct solution to your problem is not the final thing you should do. Explore the problem completely with all possible solutions and then write down the most efficient or optimized solution for your code. So once you are done with writing the solution for your code below are some questions you should ask yourself. 

Optimizing a solution in DSA (Data Structure and Algorithm) refers to improving the efficiency of an algorithm by reducing the time and/or space complexity. This can be done by using techniques such as dynamic programming, greedy algorithms, divide and conquer, backtracking, or using more efficient data structures.

It’s important to note that the optimization process is not always straightforward and it can be highly dependent on the specific problem and constraints. The optimization process usually starts with a brute force approach, and then various techniques will be applied to make the algorithm more efficient. The optimization process will often require a trade-off between time and space complexity.

Also, measuring and analyzing the performance of the algorithm is an essential step in the optimization process. The use of mathematical notation and analysis tools like Big O notation and complexity analysis, can help to understand the performance of an algorithm and decide which one is the best.

• Does this code run for every possible input including the edge cases.
• Is there an alternate solution for the same problem?
• Is the code efficient? Can it be more efficient or can the performance be improved?
• How else can you make the code more readable?
• Are there any more extra steps or functions you can take out?
• Is there any repetition in your code? Take it out.

Below is the alternate solution for the same problem of the array which returns even numbers… 

          Dry-run your solution

Dry-running a solution on test cases and edge cases involves manually going through the steps of the algorithm with sample inputs and verifying that the output is correct. This process can help to identify any bugs or errors in the code, as well as ensure that the algorithm is correctly handling all possible inputs, including edge cases.

When dry-running your solution, it’s important to consider both the expected test cases and any unexpected edge cases that may arise. Edge cases are inputs that are at the boundaries of the problem’s constraints, for example, the maximum or minimum values.

To dry-run the solution, you will need to:

• Write down the sample test case inputs and expected outputs.
• Go through the steps of the algorithm manually, using the test case inputs.
• Compare the output of the algorithm to the expected output, to ensure the solution is correct.
• Repeat the process for each test case and edge case.
• Dry-running your solution on test cases and edge cases can help you to identify any issues with your algorithm, and make any necessary adjustments before running the code on a computer.

             Code & Test it On Edge Cases

After dry-running your solution and verifying that it is right, the next step is to code it and test it using the test cases and edge cases.

To code the solution, you will need to:

•  write the code for the algorithm.
• Make sure to include any necessary data structures and methods.
• Test the code with sample inputs, including the test cases and edge cases that were used during the dry-run.
• When testing the code, it’s important to not only check for the expected outputs, but also for any unexpected behavior or errors. Testing with edge cases is especially important as it can reveal bugs or errors that might not be present in other test cases.

It’s also a good practice to test the code with additional test cases and edge cases, to further ensure the correctness and robustness of the solution.

Once the code has been tested and all the bugs have been fixed, you can submit it.

 Submit solution

After coding and testing the solution on the sample test cases, the next step is to submit it, usually to a platform for review or for a contest.

The submission process can depending on the platform, but basically it involves submitting the code and any necessary documentation. After the submission, the solution is usually reviewed by other participants or judges, and feedback is provided on whether the solution is correct or if there are any errors. If the solution is wrong or does not work as expected, the next step is to debug and fix it. Debugging is the process of identifying and resolving errors in the code. This can involve using tools such as a debugger, print statements, or logging to find the source of the problem.

Once the error has been identified, the next step is to fix it. This can involve making changes to the code, data structures, or algorithms used. Once the changes have been made, it’s important to test the solution again to ensure that the error has been resolved and that the solution is correct.

If the solution is correct, you can submit it again or move on to other problems.

It’s important to note that the debugging and fixing process can be an iterative one and it may take several iterations to get the solution working correctly.

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Problem-Solving. How to Boost Your Ability to Solve Programming Tasks and Challenges

8 Steps to Improve Your Problem-Solving Skills as a Rookie Programmer

1. make sure you understand the problem, 2. break down the problem into smaller ones, 3. plan the solution first, 4. solve programming problems on various preparation platforms.

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Besides programming problems, this platform allows you to test yourself in mock interviews, as well as to participate in coding competitions and hackathons.

5. Use CodeGym to practice and learn how to approach programming problems

6. play coding games to practice problem-solving while having fun, 7. extend your knowledge of design patterns, algorithms, and data structures, 8. get feedback, 4 major applied programming techniques for problem solving, 1. debugging.

2. Code Refactoring

3. using data structures & algorithms.

4. Using Version Control Systems

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How to Write Code to Solve a Problem, A Beginner's Guide

Introduction

All the code here is in C# - but it's all pretty simple stuff, and the process is the same in any language. Just "bleep" over the brackets and semicolons if you don't understand them!

Recently, there was a question which involved a chunk of homework: write a method that reads a file and returns all the lines which are followed by a line containing three asterisks. And the code was terrible, even for a beginner - so bad I won't embarrass anyone by linking to it.

Quote: Good day everyone, I don't know if there is an option after the return method to continue or if I should otherwise construct a code. I would like to after the return I continue to the end of the txt file and let the return list more values.

You look at that code and you just start to wonder ... Why? What is that indentation? What is that there for? Why do this? How you do expect that to work?

And of course, it doesn't. It can't work - and the reason why is the author just threw it together without thinking about the task at all.

My Answer (Expanded a Little)

That looks like it was thrown together without any thought about what you are trying to do!

Blunt, I know. But I wanted to get his attention.

Throw it away, and think about your task: Read a file, find all the lines which are above lines with an asterisk, and return them.

Still blunt, but let's think about it.

So let's take it from the top: You need to return more than one line - so the obvious thing to do is to return a collection of strings instead of a single string. Because although you can return them as a single string, it makes life a lot harder for the code that calls your method - it has to "break it back up again" in order to use the information. Let's change that:

Now, it returns a collection of strings so the outside world can work with it.

Think about what you are trying to get the method to do: don't complicate things for the calling code - because you are going to call it one or more times, and you will write it once. If you make the outside world work harder, then you are just adding work you have to do every time you use the method.

So if you need a collection of items, return a collection - don't bodge round so that the outside world has to do more processing each time it calls you.

But ... why are you passing it a TextReader ? That means each time you call it, the outside world has to do the work of creating, opening, passing, and closing the reader - which is silly. Pass the path instead, and let the method do what it wants with it:

Now, the caller looks easier to work with.

Again, make life easier for yourself: you want to read a file? Pass the path and let the method decide what to do with it. If you pass a TextReader, or a Stream, then you are limiting what the outside world can do, and forcing a "shape" on code that may not be the easiest or most efficient for the job it has to do.

The more "generic" you make parameters, then more flexible your code can be - and that means it can be reused - which saves you writing another, similar method to do much the same thing..

Let's start filling in the method: We need a List to return, and to process every line in a file. If we want to use every line, then let's just get them all and let the system handle it! That's pretty easy:

What could be simpler? We know there are two things we must do: return a collection of lines, and process all the lines in a file. So create the collection at the top of the method; return it at the end. Add a simple loop to give us each line at a time. Result: the code is simple, and easy to write. And if it's easy to write, it's probably going to work ...

Now, what do we have to do with the lines? Simple; we need to collect all the lines where the next line contains three asterisks. So we need to know what the last line was.

Think about it for a moment: inside the loop, how can we tell what the next line contains? Practically speaking, we can't (unless we complicate the code and use a different looping construct, but that's messy). What we do know though is what the previous line was - because we have already processed it and can keep a copy for next time.

So turn the problem on its head and think of it as "find all the lines which contain three asterisks, and return the previous line for each". a moments thinking tells you that gives the same result, and means we can work with "historical data" which we have already looked at instead of "future data" that we haven't..

Let's add that:

Each time, we are adding a tiny amount of simple code - nothing complicated, so there is less to go wrong.

We need to check if the current line contains " *** ". If it does, add the last one to the collection. That's easy too - a quick if test will do it:

Hang on ... it's finished, isn't it?

All we have to do now is call it and test it:

I could have shown you the original code for that ... but you might have just finished eating ...

Oh look - it works!

So What Did We Do?

Basically, all we did was take a whole task and break it into littler ones:

Quote: Write a method that reads a file and returns all the lines which are followed by a line containing three asterisks.

• Decide what it needs to return
• Decide what it needs as parameters
• Create the returnable value, and set us up to return it.
• Add a loop to look at each line.
• Save the current line for next time at the end of the loop, when we are finished looking at it.
• Check if the line has asterisks.
• If so, add the line we saved last time round the loop to our output collection.

None of those tasks are difficult: they are a line or two of code and it's pretty simple code as well.

And that's the secret: big tasks are made up of smaller ones, and those are made of even smaller ones.

You are used to that: you use it every day!

Task: "Have breakfast."

Smaller tasks:

• Go to kitchen.
• Decide what to eat for breakfast.
• Prepare it.
• Wash up after yourself.

Each of those tasks may be quite complicated:

Subtask: "Go to kitchen"

• Work out where you are.
• Work out how to get from here to the kitchen.
• Move there.

Those may have sub-sub-sub tasks:

Sub-sub-task: "Work out where you are"

• Look around: where am I? Do I recognise this room? What the hell did I do last night?

The point is that every task can be broken down into smaller pieces until you reach a task you either can do, or know how to find out how to do. If you wake up in a strange room, then you need to check for other people, and maybe ask them where the kitchen is - and so on.

Software tasks are the same; refine the task into smaller bits and some - probably all - can be done easily, and build up to completing bigger, more complex tasks that sound impossible.

Just start by thinking instead of jumping into code: five minutes planning can save you hours of work!

• 6 th October, 2020: Original version
• 6 th October, 2020: Typos. Always typos ...
• 8 th October, 2020: A couple of less than and greater than symbols were fixed: they were showing as the HTML equivalent: "&lt;" and "&gt;"

This article, along with any associated source code and files, is licensed under The Code Project Open License (CPOL)

Comments and Discussions

to use this message board.

Layout   Per page     First Prev 11-Jul-22 6:13 11-Jul-22 6:13  I was looking for this. In C and C++, and not in C#, but I can use the logic. Nice. Thank you OriginalGriff again. ·   11-Jul-22 6:10 11-Jul-22 6:10  I was looking for this. ·   15-Feb-22 23:54 15-Feb-22 23:54  I've only just read this article because I followed the link from part 2. I will follow this series with interest. I feel a lot of the previous posters missed the point. Too often an instructor starts out really basic (in any language) and then by chapter 2 is into lamdas and IEnumerables ·   5-Sep-21 5:34 5-Sep-21 5:34  The article is precise yet very informative ·   26-Apr-21 22:03 26-Apr-21 22:03  Excellent! If people were forced to read and accept the insights of this article when downloading and installing a compiler rather than 20MB of weird legalize, it would actually be worth every second to read it! ·   13-Apr-21 9:03 13-Apr-21 9:03  Great! ·   23-Feb-21 14:13 23-Feb-21 14:13  My vote of 5 Just one small change, grammar. You look at that code and you just start to wonder ... Why? What is that indentation? What is that there for? Why do this? How expect that to work? You look at that code and you just start to wonder ... Why? What is that indentation? What is that there for? Why do this? How expect that to work? Good article. ·   3-Feb-21 10:59 3-Feb-21 10:59  A really lucid example of how to write code in a readable and concise fashion that can be used for everyday purposes. ·   19-Nov-20 6:53 19-Nov-20 6:53  Great summary and entertaining read; I know a lot will disagree with some of your suggestions, although one thing I've learned is that programmers (or should I say academic and not real-world programmers) rarely ever agree, so the most important thing is to just put it out there. Well done! ·   17-Nov-20 3:13 17-Nov-20 3:13  No way. Its not right to pass a string expecting it to be a filename to the method and let the method handle it. This will require lots of string and path and file handling, which has nothing to do with the method itself. The approach with the Stream was just right. Each method does the minimum of extra work. This also opens the method up to other uses. You can always write an overloaded version that takes a string or whatever and opens the file and THEN calls the core method. Dont teach wrong beginnings. ·   12-Nov-20 1:45 12-Nov-20 1:45  not useful. ·   As your comment is. Explain. ·   11-Oct-20 23:56 11-Oct-20 23:56  This will return a blank line, but it's not really specified behaviour, is it? I agree that as a beginners example it's not a good idea to use linq. It could be instructive however to rewrite it to linq later. I agree with those who think that reading the file and splitting the rows separate from this method is a good idea. It will be more reusable. /Mathias ·   7-Oct-20 3:33 7-Oct-20 3:33  Nice article, . Whilst this is most definitely not intended to detract from the excellent point of the article (to explain to beginners how to solve problems by breaking things down into simple tasks) assuming that the asterisks are all below the required lines this particular task could easily be done as a simple one liner: File.ReadAllLines(filePath).Where(x => !x.Contains("***")); It could be argued that this is even simpler than building loops as the complexity is hidden away, but on the other hand you have to bear in mind the need to know that ReadAllLines and Linq exist. ·   7-Oct-20 4:09 7-Oct-20 4:09  And what a lambda expression is, what deferred execution means, ... And also accept that it returns the wrong lines ... he needs the line before each line containing "***"! is now a follower! ·   7-Oct-20 4:58 7-Oct-20 4:58  Hmmm... Then the what you reported as the original question is perhaps not entirely clear? You said: write a method that reads a file and returns all the lines which are followed by a line containing three asterisks I used that as the basis for the comment and code, and as far as I can see it does exactly that - it returns all the lines prior to the line that contains three asterisks. It clearly says 'a line' and does not at any point mention multiple lines with three asterisks... Based on your reply, perhaps they (or you) meant: line which followed by a line containing three asterisks However, surely that is not the same thing at all? Am I wrong? Either way it still does not detract from an excellent article ·   7-Oct-20 5:12 7-Oct-20 5:12  I thought is was fairly clear: but your code returns all lines which don't contain "***" which is a different: even if the original brief was 'all lines followed by a line containing "***"', then for an input like this: I would only expect to get "a" and "b", not "d" or "e". is now a follower! ·   7-Oct-20 6:23 7-Oct-20 6:23  The correct result can be obtained using one line of Linq but my feeling is that a basic solution is more appropriate here. List<string> { "A", "***", "B", "C", "***", "D" }; var results = names.Where((n, index) => index < names.Count - 1 && names[index + 1] == "***").ToList(); //results contains A,C ·   7-Oct-20 8:55 7-Oct-20 8:55  Hi George, I agree, that is much more complex just to get it on one line. Still it is a good solution if you want it in a single line. As I said originally my suggestion required more knowledge than assumed for the intended audience, and even then I misunderstood the requirement ·   8-Oct-20 3:41 8-Oct-20 3:41  I think you missed the point of the article. It is not about extracting some data from a file, it is about learning how to approach a problem and break it down into manageable chunks. Too many people these days tend to throw code together before they have properly thought out what they are trying to do, and this QA was a prime example (and not that poster's first such). OG posted some suggestions to the question, and I (half jokingly) suggested he write an article/tip on it. As usual with such a genius he produced the finished article in double quick time. ·   8-Oct-20 4:18 8-Oct-20 4:18  Hi Richard, Nope, didn't miss the point at all... in fact if you read the messages in the thread you will see that I specifically said and repeated that my original comment was not about detracting from an excellent article but about showing that simplicity could be achieved in other ways. Of course, it would have been much better had I interpreted the original question in the same way that interpreted it ·   11-Jul-22 6:31 11-Jul-22 6:31  Thank you for more to study. And you gave it with (maybe?) how it fits into the example. That looks useful for what I am doing, IF it will work with utf-8 and Unicode encoded files. Thanks. ·   6-Oct-20 22:16 6-Oct-20 22:16  Thanks for the excellent article, there‘s some great advice in it. Could I raise a couple of points? Is it ok to give the method two tasks to perform -loading data from a disc and then processing the data? Wouldn‘t it be better to have an as the input parameter and give the method the single responsibility of processing the collection? It seems to me that there would still be the opportunity to accept many different types of collections and it would also allow testing to be carried out entirely in memory. ·   7-Oct-20 4:17 7-Oct-20 4:17  I know what you mean, but ... that means adding a lot of complication to something aimed at total beginners. At least if they look at they can think "I know what a List is - I'll just bleep over the odd syntax" when it comes to that's a "mental blocker" right there as it's not obvious at all what an enumerable is. I would have used an array (since they have probably met them already) but then I'd have to complicate the code unacceptably or return an array that was bigger than the data it contained. Which leads to other complications! In this case I'm happy to call "process all the lines in a file" an atomic operation (even if it isn't) just to reduce the complexity to readable levels. is now a follower! ·   7-Oct-20 20:34 7-Oct-20 20:34  Thanks for the explanation. I hope that you are going to write a sequel to your piece. It seems to me that well-structured beginners' articles written in a convivial style are always appreciated on here. ·   Last Visit: 31-Dec-99 18:00     Last Update: 24-Jun-24 22:48 Use Ctrl+Left/Right to switch messages, Ctrl+Up/Down to switch threads, Ctrl+Shift+Left/Right to switch pages. Best Article of October 2020 : First Prize Walkthrough Programming problem solving walkthrough. A programming problem solving walkthrough is a written guided description of the journey from a problem to a solution. It aims to teach how to solve programming problems in a methodical and thoughtful manner using the model. In other words, the knowledge to be learned is focused on the "how", and not on the programming language per se. The walkthrough, as a teaching method, is based on two concepts: worked example from learning sciences and literate programming from computer science. A worked example is a step-by-step demonstration of how to solve a problem. Learning scientists found out that worked examples are most effective for novices (i.e., the audience of a walkthrough), while performing problem-solving is more beneficial for experts. There are multiple ways of presenting and supporting worked examples , and one of the evidence-based techniques is to include sub-goal labeling, which is about labeling groups of steps in the worked example. Literate programming by Donald E. Knuth is a programming paradigm in which a program is written as interspersed snippets of executable code and text. The text, which is written in ordinary human language, explains the logic of the code and explains the programmer's thoughts and decisions. Thus a program is perceived much more like an essay. The walkthrough combines these two powerful ideas for learning the craft of problem solving by programming. It uses the programming problem solving model and its supplements to give a framework for establishing the learning objectives, as well as defining the walkthrough's structure and flow. The learning objective of a walkthrough is rooted in one of the phases (for example, acquiring the ability to use a specific design strategy). That's in addition to the always-present learning objective of mastering the instrumentation of end-to-end problem solving . Many times the solving process is hidden, and one gets only the final result, the executable code. Therefore, an essential feature of a walkthrough is making the reasoning explicit, as suggested by literate programming. In other words, it brings the solving process to the surface and documents the train of thought of the problem-solver as they go through each of the phases. In fact, a walkthrough aims to prompt self-explanation by the learners. A similar but different flavor of a walkthrough is one that is developed by the learners. They choose a programming problem and fill in a provided walkthrough template. The learners improve their ability to solve problems by explicitly documenting their own process. This page was written with Python in mind, with Jupyter Notebook that serves as the medium for the walkthrough. Notebooks are natural for literate programming , with their capability to mix text, media, and code in cells. Nevertheless, a walkthrough is a teaching method which is beyond one programming language or another, and it can also be developed as a source code file. Few (opinionated) Principles and Practices A walkthrough is an active learning activity. It is similar to a tutorial in the sense that it is most effective if the reader follows along by actually performing the tasks being described. In our particular case the tasks are based on the phases of the problem-solving model . For example: Reinterpret the Problem phase - suggest input-output instances. Design a Solution phase - write about choosing a data structure, what attributes make it fit. While it is important to focus on one particular phase so as not to overwhelm the learner, other phases should not be neglected. To keep the student engaged throughout the walkthrough it is suggested to use less demanding, yet active, tasks. Tasks suggested by phase appear later on this page. The walkthrough is designed to achieve teachable moments , in which it leads the learners to a point where they discover or apply a concept, an idea or a technique from the learning objectives. At the same time a walkthrough must manage cognitive load , with a great focus on the external one. The walkthrough is a "better version of reality" that focuses on the learning, and not on accurate journaling of the problem solving process . By its nature, this process is often messy and non-linear. Meanwhile, the goal of the walkthrough is to guide the learner through solving the problem in a logical and clear manner, without recording all the twists and turns. In that sense, the walkthrough is a "better version of reality", in which the actual steps are filtered and distilled to support the designer's learning objectives efficiently. The text and code should be written in expository style . Even if a program has a hierarchical (tree) design, it this might not mean that this structure is the best for its development. A problem should be solved and explored in a psychologically correct order , following the solver's "stream of consciousness" . The objective is to go through the process of solving, and a walkthrough inherently performs a "linearization" of this path. As Donald E. Knuth wrote: My experiences have led me to believe that a person reading a program is likewise, ready to comprehend it by learning its various parts in approximately the order in which it was written. The walkthrough is intended to be perceived as a dialogue with the learner . Of course, this is impossible due to the non-interactive format, but aimed as aspiration. Walkthroughs are not stand alone but should be considered in context of a unit or a course. After the learners worked on the walkthrough, a wrap-up session (that might include a presentation or live coding of partial or complete solution) should take place. Use of real-word problems or cover story can increase the motivation of the learners. It is advised to limit the external permitted materials for the learners. Checklist / Rubric This is an opinionated checklist of all the points that a decent walkthrough should fulfill. It refers to the complete walkthrough after a learner performs all the tasks. It is up to the developer to decide which parts are already presented at the beginning and which are left to the learners. Get something working and keep it working: First writing code in cells, testing it and only then encapsulating into functions Reinterpret the Problem Rephrasing the problem statement in their own words Writing the solution contract Meaning and (Python) type One or few input-output pairs of concrete instances (it doesn't need to be comprehensive right now, it is not the Test phase) Design a Solution Ultimately, a walkthrough should break down the problem into hierarchical sub-problems; in other words, it should present an outline of the solution decomposed into sub-problems. Following the DRY (Don't Repeat Yourself ) design principle - Identifying repeating sub-problems A mapping between the information in the problem/solution domain to a data-structure (either primitive or composed, flat or nested) in Python Describing the meaning of the data structure, the relationship between its components and the required operation (a.k.a questions) Transforming well the design into code Pythonic Code - Python Idioms Meaningful Names Using Comments Using Helper Functions when needed (e.g., for following DRY) Black box (e.g., trivial cases, simplest non-trivial cases, edge cases, corner cases - but it is not mandatory to write the type) White box - coverage / path-complete Scenario - Using the language of the problem phase/domain Instance - Concrete Input-Output pairs The test case follows the simplicity principle - the instance(s) should be the simplest possible to test the scenario. Following the empirical approach for debugging (reproduce, diagnose, fix, repeat, reflect) Diagnose - Focus on reasoning on the available clues (e.g., the bug itself - input/output and trace-back, reading the code with a critical eye, using the print function) Evaluate & Reflect Functionality Design & Code Readability, Style & Documentation Alignment between the presented problem solving process and the takeaways Postmortem of the problem solving or debugging process Self-debugging - what the programmer can learn from solving this problem. Solution Program - Solving the Problem Copy-paste and organize all the necessary code for a complete solution of the problem in one cell or py file, and execute it to solve the original problem. Note that it might require asking the learners to combine code snippets from different parts of the notebook. The code in the solution section is self-contained for execution, and doesn't depend on other snippets of code from the previous steps. This section also contains tests of the solution code. Tips for Developing a Walkthrough The Carpentries Curriculum Development Handbook is an excellent resource for how to develop a curriculum in computing and what it says is equally applicable to developing a walkthrough. First of all, set the learning objectives using the programming problem solving model terminology. Form a problem - choose an algorithmic one or real-world one. Solve the problem, document your process based on the model, pay attention to your mistakes and bugs. Reflect on your problem solving process and try to distill it into steps and teachable moments. Refactor your code and remove clutter. While it doesn't have to be the best possible, make sure to adjust for the required ability of your learners. Write an outline of the walkthrough and embed your code in the relevant sections. Validate it with a checklist . Decide what tasks the learners should do, making sure they align with the learning objectives. Write the complete text of the walkthrough that guides the learners. It is advised to use the plural first person pronoun "we". Run a pilot of the walkthrough on a small group of learners. Repeat and improve! Suggested Tasks by Phase Phrase the problem in your own words Write three examples of input-output pairs for the problem Write the solution of the problem or of a function (in the docstring) Write a design (either as text or as a diagram) for a problem or a sub-problem Choose a data structure and reason about it Describe how to solve the problem "by hand" for one specific input Solve a Parson's Puzzle (or the two-dimensional flavor ). It can be created and embedded in Jupyter Notebook with http://parsons.problemsolving.io Write code according to a design (either done by the learner or given in the walkthrough) Draw an environment diagram Answer questions about it Write a docstring to a function Give meaningful names for variables in the code Extract its design (e.g., write a "design tweet" with a maximum of 240 characters) Discuss its design - why did the solver choose that particular design and not another, especially pay attention to the data structures Write test cases for the problem or function Fix a bug in a given piece of code Describe a bug you had while solving the problem, and explain how you fixed it Evaluate a given piece of code Evaluate your code Reflect on your problem solving process Repeat & Improve Refactor a given piece of code (e.g., because of speed or design issues) Additional ideas and inspiration for tasks can be found in the Exercise types chapter from "Teaching Tech Together" and in the Catalog of pedagogical patterns chapter from "Teaching and Learning with Jupyter". A Walkthrough is a written guided description of the journey from a problem to a solution. It aims to teach how to solve programming problems in a methodical and thoughtful manner using the model. The conceptual roots of the walkthrough as a teaching method are the ideas of worked examples and literate programming . It is designed to prompt self-explanation by the learners. Jupyter Notebook serves as the medium, and it includes active learning tasks. Walkthroughs - Open Education Resources Worked and faded examples - MIT Open Learning Skudder, B., & Luxton-Reilly, A. (2014, January). Worked examples in computer science . In Proceedings of the Sixteenth Australasian Computing Education Conference-Volume 148 (pp. 59-64). Australian Computer Society, Inc.. Lauren Margulieux - Research and Papers - Subgoal Labels and Worked Examples Literate Programming website Knuth, D. E. (1984). Literate programming . The Computer Journal, 27(2), 97-111. Exercise Types - Teaching Tech Together Catalog of Pedagogical Patterns - Teaching and Learning with Jupyter The Carpentries Curriculum Development Handbook Copyright © 2020 Shlomi Hod. All rights reserved. results matching " " No results matching " ". Dev Skills: Problem Solving & Pseudocoding Learning goals. Understand what pseudocoding is and its purpose Practice talking about code without writing code Develop a strong strategy for approaching complex problems pseudocoding Literally, fake code! Writing out steps to solve a problem or achieve functionality, without writing actual code terms of art Technical vocabulary, the words and terms that accurately describe code Your friend asked you to build them a bookcase and you said yes! Before you started actually building the bookshelf… …what questions would you have for your friend? …what materials would you need to gather? …what research would you need to do? …what other planning would you need to do? Problem Solving Approaching complex tasks in code is very similar to approaching complex tasks in real life! For example, let think about this scenario: Your Turing instructor asked you to build an application that helps track her dog’s meals. Before you started coding… …what questions would you have for your instructor? Just like there is a lot to think through before we start building that bookcase, there is a lot that we need to think through before we start to code. Today, we will develop a strategy for how to approach complex problems in our code. What is Pseudocoding? One of the greatest tools in your developer toolbelt is pseudocoding . Pseudocode is written in plain English and outlines the steps necessary to complete the task at hand. Pseudocode examines each step that needs to be taken, but it does not worry about writing the code to accomplish that step. Pseudocode functions as a way for you to work logically through a problem, even if you don’t know the code to actually accomplish it. It’s like planning out a road trip without having actually driven the route before. You can get a pretty good guess of what you want to do and where you want to go. Things may change when you’re actually driving, but you’ll still have a general map and itinerary to follow! We will write pseudocode in the space where we will eventually write code. We won’t just think about it in our heads. This is important! Draw a line on your map! If you try to memorize your route through unfamiliar cities and roads, when you’re actually driving, you’re sure to forget something or to get lost or distracted. If you wrote it down, you can be reminded of where you’re trying to go. Take some time to reflect on the following questions and then we will share out as a class. Why do you think we write our pseudocode down? Can you think of a time where not writing something down ended up backfiring? Problem Solving Process While pseudocoding is a very important part of the problem solving process, it is not enough on its own. Let’s look at the full process. Restate the goal in your own words. Take note of EXACTLY what the final output(s) should be. Consider the data that you’re working with. What data types are you working with? Are there any parameters/arguments? What data in particular do you need access to? Ask clarifying questions that you have about the goal and/or the data. Is there anything that still unclear? It is critical that you have a complete and accurate idea of the goal and data before you move on. Pseudocode the steps needed to get to the goal. Write out your plan, with specific steps, in plain English. What will you need to do first? Then what?… Note: You may only be able to pseudocode out the first couple of steps - that’s okay! Plan out as much as possible now. Research what you don’t know . Is there something you’ve noted in your pseudocode that you don’t know how to do? Take note of that and google. Start coding by referencing the pseudocode you’ve written. Stuck? Go back to step 4 and repeat steps 4-6 until you’ve reached your goal. Refactor your code, if necessary. You should not be worried about writing the “best” code possible while solving the problem. Get it to work, then you can work on improving the code. Problem Solving in Action! Let’s go through an example together. ( Link to repl ) Here’s an example for what that problem solving approach could look like: Compare the code to the pseudocode. What do you notice? What do you like about this process? What might make this process difficult to do? Are there any steps you would add/change? Time for YOU to Practice! Solo practice. Strengthen your problem solving skills by going through steps 1-5 of the Problem Solving Process with this challenge. We do not want you to write any code. ( Link to repl ) Swap and Share Now you will get in a breakout room with a partner and share what you worked on. You will each time a few minutes to screen share and talk through your process. When Should We Use This? This process is appropriate to use anytime you’re tackling a complex task with code. It could be used for technical challenges like the ones we’ve seen so far in class. It is also useful for when you’re building out a feature of an application or trying to pass a particularly difficult test in javascript-foundations 😉. Let’s look at one more example so we can see how this process works in a different context. Check out the JS file of this codepen . We haven’t talked much about how to manipulate HTML and CSS with JS, but that’s okay! You can still follow along the problem solving process shown here. Take a few minutes to look through the comments and code and then reflect on the questions below. What looks different when applying this process to a frontend application versus a technical code challenge? What looks similar? Continuing to Strengthen this Skill This was just an introduction to problem solving and pseudocoding. It’s a skill that you will continue to develop for years, so don’t beat yourself up if it’s still confusing or hard! Throughout the rest of mod 1, we have daily practice worked into the calendar to give you more opportunities to develop your problem solving process. Final Reflections Take a few minutes to write about each prompt below: This problem solving process seems like it slows down the overall coding process. Why would anyone bother doing it? Why don’t we just tell you to pseudocode? Why even bother with the other steps? What are the characteristics of solid, beneficial pseudocode? Additional Resources Problem Solving - Odin Project Lesson Search Results Showing top 10 results. Mastering the Art of Coding Problem-Solving self.__wrap_b=(t,n,e)=>{e=e||document.querySelector(`[data-br="${t}"]`);let a=e.parentElement,r=R=>e.style.maxWidth=R+"px";e.style.maxWidth="";let o=a.clientWidth,c=a.clientHeight,i=o/2-.25,l=o+.5,u;if(o){for(;i+1 {self.__wrap_b(0,+e.dataset.brr,e)})).observe(a):process.env.NODE_ENV==="development"&&console.warn("The browser you are using does not support the ResizeObserver API. Please consider add polyfill for this API to avoid potential layout shifts or upgrade your browser. Read more: https://github.com/shuding/react-wrap-balancer#browser-support-information"))};self.__wrap_b(":Rid9j6:",1) The Mindset for Problem-Solving in Coding Approaching a coding problem, common techniques for problem solving. Coding is a powerful skill, one that is becoming increasingly important in today's technology-driven world. It's like a universal language, enabling you to build applications, websites, and software that can impact millions of lives. However, mastering the art of coding is not just about learning different programming languages or memorizing algorithms. It is, at its core, about problem-solving. Every line of code you write is part of a solution to a problem, whether it's a simple issue or a complex business challenge. This blog post aims to guide beginners on how to master the art of problem-solving in coding. We'll delve into the mindset required, explore the steps to approach a problem, and use examples to understand how to apply these skills effectively. Before we start looking into the specifics of problem-solving techniques, we must first understand the mindset required. When it comes to programming, having the right mindset is half the battle. Embrace the Challenge Coding is all about challenges. Sometimes, you'll face problems that seem impossible to solve. In such instances, remember that every problem has a solution. Your job as a programmer is to find that solution. Embrace the challenge instead of running away from it. Understand that Failure is a Step Towards Success You'll often write code that doesn't work as expected. That's completely fine! Failure is a part of the learning process. Each failed attempt provides insights into what doesn't work, pushing you closer to a solution. Patience is a virtue in programming. Some problems require a lot of time to solve. You may need to try multiple solutions before you find the right one. Don't rush. Take your time to understand the problem and its possible solutions. With the right mindset, you're ready to approach any coding problem. Here's a step-by-step guide to tackle it: Step 1: Understand the Problem Before you start writing any code, ensure that you understand the problem fully. Read the problem statement carefully. Identify the inputs and expected outputs. Try to understand the constraints and edge cases. For example, let's consider a simple problem: Write a function in Python to calculate the factorial of a number. In this case, the input is a number ( n ) and the expected output is the factorial of that number. Step 2: Break Down the Problem Once you understand the problem, break it down into smaller, manageable sub-problems. This process is also known as "decomposition." For the factorial problem, it can be broken down into: If the number is 0 or 1, return 1. If the number is positive, multiply it with the factorial of the number minus one. Step 3: Plan Your Solution Next, plan how to solve each sub-problem. This could involve deciding on the algorithms to use or the data structures that might help solve the problem effectively. For our factorial problem, we'll use recursion to solve the problem. Step 4: Write Code With the plan ready, start writing your code. Focus on one sub-problem at a time. Ensure your code is clean and readable. Don't worry about optimization at this point. Here's how we might write the code for our factorial problem: Step 5: Test Your Code Once you've written the code, it's time to test it. Start by using the test cases provided with the problem.Then, think of additional test cases, especially edge cases that might break your code. For our factorial function, we might test with n=5 , n=0 , and n=-1 . Step 6: Refine Your Solution After testing, you might find parts of your code that could be optimized or made more readable. This step is known as "refactoring." It involves improving your code without changing its external behavior. For our factorial function, there's not much to refine, but in more complex problems, you might find opportunities to make your code cleaner or more efficient. Knowing some common techniques for problem-solving can also be beneficial. Here are a few that you should be familiar with: 1. Brute Force The brute force approach involves trying every possible solution until you find the right one. It's usually not efficient, but it can be helpful when the problem space is small, or when you just need a starting point. 2. Divide and Conquer In divide and conquer, you break the problem down into smaller sub-problems, solve each independently, and then combine their solutions to solve the original problem. We've used this approach in the factorial example, where we broke down the calculation into a series of smaller calculations. 3. Greedy Algorithms Greedy algorithms involve making the optimal choice at each decision point in the hope that these local optimums will lead to a global optimum. These algorithms are useful when the problem has an optimal substructure, meaning an optimal solution can be constructed efficiently from optimal solutions of its subproblems. 4. Dynamic Programming Dynamic programming involves breaking down a problem into simpler sub-problems, solving each just once, and storing their solutions – ideally in a table structure. If the same sub-problem occurs, instead of recomputing its solution, one simply looks up the previously computed solution, thereby saving computation time. This technique is used when the problem has overlapping subproblems. 1. How can I improve my coding problem-solving skills? Practice is key to improving your coding problem-solving skills. Websites like LeetCode, HackerRank, and CodeSignal offer a vast range of problems that can help you hone your skills. Additionally, learning about different algorithms and data structures can give you a toolbox of methods to approach problems. 2. What language should I use for coding problem-solving? The language you use for problem-solving depends on your comfort level with the language and sometimes, the problem itself. Some languages like Python are often recommended for beginners due to their simplicity, but the concepts of problem-solving remain the same across all languages. 3. How do I handle a problem that I can't solve? If you encounter a problem that you can't solve, try breaking it down into smaller parts, and focus on solving those first. If you're still stuck, don't hesitate to search for help. Websites like StackOverflow have vast communities of programmers who are willing to help. Lastly, stepping away from the problem for a while can also help. Often, solutions come to mind when you're not actively thinking about the problem. 4. I understand the theory of problem-solving, but I struggle to implement it in code. What should I do? Coding is a skill that improves with practice. If you understand the theory, you're halfway there. Try to write the code for the problem, even if you struggle. With time, you'll find it easierto translate your thoughts into code. Don't shy away from seeking help or looking at other people's code to understand different ways to approach a problem. 5. Is there a 'best' way to solve a problem? Not necessarily. Often, there are multiple ways to solve a problem in coding. Some solutions might be more efficient, readable, or elegant than others, but the 'best' solution can depend on a variety of factors, including the specific requirements of the problem, the constraints of your environment, or even your personal coding style. 6. What are the common mistakes beginners make while problem-solving in coding? Some common mistakes include not fully understanding the problem before starting to code, not considering edge cases, focusing on optimization too early in the process, and not testing the code thoroughly. It's important to develop a systematic approach to problem-solving to avoid these pitfalls. 7. How important is understanding algorithms in coding problem-solving? Understanding algorithms is a crucial part of problem-solving in coding. An algorithm is like a recipe; it's a set of step-by-step instructions to solve a problem. Knowing a wide range of algorithms allows you to choose the most appropriate one for the problem at hand. It's not just about memorizing algorithms, but understanding their logic, their pros and cons, and when to use which one. Remember, coding is as much an art as it is a science. Developing the mindset of a problem solver and practicing the systematic approach to solving coding problems is a continuous journey. Don't rush it. Enjoy each problem you solve, learn from your mistakes, and celebrate your progress. The skills you'll gain will not only make you a better programmer but a better thinker overall. And with that, we come to the end of this beginner-friendly guide to mastering the art of coding problem-solving. We hope you found it useful and informative. Happy coding! Sharing is caring Did you like what Mehul Mohan wrote? Thank them for their work by sharing it on social media. No comment s so far Curious about this topic? Continue your journey with these coding courses: 3.36k students learning Piyush Garg Mastering Algorithms Navigation Menu Search code, repositories, users, issues, pull requests..., provide feedback. We read every piece of feedback, and take your input very seriously. Saved searches Use saved searches to filter your results more quickly. To see all available qualifiers, see our documentation . Notifications You must be signed in to change notification settings Official Implementation of "Multi-Head RAG: Solving Multi-Aspect Problems with LLMs" Folders and files Name Name 2 Commits Repository files navigation Multi-head rag (mrag). This is the official implementation of Multi-Head RAG: Solving Multi-Aspect Problems with LLMs . This framework implements Multi-Head RAG (MRAG), a novel scheme focused on queries that may require fetching multiple documents with substantially different contents. Such queries occur frequently, but are challenging because the embeddings of these documents may be distant in the embedding space, making it hard to retrieve them all. The idea of MRAG is simple yet powerful: leveraging activations of Transformer's multi-head attention layer, instead of the decoder layer, as keys for fetching multi-aspect documents. The driving motivation is that different attention heads can learn to capture different data aspects. Harnessing the corresponding activations results in embeddings that represent various facets of data items and queries, improving the retrieval accuracy for complex queries. Setup Guide In order to use this framework, you need to have a working installation of Python 3.9 or newer. Installing MRAG Before running either of the following two installation methods, make sure to activate your Python environment (if any) beforehand. If you are a user and you just want to use MRAG , you can install it from source: If you are a developer and you want to modify the code, you can install it in editable mode from source: Quick Start The first steps are the generation of a synthetic datasets as well as synthetic queries. These three commands will recreate a synthetic dataset with the same number of categories and documents in each category as used during the evaluation in the paper. The same goes for the synthetic query generation. Please note that the generation of the synthetic queries uses OpenAI LLMs, which incur a cost. If you wish to use different parameter, please read the documentation of the command line interface of both commands: If you want to avoid those costs or do not want to wait for the generation (roughly 40 minutes for both), you can use the already prepared Wikipedia-based dataset and queries in the datasets folder. The next step is the generation of the embeddings for the dataset and the queries. The command above will use the Salesforce/SFR-Embedding-Mistral embedding model and only generates the attention head embeddings for the last layer. The documentation of the command line interface can be found here . After setting up the vector database, the embedding data is imported into the vector database. The documentation of the command line interface can be found here . The evaluation command will run several different strategies on the query embeddings and the document embedddings in the vector database. The documentation of the command line interface can be found here . The plot command generates various plots to visualize the evaluation data. Its command line interface is described in the documentation of Plot module. Documentation The paper gives a high-level overview of the framework and its components. In order to understand the framework in more detail, you can read the documentation of the individual modules. The Dataset module describes the generation of the synthetic dataset as well as the generation of the synthetic queries. The Embed module describes the embedding generation for the dataset and the queries. The Storage module describes how to interact with the vector database. The Evaluation module describes the various strategies used during the evaluation. The Plot module describes the visualization of the evaluation data. Paper Results The datasets directory contains the datasets that we used to evaluate MRAG, which generated the results presented in the paper. They can serve as starting point for learning how to use the framework. However, if you just want to inspect and replot the results, you can use the paper directory. If you find this repository valuable, please give it a star! Got any questions or feedback? Feel free to reach out and open an issue. Using this in your work? Please reference us using the provided citation: Python 100.0% Peter Dutton has promised to solve our energy problems – but his nuclear policy still leaves Australians in the dark Professor, School of Economics, The University of Queensland Disclosure statement John Quiggin is a former Member of the Climate Change Authority University of Queensland provides funding as a member of The Conversation AU. View all partners In 1971 on a family holiday, my father drove us to look at a huge concrete slab at Jervis Bay, on the South Coast of New South Wales. Still visible today, it was the foundation for what would have been Australia’s first nuclear power plant. The project had just been cancelled by then-prime minister Billy McMahon who had recently replaced John Gorton. A Treasury analysis showed coal-fired power was much cheaper . That long-ago episode is still relevant to Australia’s policy choices. Today, Opposition leader Peter Dutton revealed seven sites across Australia where the Coalition, if elected, would build nuclear power stations. Unsurprisingly, the plan has already run into opposition from state politicians, both Labor and the LNP. The announcement answers a few basic questions about the Coalition’s nuclear plans. For example, Dutton said the plants would be Commonwealth-owned, and built at the site of decommissioned coal plants. But central issues remain unaddressed. Exactly what kind of reactors will be built? Who will build them? And how much they will cost? As the Jervis Bay experience shows, nuclear energy can be a hard sell in Australia. Times have obviously changed since the 1970s, but significant political and economic barriers remain – and the problem of cost is still unsolved. What the Coalition has revealed The seven sites for nuclear power plants mooted by the Coalition are: Tarong and Callide in Queensland Liddell and Mount Piper in NSW Port Augusta in South Australia Loy Yang in Victoria Muja in Western Australia. At a press conference in Sydney, Dutton said: We know the government has [a] renewables only policy which is not fit for purpose. No other country in the world can keep the lights on 24/7 with the renewables only policy. We want to utilise existing assets that we have got […] new poles and wires that are used at the moment on the coal-fired power station sites can be utilised to distribute the energy generated from the latest generation nuclear reactors. Under the Coalition plan, the federal government would own and pay for the plants. In this respect, Dutton is following the precedent set by the Snowy Scheme – and more recently, by the National Broadband Network. This is a welcome acknowledgement of the reality that, whatever technology we adopt, private investment is likely insufficient to manage the transition away from coal and gas in the electricity sector – let alone the massive electrification in other sectors needed to meet Australia’s 2050 emissions targets. Dutton says he remains committed to the 2050 target for now, despite flagging the Coalition will abandon Australia’s 2030 emissions goal. The Coalition says it will develop two “establishment projects” using either small modular reactors or larger plants. It claims the small reactors will start producing electricity by 2035, and the larger plants by 2037. These timeframes are at odds with analysis by the CSIRO, which recently found reactors could not be operational in Australia until 2040 at the earliest. The same report found construction of a large-scale nuclear power facility would cost at least A$8.6 billion, and possibly up to $17 billion. It said the electricity produced would be about 50% more costly than renewable energy. On Wednesday, Dutton refused to provide a price tag for the Coalition policy. But he claimed it would be a “fraction” of Labor’s renewable energy policy. Lessons from Jervis Bay Dutton this week ruled out Jervis Bay as a nuclear reactor location, should the Coalition win the next federal election. But the 1970s experience still holds valuable lessons. The Jervis Bay territory was ruled directly by the federal government – circumventing any potential state opposition. The Coalition faces a different battle with regards to its proposed sites. Queensland LNP Leader David Crisafulli on Wednesday said he did not support Dutton’s plan for a nuclear power station in Central Queensland, and has previously ruled out lifting a state ban on nuclear power if elected in October. NSW Labor Premier Chris Minns says building a nuclear reactor in the Hunter Valley is impossible under existing laws, and would disrupt the renewable energy transition. Dutton pledged to work with state premiers to resolve such issues, and suggested financial incentives would be offered. It’s unclear whether existing coal plant owners, including state-owned generators, will be willing to sell the sites to the federal government. However, Dutton said on Wednesday that, according to legal advice, the government could compulsorily acquire the sites if needed. When Jervis Bay was on the table as a nuclear site, there was no question the federal government would build, own and operate it. The idea that something as crucial as a nuclear power plant might be entrusted to a state government, let alone a foreign corporation, was never entertained. The national government was at the postwar height of its power and confidence. It employed the best and brightest, and was expanding the scope and scale of its activity. The Snowy Mountains Scheme, a massive engineering endeavour built under the Commonwealth’s defence power, was nearing completion. Dutton says the government will own the proposed nuclear plants, but form partnerships with nuclear companies to build and operate them. But which companies? Internationally, about 60 nuclear plants are under construction, mostly in Asia. The vast majority are Chinese and Russian designs , built by Chinese and Russian firms. Presumably, for national security reasons, that is not an option for Australia. The only real contenders for large modern projects in Australia are South Korea’s KEPCO, and Electricity de France (EDF). KEPCO built four plants at Barakah, in the United Arab Emirates, between 2009 and 2024. But no new orders for KEPCO plants outside South Korea have been announced since 2009. EDF is building a reactor at Flamanville in France and two at Hinkley Point in the United Kingdom. The projects have suffered massive delays and cost overruns . The UK government is also struggling to organise finance for an additional EDF reactor proposed at the existing Sizewell plant. And what about the so-called small modular reactors suggested by Dutton? This term is applied to two types of technology. First, there are reactors of less than 100 megawatt capacity, which would be built in a factory and shipped to the required site where they would be installed as individual modules. The most promising contender was the NuScale Voygr design, however its pilot project has been abandoned . Similarly, Rolls Royce has spiked its plans for a factory in Wales that would have progressed technology used in small modular reactors. The term is also applied to cut-down versions of existing large-scale designs: reactors of 300 to 500 megawatt capacity compared to the traditional 1,000 to 1,500 megawatts. These are “modular” only in the sense that most parts are built in factories and assembled onsite. The government of Ontario in Canada has announced plans for four such reactors to be built by GE-Hitachi, but no final commitment has been made. Meanwhile, the climate crisis continues As the next federal election rolls closer, Dutton will come under pressure to reveal crucial details underpinning the Coalition’s nuclear plan – most importantly, how much it will cost. Nothing announced by Dutton today changes the fact that nuclear energy is, according to reams of expert analysis, economically unfeasible in Australia. This is as true today as it was in the 1970s. Meanwhile, the climate crisis continues to worsen. Solar panels, wind turbines and energy storage must be rolled out as rapidly as possible – and we must not allow Dutton’s policy detour to distract from the task. Climate change Renewable energy Nuclear energy Peter Dutton Nuclear reactors Coalition nuclear policy Centre Director, Transformative Media Technologies Stephen Knight Lecturer in Medieval Literature Postdoctoral Research Fellowship Social Media Producer Dean (Head of School), Indigenous Knowledges Add accounts Import passwords Back up accounts Restore accounts Troubleshooting Entra authentication for IT admins What is two-step or multi-factor authentication? Signing in with a passkey Passkeys for Windows Passkeys for IT admins Troubleshoot problems with Microsoft Authenticator You can resolve problems with Microsoft Authenticator by checking the tips in this article and reviewing some of the known errors. If you're using mobile data, try switching to Wi-Fi and vice-versa. Make sure Airplane mode is off. Make sure you're using the latest version of Authenticator - Microsoft does not support any app versions more than 12 months old. Tap  Settings and make sure App updates is turned on. Get the latest . Tap  Settings and select Turn off battery optimization for better sync performance. Tap  Settings  > Notification Settings  and make sure  Show notifications is turned on.  Make sure your device is up to date, and that any other security apps (such as Microsoft Defender and Intune Company Portal) are also up to date. Make sure the device's  Date & time  are correct too. If you're using VPN, try disconnecting to see if the issue persists. Select the headings below to see more information. Microsoft Authenticator account tile gray and inactive  Microsoft Authenticator acts as a secure repository for your account credentials to help you authenticate and access various applications conveniently. Authenticator may list inactive accounts that are created by other applications that use Authenticator for single sign-on support. These inactive accounts don't need any management and can be safely ignored.  Microsoft Authenticator sign-in denied Authenticator will deny authentications where there is a discrepancy between GPS-reported locations. Microsoft Authenticator notifications show an incorrect address or location  Authenticator push notifications can include your location to provide better sign-in security. The app uses your phone's operating system to provide the location, and in some cases, may show an incorrect or approximate address. Microsoft Authenticator notifications always expired Authenticator requires your mobile device clock to accurately report your local time. If your device clock is set to manual, reconfigure your system clock to automatic. After updating your clock, restart your device and make sure the new time is set correctly. 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Use the faceID or fingerprint to unlock the device after restart, then try to re-enable passwordless for the account in Microsoft Authenticator. If you are using Android for Work or Work Profile, make sure the PIN or biometric is enabled for the profile in Microsoft Authenticator. Make sure the device has hardware encryption enabled. For steps to enable hardware encryption, see Encrypt your Android device . Make sure the device is registered. Open Authenticator > Settings > Device Registration. Make sure the account is registered for passwordless and is joined to you work or school. Sign-in with this account on the device registration page, then try enabling passwordless for the account. Check that your phone is not running any malware like a rootkit for example. If you are still not able to add your account, please contact Support or reach out to your IT admin. Error message "Please ensure push notifications are enabled in Settings" Error message "the account you're trying to add is not valid at this time". Please contact Support for personal accounts or reach out to your IT admin for work/school accounts. Error message "Sorry, only part of the set up completed successfully" Make sure the device requires a PIN or biometric to unlock. Try to re-enable faceID or fingerprint in the device settings and restart the device. Use the faceID or fingerprint to unlock the device after restart, then try to re-enable passwordless for the account in Microsoft Authenticator. If you are using Android for Work or Work Profile, make sure the PIN or biometric is enabled for the profile in Microsoft Authenticator. Make sure the device has hardware encryption enabled. For steps to enable hardware encryption, see Encrypt your Android device . Make sure the device is registered. Open Authenticator > Settings > Device Registration. Make sure the account is registered for passwordless and is joined to your work or school. Sign-in with this account on the device registration page, then try enabling passwordless for the account. Check that your phone is not running any malware like a rootkit for example. Error message "We could not complete the sign-in at this time." Go to Settings and make sure push notifications are enabled and you have network connectivity. You can also remove your account and attempt the sign in again. If you are still not able to add your account, please contact Support or reach out to your IT admin. Troubleshooting password import and export The most common cause of failed imports is incorrect formatting in the CSV file. One of the following steps could help you troubleshoot the issue. If we don’t currently support importing the format of your password manager, try creating your CSV file manually using the steps in Export by creating a CSV , above. 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Microsoft 365 subscription benefits Microsoft 365 training Microsoft security Accessibility center Communities help you ask and answer questions, give feedback, and hear from experts with rich knowledge. Ask the Microsoft Community Microsoft Tech Community Windows Insiders Microsoft 365 Insiders Was this information helpful? Thank you for your feedback. Help | Advanced Search Mathematics > Numerical Analysis Title: a sherman--morrison--woodbury approach to solving least squares problems with low-rank updates. Abstract: We present a simple formula to update the pseudoinverse of a full-rank rectangular matrix that undergoes a low-rank modification, and demonstrate its utility for solving least squares problems. The resulting algorithm can be dramatically faster than solving the modified least squares problem from scratch, just like the speedup enabled by Sherman--Morrison--Woodbury for solving linear systems with low-rank modifications. Comments: 6 pages Subjects: Numerical Analysis (math.NA) classes: 65F20 Cite as: [math.NA]   (or [math.NA] for this version)   Focus to learn more arXiv-issued DOI via DataCite Submission history Access paper:. HTML (experimental) Other Formats References & Citations Google Scholar Semantic Scholar BibTeX formatted citation Bibliographic and Citation Tools Code, data and media associated with this article, recommenders and search tools. Institution arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . NTT Data CEO, one week into the job, faces a daunting task: Getting people to know who they are Good morning, I grew up in an era when Japan was cast as America’s leading economic rival, from Toyota transforming production methods to Mitsubishi buying Rockefeller Center, which they  later sold at a loss . Now, it more often grabs headlines for its shrinking population, economy, and exchange rate that’s made tourism a booming industry. (One wonders if China will follow a similar trajectory.) But Japanese companies have also been on the front lines of digital transformation, from EVs (Nissan/Toyota) and semiconductors (Toppan) to retail (Rakuten) and recruiting (Recruit). The investments of SoftBank’s Masayoshi Son have made him one of Japan’s richest men, though he did miss out on a $155 billion payday  by dumping his 5% stake in Nvidia  when it was worth about $4 billion. Another company that’s quietly gaining traction is NTT Data. I recently met with Abhijit Dubey, who was appointed CEO of its global operations  last week , leading 150,000 employees in an IT services business that generates $18 billion of its $30 billion in revenue outside Japan. We talked about a range of topics from advances in photonics-powered data centers that use light to transmit data instead of electrical signals to how the company is helping clients transform their businesses with AI. Says Dubey: “Applying AI in your core operations is significantly harder than applying AI on a function.” The biggest challenge for Dubey right now may be getting NTT Data on the radar of potential customers. NTT, or Nippon Telegraph and Telephone Corporation, was established in the aftermath of WWII as a state monopoly that displaced AT&T in running the country’s telecommunications system. The company was later privatized, and NTT Data was spun off, reorganizing as a holding company dividing the domestic and international operations. NTT is a familiar brand but not one that I associate with services that compete with, say, Accenture , TCS or Infosys . It helps to have a strong presence in India, where NTT Data is powering a substantial part of the digital infrastructure. Its work with the U.S.’s IndyCar series may help, too. Building brands in new markets is hard. Certainly, it could be a plus to have roots in Japan’s long-held business philosophy of continuous improvement ( Kaizen ) and selfless service ( Omotenashi )—or a challenge coming from a culture traditionally associated with lifetime employment and homogeneity at the top. That’s changing, as Japanese companies like NTT have been especially active in M&A activity to grow their global footprint. In the meantime, Dubey is getting out there. “We have to work towards preeminence,” he says. Right now, as the new head of a reorganized global operation, his first task may be getting people to simply know who they are. More news below. Diane Brady [email protected] Follow on LinkedIn A business model for addiction recovery Chris Thompson, founder of addiction recovery app Sober Sidekick, is searching for a business model that doesn’t take advantage of desperate customers. Three years ago, Thompson stopped taking referral fees from rehab centers—his only source of revenue—due to concerns that they were illegally paying people to check themselves in. The app is now trying to partner with health insurers, saying it can help reduce costs associated with relapses. Fortune Ads agencies grapple with a TikTok ban Ad agencies are preparing for a possible U.S. ban of TikTok, including implementing “kill clauses” that allows them to escape financial commitments. TikTok executives “didn’t have a good answer on how they sell ads in the U.S. right now,” one advertising executive said. TikTok-owner ByteDance has until January to sell the social media app or be banned. Financial Times Prosecuting Boeing U.S. prosecutors are recommending that the U.S. Justice Department bring criminal charges against Boeing. The prosecutors argue that Boeing has violated a 2021 agreement that shielded it from prosecution following two fatal 737 Max crashes in 2018 and 2019, so long as the plane manufacturer overhauled its compliance practices. The DOJ must decide on whether to prosecute by July 7. Reuters AROUND THE WATERCOOLER Nvidia’s stunning rise offers flashbacks to Cisco and the dotcom era by Jeff John Roberts So long, chief diversity officer? Gen Z and millennial professionals say these C-suite roles are going extinct by Emma Burleigh Gen Z are increasingly becoming NEETs by choice—not in employment, education, or training by Orianna Rosa Royle Tiger mosquitos, Asian hornets and bed bugs: What climate change means for Europe’s ‘pest demographics’ haunting the Paris Olympics by Adam Gale  90% of C-suite executives believe their company promotes worker well-being. Why do only 60% of workers agree? by Beth Greenfield Europe and China agree to talk about EV tariffs, a ‘first step’ to avoid a potential trade war between two of the world’s largest economies by Lionel Lim T his edition of CEO Daily was curated by Nicholas Gordon. Latest in Newsletters The U.S. Supreme Court grapples with a leadership crisis Apple’s war with the EU heats up with new antitrust charges and an AI threat U.S. lawmakers turn up the heat over Nigeria’s unlawful detention of Binance exec Employer protections remain a lifeline to women two years after Roe v. Wade was overturned Here’s how CHROs are actually using AI Benchmark’s Victor Lazarte on what changes (and what doesn’t) when transitioning from operator to VC Most popular. 8 out of 10 women change their name after marriage—they might not realize the impact it has on their careers, work relationships and job prospects San Francisco home crashes more than 60% in value after listing says buyers must wait decades to move in A Tennessee mom lost Medicaid after the state launched a Deloitte-run system that managed eligibility. Then her life turned upside down Gen Z are increasingly becoming NEETs by choice—not in employment, education, or training Why going cashless has turned Sweden from one of the safest countries into a high-crime nation Gen Z workers think showing up 10 minutes late to work is as good as being on time—but baby boomer bosses have zero tolerance for tardiness, research reveals 480 IMAGES Problem Solving with Code Elevate Your Problem-Solving Skills With A Powerful Problem Statement How to Practice Problem Solving for Web Development without Writing Create and Solve the Code Message Handwriting and Problem Solving The Beginner Programmer's guide to Problem Solving [With Example Top 10 Problem Solving Templates with Samples and Examples VIDEO Problem Solving : Write a C program to find reverse of a given string using loop Problem solving : change every letter in given string with the letter following it in the alphabet How to Solve Problems Like a Software Engineer Ray NPTEL Problem Solving Through Programming In C Week 1 Quiz Assignment Solution CODING activity for kids: Writing MY FIRST PROGRAM [4+ YEARS, using BLOCKS] COMMENTS How to Solve Coding Problems with a Simple Four Step Method In this post, we've gone over the four-step problem-solving strategy for solving coding problems. 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How to think like a programmer Simplest means you know the answer (or are closer to that answer). After that, simplest means this sub-problem being solved doesn't depend on others being solved. Once you solved every sub-problem, connect the dots. Connecting all your "sub-solutions" will give you the solution to the original problem. Congratulations! Programming Tutorials and Practice Problems Functional Programming. Higher Order Functions and Decorators. Practice programming skills with tutorials and practice problems of Basic Programming, Data Structures, Algorithms, Math, Machine Learning, Python. HackerEarth is a global hub of 5M+ developers. 10 Steps to Solving a Programming Problem 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. 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