how to approach problem solving in programming

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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A Guide to Problem-Solving for Software Developers with Examples

If I ask you, out of the blue, what’s the role of a developer, what would you answer? Coding all day? Drinking coffee? Complaining about the management?

To me, a developer is first and foremost a problem solver, simply because solving problem is the most important (and the most difficult) part of our job. After all, even if our code is perfect, clear, performing great, a masterpiece of form and meaning, it’s useless if it doesn’t solve the problem it was meant to solve.

So, let’s dive into problem-solving today. More specifically, we’ll see in this article:

• How to define a problem, and the difference sometimes made between problem-solving and decision-making.
• Why some problems should not be solved.
• The two wide categories of problems you can encounter.
• Why it’s important to correctly define the problem, and how to do so.
• How to explore the solution space.
• Why deferring a problem might be the best decision to make in specific situations.
• Why reflecting on the whole process afterward can help you in the future.

This article is mostly based on my own experience, even if I apply here some ideas I found in books and papers.

We have our plan. Now, it’s time to dive deep into the difficult, but rewarding, process of problem-solving.

Problem-Solving and Decision-Making

“When I use a word,” Humpty Dumpty said in rather a scornful tone, “it means just what I choose it to mean — neither more nor less.” “The question is,” said Alice, “whether you can make words mean so many different things.” “The question is,” said Humpty Dumpty, “which is to be master — that’s all.” Lewis Caroll Source

Words are ambiguous; they can mean different things for each of us. So let’s first begin to agree on the definition of “problem-solving” here, to be sure we’re on the same page.

Let’s first look at the definition of the word “problem” in a dictionary:

• According to the American Heritage Dictionary , a problem is “a question to be considered, solved, or answered”.
• According to the Oxford Learner’s dictionary , a problem is “a thing that is difficult to deal with or to understand”.

In short, in any problem, there is some degree of uncertainty. If you’re certain of the solution, the problem is already solved. Nothing would need to be “considered, solved, or answered”.

Information is useful to reduce this uncertainty. The quantity is often not the most important, but the quality will be decisive. If I tell you that 90% of my readers are extremely intelligent, would it help you to solve a problem in your daily job? I bet it wouldn’t. It’s information nonetheless, but its usefulness for you is close to zero.

This is an extreme example, but it highlights an important point: before collecting any data, define your problem clearly; then, according to the problem, decide what data you need. Yet, many companies out there begin to collect the data and then decide what problem to solve. We’ll come back to that soon in this article.

So, to summarize, a problem is a situation with some degree of uncertainty. Sometimes, this uncertainty needs to be reduced to come up with an appropriate solution, or, at least, a decision to move forward to your specific goal.

Is there a Problem to Solve?

Whenever you (or somebody else) see a problem, you should always ask yourself this simple question first: is it really a problem, and should we solve it now ?

In other words, ask yourself the following questions:

• Why is this problem important to solve?
• Would be solving the problem creates some value? What value?
• What would happen if the problem was not solved?
• What desired outcome do we expect by solving the problem?

If the problem doesn’t bother anybody and solving it doesn’t create any value, why allocating effort and time to solve it?

It sounds obvious, but it’s an important point nonetheless. More often than not, I see developers heading first in solving problems without asking themselves if they should solve them at the first place.

The most common examples I can think of are useless refactoring. I saw developers refactoring parts of codebases which never change, or is rarely executed at runtime. In the mind of the developer, the code itself is the problem: refactoring is the solution.

I remember a similar case: a developer refactored part of the codebase which was basically never used. We discovered, months later, when we had more and more users using this specific part of the codebase, that the refactoring didn’t really simplify anything. To the contrary; we had to refactor the code again. The first refactoring tried to solve a problem which didn’t exists.

Of course, the developer could argue that the value created is a “cleaner” codebase, but it’s arguable, especially when the code is neither often modified nor used. The value created here is not clear, and it would have been easier if the first refactoring never happened. In this specific situation, I recommend refactoring when you actively change part of the codebase for another reason (implementing a new feature for example).

Whether a problem is worthy to be solved is subjective. It also depends on the problem: if the solution is clear and straightforward, it might be useful to solve it, if the consequences of the solution are also clearly known and the risks are low. Unfortunately, these kinds of problems, in practice, are quite rare.

Types of Problems

I would define here two wide categories of problems: the problems with a (or multiple) clear solution (what the literature call “problem-solving”), and the problems without clear solution (it’s sometimes called “decision-making” instead of “problem-solving”).

In fact, if the problem you’re trying to solve has a clear, accepted answer, it’s very likely it has been solved already. It’s often the case for mechanical, technical problems. For example, let’s say that you need to order a list; you just have to search on the wild Internet how to do so in your programming language of choice, and you’re done! You can ask an “AI” too, or stack overflow, or whatever.

In my experience, most technical problems have one (or multiple) accepted solution. I won’t speak about these kinds of problems at length in this article, since they’re the easiest to solve.

When you’re in front of a problem which has no clear solution (even after doing some research), it’s where things get more complicated. I’d argue that most problems you’ll face, as a software developer, are of this category. Problems which are directly linked to the domain of the company you work with are often specific (because they depend on the domain), and complex.

For example, I’m working for a company providing a learning platform for medical students who want to become doctors, among other services. This context is changing because the real world is changing; medicine is no exception.

Recently, we had to create new data structures for the knowledge we provide; these data structures are directly linked to the domain (medicine) here. But what data structures to create? How can they adapt to the ever-changing environment? How to capture the data in the most meaningful way, with understandable naming for other developers?

Decisions had to be made, and when there are no clear solutions, you need to come up with a couple of hypothesizes. They won’t feel necessary like solutions , but rather decisions to take to move forward toward the desired outcome. It often ends up in compromises, especially if you’re working in a team where the members have different opinions .

Also, architectural decisions have often no clear solutions because they depend, again, on the changing context. How to be sure that an architectural decision is good today and in three months? How can we make the architecture flexible enough to adapt to the blurry future?

As developers, we deal with complex codebases, which are somewhat linked to the even more complex real world. It’s difficult to know beforehand the consequences of our decisions, as well as the benefits, the drawback, and the potential bugs we introduce.

Before jumping into the solution space however, we first need a good detour in the problem space.

Defining the Problem

Correctly stating the problem.

After determining that we indeed have some kind of problem, it’s tempting to try to find a solution directly. Be patient: it’s better to look at the problem more closely first.

If you don’t specify well the problem, you might not solve it entirely. It’s also possible that you end up solving the wrong problem, or the symptoms of a problem, that is, other minor problems created by a root problem. Often, the ideal scenario is to find the root problem, even if you don’t want to tackle it first. In any case, it’s always useful information.

For example, not long ago, our users didn’t find the content they were searching for, using our search functionality on our learning platform.

We could have directly solved the problem by asking the search team to adjust that for us, but this problem was only a symptom. It wasn’t the first time that we had to spend time and energy trying to communicate to the search team what we wanted to fix; the real root problem here was that we didn’t have any ownership of our search results.

The solution: we created a better API communicating with the search team, to be able to adjust ourselves the search results in a more flexible manner.

When looking at a problem, a good first step is to write it down. Don’t do it once; try to find different formulations for the same problem.

Writing is nice (I love it!), but other ways to represent ideas can be really useful too. You can try to draw what you understand from the problem: a drawing, a diagram, or even a picture can help you understand the problem.

From there, you can ask yourself: do you have enough information to take a decision? The answer will be mostly based on the experience of the problem solver, there is no magical formula to be sure that you can and will solve the problem.

You should also try to look at the problem from different angles, to really frame it correctly. The best way to do so is to solve problems as a team.

Solving Problems in a Team

Trying to describe and think about a problem is a great beginning, but it’s even better if you do it as a team. You can exchange experience, opinions, and it’s easier to look at a problem from multiple angles when multiple developers are involved.

First, make sure that everybody in the team is aware of the problem. Defining it altogether is the best. If you have a doubt that somebody is not on the same page, you can re-explain it using different words. It might bring more insights and ideas to the discussion.

Don’t assume that everybody understands the problem equally. Words are powerful, but they are also ambiguous; never hesitate to ask questions (even if they seem stupid at first), and encourage the team to do the same. If your colleagues see that you’re not afraid to ask, it will give them confidence to do the same.

The ambiguity can also build overtime, after the problem was discussed. That’s why it’s really important to document the whole process, for anybody to be able to look at it again and fix the possible creeping misconceptions. Don’t try to describe everything, but try to be specific enough. It’s a delicate balance, and you’ll get better at it with experience.

If you don’t like writing, I’d recommend you to try anyway: this is a powerful skill which will be useful in many areas of your life.

Regarding the team of problem solvers, diversity is important. Diversity of opinion, experience, background, you name it. The more diverse the opinions and ideas are, the more chances you’ll have to solve the problem satisfyingly (more on that later). If the members of the team have enough respect, humility, and know how to listen to their colleagues , you’re in the perfect environment to solve problems.

As developers, we’re dealing with moving systems, because they need to reflect the ever-changing business domain of the company you’re working with. These problems are unique, and even if similar problems might have been solved in the past, they’re never the exactly same. The differences can have an impact on the solution, sometimes insignificant (allowing you to re-apply the solution found previously), sometimes important enough to change the solution entirely.

Exploring the Solution Space

Now that we’ve defined the problem, thought about it with our team, tried to look at it from different angles, it’s time to try to find solutions, or at least to make a decision.

What is a good decision? The one which will bring you closer to your desired outcome. It sounds obvious, but there can be some ego involved in discussions, which will push us to try to be right even if it’s not the best solution in the current context. Our personal incentives can conflict with the company’s best interest; it’s always good to try to stay aware of that.

The solution should also be the simplest possible, while still moving forward to the desired outcome. It should also have an acceptable level of risk when we decide to apply the solution. In my experience, complicated solutions are the ones which come up first: don’t stop there. Take some time trying to find the best solution with your team.

For example, here’s what we do with my actual team:

• We define the problem altogether.
• We try to think about different hypothesizes. Not only one, but a couple of them.
• We write the benefits and drawbacks of each hypothesis (which can lead to more ideas, and possibly more hypothesizes).
• We commit to a hypothesis, which then needs to be implemented.

What I meant by “hypothesis” here is a solution which might work; but only the implementation of the hypothesis can be considered as a solution. Before the implementation, it’s just an informed guess. Many things can go wrong during an implementation.

This process looks simple, but when you have multiple developers involved, it’s not. Again, if each member of the team have good soft skills and some experience, it can be an enjoyable and rewarding process. But you need a good team for it to work efficiently (that’s why it’s so important to ask the good questions when joining a company). It’s even better if the members of the team are used to swim in uncertainty, and take it as a challenge more than a chore.

The process described above is just an example; in practice it’s often more chaotic. For example, even when a decision is made, your brain might still continue to process the problem passively. If you find some flaws in the hypothesis you’ve committed to, congratulations! You have now a brand-new problem.

I can’t emphasize it enough: try to be as detached as possible from your ideas, opinions, and preferred hypothesizes. The goal is not for you to be right and feel good, but for your company to move in the good direction. It’s hard, but with practice it gets easier.

I also want to underline the importance of finding both benefits and drawbacks for the different hypothesizes you (and your team) came up with.

To find good solutions, we might also need to reduce the uncertainty around their possible consequences. Doing some external research can help, like gathering data around the problem and the possible hypothesizes. In the best case scenario, if you can find enough data, and if you feel confident that you can move forward with a hypothesis, that’s already a great victory.

If you don’t have enough external information to reduce the uncertainty to a level you feel comfortable with, look at your past experience. Try to find problems similar to the one your deal with in the present, and try to think about the solutions applied at the time, to see if they could also be applied in your current case. But be careful with this approach: complex problems are context-sensitive, and the context you were in the past will never be exactly the same as the present and future contexts.

For example, I recently changed the way we display search results in our system, because we had some data indicating that some users had difficulties to find what they really wanted to find. The problem: users have difficulties to find the good information; it’s a recurrent problem which might never be 100% solved. That said, thanks to the data gathered, we found an easy way to improve the situation.

The data was very clear and specific, but it’s not always the case. More often than not, your data won’t really prove anything. It might only show correlations without clear causality. It will be even more true if you begin by gathering data without defining first the problem you try to solve. You can find problems looking at some data, that’s true, but it needs care and deep understanding of what you’re doing; looking at data when you know exactly what you want to solve works better.

Using this kind of process, the hypothesis is often some sort of compromise. That’s fine; committing to a hypothesis is not the end of the process, and there will be other occasions to revisit and refine the solution.

If you don’t feel comfortable with the level of uncertainty of the problem (or the risk involved by applying your hypothesis), you need to dig more. Writing a prototype can be useful for example, if you hesitate between two or more approaches. If your prototype is convincing enough, it can also be useful to gather feedback from your users, even if the ones testing your hypothesis will always be more invested if they test a real-life functionality, instead of a prototype which might use dummy data, or be in a context which is too remote from the “real” context.

In my opinion, prototypes are not always useful for complex problems, because a prototype only test a new feature at time T, but doesn’t allow you to see if the solution stay flexible enough overtime. That’s often a big concern: how will the solution evolve?

But prototyping can still help gather information and reduce the uncertainty of the problem, even if the prototype doesn’t really give you the solution on a silver platter. It’s also great for A/B testing, when you’re in the (likely) case when you have not much information about the real needs of your users. You could ask them of course, but nothing guarantee that they know themselves what these needs are.

If you don’t find any satisfying hypothesis to your problem, you might also challenge the desired outcome. Maybe a similar, simplest hypothesis, with slightly different outcomes, could work better? If it makes things easier, faster, and less complex, it could be the best solution. Don’t hesitate to challenge your stakeholders directly on the desired outcomes.

Deferring the Problem

In some cases, you might be hesitant to try to solve a problem if there is still too much uncertainty around it. In that case, it might be best to defer solving the problem altogether.

Deferring the problem means that you don’t solve it now ; you keep things as they are, until you get more information to reduce the uncertainty enough.

We had a problem in the company I worked with some time ago: we have dosages which can be discovered in articles, but users didn’t really find them, and nobody really knew why. Because of this lack of information, the problem was not tackled right away, but differed. From there, data have been collected overtime, allowing us to understand the scope of the problem better.

Don’t forget that deferring a problem is already taking a decision. It might be the less disruptive decision for the application and its codebase, but it’s s decision nonetheless, and it can have consequences. Seeing a differed problem as a decision will push you to think about the possible consequences of your inaction, and you’ll look at it as a partial “solution”, with some uncertainty and risk associated to it.

In my experience, deferring the problem works well only when you try to actively seek more data to solve it later. It can be some monitoring to see how the problem evolves, or some data taken from users’ actions. Sometimes, simply waiting can also give you important information about the nature of the problem.

What you shouldn’t do is try to forget the problem. It might come back in force to haunt your sleepless nightmares later. Avoiding a problem is not deferring it.

Here’s another example: we began recently to build some CMS tooling for medical editors, for them to write and edit content on our learning platform. We had one GraphQL API endpoint at the beginning, providing data to two different part of the application:

• Our CMS for medical editors.
• Our learning platform for medical students.

We knew that using one single GraphQL endpoint for these two types of users could cause some problems.

But we didn’t do anything about it, mostly because we didn’t see any real, concrete problem, at least at first. When a minor symptom, related to this unique endpoint, popped up, we spoke about it, and we still chose not to do anything. We preferred deferring the problem once more, to try to solve the real problem (one API for two different kinds of applications) later.

Finally, when we had enough symptoms and some frustration, we decided to split our graphQL API in two different endpoints. It was the best moment to do so: we had enough information to come up with a good decision, we applied it, and we stayed vigilant, to see how our applied hypothesis would evolve.

Moving fast and breaking things is not always the best solution. In some situations, waiting a bit and see how things evolve can allow you to solve your problems in a more effective way. But, as always, it depends on the problem, its context, and so on.

Reading this article, you might have wondered: how much information is enough to be comfortable enough to apply a solution? Well, again, your experience will be the best judge here. You’ll also need to consider carefully risks, benefits, and drawbacks. It doesn’t mean that you need to chicken out if you don’t have 100% certainty about a problem and some hypothesizes; being a software developer implies to have some courage and accept that mistakes will be made. It’s not an easy task, and there is no general process to follow in any possible case.

In short: use your brain. Even if you’re totally wrong, you’ll have the opportunity to fix the bad decisions you’ve made before the implementation, during the implementation, and even after it. We don’t code in stone.

The Implementation: The Value of Iteration

You’ve gathered with your team, tried to define the problem, found multiple hypothesizes, and agreed to try one of them. Great! Problem solved.

Not so fast! We still need to apply the hypothesis, and hope that it will become a good solution to the problem. Doing so, you’ll gather more information along the way, which might change your perspective on the problem, on your hypothesizes, and can even create some baby problems on its own.

It’s where the agile methodology is useful: since we’ll never have 100% certainty regarding a problem and its possible solution, we’ll learn more about both while implementing the hypothesis. That’s why it’s so valuable to iterate on the implementation: it gives you more information to possibly adjust your code, or even the problem, or even switching hypothesizes altogether. Who knows? A solution which is not implemented is just a guess.

If the hypothesis applied is not the ones you would have personally preferred (compromising, or even giving up on your preferred solution is common in a team), only applying it will tell you if you’re right or wrong; that is, if the hypothesis can become a solution solving the problem, at least in the present context.

If you’re worried about how a specific solution will evolve overtime, it’s more complicated, because an implementation won’t give you the information you seek. Still, implementing a hypothesis can be a great source of learning (the most valuable to me is when I’m wrong, because I learn even more). If you think that your hypothesis can have better outcome at time T, you might also try to implement it and compare it. Again, it’s where prototyping is useful.

When applying the solution, you need to look at the details of the implementation, as well as the big picture, to judge if the solution you’re creating is appropriate (leading to the desired outcome). This is a difficult exercise. In general, a developer should be able to reason on different levels of abstraction, more or less at the same time. Again, if you’re aware of it, your experience will help you here, and you can also push yourself to think of all the possible risks and consequences at different levels.

If you work in a team, try to participate (at least a bit) into the implementation of the solution. It’s not good to create silos in teams (that is, only a couple of members have some information others don’t have).

You can go as far as looking at other projects, and ask yourselves these questions:

• Did we had similar problems on these other projects? How did we solve them?
• What was the context of these projects? Is it similar to our current context?
• What did we learn from these other problems, and their implementation? Is the implementation similar to what we’re doing now?

In any case, I would definitely recommend you to write a development journal. I write mine for years, and it has been valuable in many cases. I basically write in there:

• The interesting problems I had.
• The decisions made.
• How the implementation of the solution evolved overtime.
• The possible mistakes we made along the way.

It’s a great resource when you have a problem and you want to look at your past experience.

To evaluate your decisions overtime, nothing will beat a good monitoring process: logs, tests, and so on. It’s what the book Building Evolutionary Architecture call “fitness functions” for example, some monitoring allowing you to measure how healthy your architecture stays overtime. It doesn’t have to stop to the architecture; you can think about different monitoring system to see how something evolve, especially if the solution has still a lot of uncertainty regarding its benefits, drawbacks, and risks.

You can also do that retrospectively: looking at how the code complexity evolve overtime using Git for example.

Retrospective on the Process

We defined the problem, implemented a solution iteratively, and now the problem is gone. That’s it! We made it! Are we done now?

Decisions are sometimes not optimal, and implementing a solution successfully doesn’t mean that there wasn’t a better (simpler) one to begin with. That’s why it can be beneficial to look back and understand what went right, and what went wrong. For example, we can ask ourselves these questions:

• Looking at what we learned during the whole process, is there a potentially better hypothesis to solve the problem in a simpler, more robust way?
• What are the benefits and drawbacks we missed when speaking about the different hypothesizes, but we discovered during the implementation? Why we didn’t think about them beforehand?
• What other problems did we encounter during the implementation? Did we solve them? Did we differ some? What should be the next steps regarding these new problems?
• What kind of monitoring did we put in place to make sure that the solution won’t have undesired outcomes overtime? Can we learn something with this data?

Reflecting on past solutions is a difficult thing to do. There is no way to logically assess that the decision taken was better than others, since we didn’t implement the other hypothesizes, and we didn’t look at them overtime to appreciate their consequences. But you can still look at the implementation of the solution overtime, and write in your developer journal each time there is a bug which seems directly related to the solution. Would the bugs be the same if another solution would had been applied?

Bugs are often not an option; they will pop up, eventually. Nonetheless, it’s important to make sure that you can fix them in a reasonable amount of time, and that you don’t see them creeping back in the codebase after being solved. Some metrics, from the DevOps movement (like MTTR for example) can help here. Sometimes, bugs will show you a better, more refined solution to the original problem; after all, bugs can also give you some useful information. They are also the most direct result of the implementation of your solution.

If you want to know more about measuring complexity (which can be also used to measure complexity overtime after applying a solution), I wrote a couple of articles on the subject .

Humility in Problem-Solving

It’s time to do a little summary. What did we see in this article?

• We need to ensure that the problem we found is really a problem we need to solve. Is there any value to solve the problem? Is it even a problem?
• Try to determine what kind of problem you have: a problem which can have multiple, specific, known answers (like a technical problem), or a problem which depends on the real-life context, without known solutions?
• Defining the problem is important. Try to define it using different words. Write these definitions down. Does everybody in your team understand the problem equally?
• It’s time to explore the solution space. Draft a couple of hypothesizes, their benefits, drawbacks, and risks. You can also do some prototyping if you think it would give you more information to take the best decision.
• Do you have enough information to implement a hypothesis, becoming effectively a solution? If it’s not the case, it might be better to keep the status quo and try to solve the problem later, when you’ll have more information. But don’t forget the problem!
• If you decide to implement a solution, do it step by step, especially if you’re unsure about the consequences of your decisions. Implement an independent part of the hypothesis, look at the consequences, adjust if necessary, and re-iterate.
• When the solution is implemented, it’s time to reflect on the whole process: did we solve the problem? What other problems did we encounter? Maybe another solution would have been better? Why?

As I was writing above, most problems you’ll encounter will be complex ones, embedded into a changing environment with different moving parts. As a result, it’s difficult to train to solve problems in a vacuum; the only good training I know is solving real life problems. That’s why your experience is so important.

Experience build your intuition, which in turn increase your expertise.

You’ll never have 100% certainty that a solution will bring you the desired outcome, especially if you are in front of a complex problem with a blurry context. If you are absolutely convinced that you have the good solution without even beginning to implement it, I’d advise you to stay humber in front of the Gods of Complexity, or they will show you how little you know.

• How to solve it
• Hammock Driven Development
• When Deferring Decisions Leads to Better Codebases
• Lean Development - deferring decision

What Is Problem Solving? How Software Engineers Approach Complex Challenges

From debugging an existing system to designing an entirely new software application, a day in the life of a software engineer is filled with various challenges and complexities. The one skill that glues these disparate tasks together and makes them manageable? Problem solving . 

Throughout this blog post, we’ll explore why problem-solving skills are so critical for software engineers, delve into the techniques they use to address complex challenges, and discuss how hiring managers can identify these skills during the hiring process. 

What Is Problem Solving?

But what exactly is problem solving in the context of software engineering? How does it work, and why is it so important?

Problem solving, in the simplest terms, is the process of identifying a problem, analyzing it, and finding the most effective solution to overcome it. For software engineers, this process is deeply embedded in their daily workflow. It could be something as simple as figuring out why a piece of code isn’t working as expected, or something as complex as designing the architecture for a new software system. 

In a world where technology is evolving at a blistering pace, the complexity and volume of problems that software engineers face are also growing. As such, the ability to tackle these issues head-on and find innovative solutions is not only a handy skill — it’s a necessity. 

The Importance of Problem-Solving Skills for Software Engineers

Problem-solving isn’t just another ability that software engineers pull out of their toolkits when they encounter a bug or a system failure. It’s a constant, ongoing process that’s intrinsic to every aspect of their work. Let’s break down why this skill is so critical.

Driving Development Forward

Without problem solving, software development would hit a standstill. Every new feature, every optimization, and every bug fix is a problem that needs solving. Whether it’s a performance issue that needs diagnosing or a user interface that needs improving, the capacity to tackle and solve these problems is what keeps the wheels of development turning.

It’s estimated that 60% of software development lifecycle costs are related to maintenance tasks, including debugging and problem solving. This highlights how pivotal this skill is to the everyday functioning and advancement of software systems.

Innovation and Optimization

The importance of problem solving isn’t confined to reactive scenarios; it also plays a major role in proactive, innovative initiatives . Software engineers often need to think outside the box to come up with creative solutions, whether it’s optimizing an algorithm to run faster or designing a new feature to meet customer needs. These are all forms of problem solving.

Consider the development of the modern smartphone. It wasn’t born out of a pre-existing issue but was a solution to a problem people didn’t realize they had — a device that combined communication, entertainment, and productivity into one handheld tool.

Increasing Efficiency and Productivity

Good problem-solving skills can save a lot of time and resources. Effective problem-solvers are adept at dissecting an issue to understand its root cause, thus reducing the time spent on trial and error. This efficiency means projects move faster, releases happen sooner, and businesses stay ahead of their competition.

Improving Software Quality

Problem solving also plays a significant role in enhancing the quality of the end product. By tackling the root causes of bugs and system failures, software engineers can deliver reliable, high-performing software. This is critical because, according to the Consortium for Information and Software Quality, poor quality software in the U.S. in 2022 cost at least $2.41 trillion in operational issues, wasted developer time, and other related problems.

Problem-Solving Techniques in Software Engineering

So how do software engineers go about tackling these complex challenges? Let’s explore some of the key problem-solving techniques, theories, and processes they commonly use.

Decomposition

Breaking down a problem into smaller, manageable parts is one of the first steps in the problem-solving process. It’s like dealing with a complicated puzzle. You don’t try to solve it all at once. Instead, you separate the pieces, group them based on similarities, and then start working on the smaller sets. This method allows software engineers to handle complex issues without being overwhelmed and makes it easier to identify where things might be going wrong.

Abstraction

In the realm of software engineering, abstraction means focusing on the necessary information only and ignoring irrelevant details. It is a way of simplifying complex systems to make them easier to understand and manage. For instance, a software engineer might ignore the details of how a database works to focus on the information it holds and how to retrieve or modify that information.

Algorithmic Thinking

At its core, software engineering is about creating algorithms — step-by-step procedures to solve a problem or accomplish a goal. Algorithmic thinking involves conceiving and expressing these procedures clearly and accurately and viewing every problem through an algorithmic lens. A well-designed algorithm not only solves the problem at hand but also does so efficiently, saving computational resources.

Parallel Thinking

Parallel thinking is a structured process where team members think in the same direction at the same time, allowing for more organized discussion and collaboration. It’s an approach popularized by Edward de Bono with the “ Six Thinking Hats ” technique, where each “hat” represents a different style of thinking.

In the context of software engineering, parallel thinking can be highly effective for problem solving. For instance, when dealing with a complex issue, the team can use the “White Hat” to focus solely on the data and facts about the problem, then the “Black Hat” to consider potential problems with a proposed solution, and so on. This structured approach can lead to more comprehensive analysis and more effective solutions, and it ensures that everyone’s perspectives are considered.

This is the process of identifying and fixing errors in code . Debugging involves carefully reviewing the code, reproducing and analyzing the error, and then making necessary modifications to rectify the problem. It’s a key part of maintaining and improving software quality.

Testing and Validation

Testing is an essential part of problem solving in software engineering. Engineers use a variety of tests to verify that their code works as expected and to uncover any potential issues. These range from unit tests that check individual components of the code to integration tests that ensure the pieces work well together. Validation, on the other hand, ensures that the solution not only works but also fulfills the intended requirements and objectives.

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Evaluating Problem-Solving Skills

We’ve examined the importance of problem-solving in the work of a software engineer and explored various techniques software engineers employ to approach complex challenges. Now, let’s delve into how hiring teams can identify and evaluate problem-solving skills during the hiring process.

Recognizing Problem-Solving Skills in Candidates

How can you tell if a candidate is a good problem solver? Look for these indicators:

• Previous Experience: A history of dealing with complex, challenging projects is often a good sign. Ask the candidate to discuss a difficult problem they faced in a previous role and how they solved it.
• Problem-Solving Questions: During interviews, pose hypothetical scenarios or present real problems your company has faced. Ask candidates to explain how they would tackle these issues. You’re not just looking for a correct solution but the thought process that led them there.
• Technical Tests: Coding challenges and other technical tests can provide insight into a candidate’s problem-solving abilities. Consider leveraging a platform for assessing these skills in a realistic, job-related context.

Assessing Problem-Solving Skills

Once you’ve identified potential problem solvers, here are a few ways you can assess their skills:

• Solution Effectiveness: Did the candidate solve the problem? How efficient and effective is their solution?
• Approach and Process: Go beyond whether or not they solved the problem and examine how they arrived at their solution. Did they break the problem down into manageable parts? Did they consider different perspectives and possibilities?
• Communication: A good problem solver can explain their thought process clearly. Can the candidate effectively communicate how they arrived at their solution and why they chose it?
• Adaptability: Problem-solving often involves a degree of trial and error. How does the candidate handle roadblocks? Do they adapt their approach based on new information or feedback?

Hiring managers play a crucial role in identifying and fostering problem-solving skills within their teams. By focusing on these abilities during the hiring process, companies can build teams that are more capable, innovative, and resilient.

Key Takeaways

As you can see, problem solving plays a pivotal role in software engineering. Far from being an occasional requirement, it is the lifeblood that drives development forward, catalyzes innovation, and delivers of quality software. 

By leveraging problem-solving techniques, software engineers employ a powerful suite of strategies to overcome complex challenges. But mastering these techniques isn’t simple feat. It requires a learning mindset, regular practice, collaboration, reflective thinking, resilience, and a commitment to staying updated with industry trends. 

For hiring managers and team leads, recognizing these skills and fostering a culture that values and nurtures problem solving is key. It’s this emphasis on problem solving that can differentiate an average team from a high-performing one and an ordinary product from an industry-leading one.

At the end of the day, software engineering is fundamentally about solving problems — problems that matter to businesses, to users, and to the wider society. And it’s the proficient problem solvers who stand at the forefront of this dynamic field, turning challenges into opportunities, and ideas into reality.

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Lesson 27 of 34 By Hemant Deshpande

Table of Contents

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

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Topics covered in this problem solving in programming article are:

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

What is Problem Solving in Programming?

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

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

How Does It Impact Your Career?

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

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

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

Problem Solving Skills in Programming

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

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

Steps Involved in Problem Solving

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

Basically, they are divided into four categories:

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

Analysing the Problem

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

Developing the Algorithm

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

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

Testing and Debugging

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

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

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

Steps to Improve Problem Solving in Programming

Right mindset.

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

Making Right Decisions

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

Keeping Ideas on Track

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

Learning from Feedbacks

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

Asking Questions

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

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

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

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

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

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

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About the author.

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

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10 Steps to Solving a Programming Problem

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

Valinda Chan

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

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

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

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

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

Here are some questions that run through my mind:

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

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

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

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

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

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

Let’s go through the first array [1]

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

Let’s go through the array [1, 2]

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

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

3. Simplify and optimize your steps

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

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

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

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

4. Write pseudocode

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

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

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

Here is an example of pseudocode that has more words:

Here is an example of pseudocode that has fewer words:

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

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

5. Translate pseudocode into code and debug

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

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

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

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

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

I get rid of the pseudocode to avoid confusion.

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

6. Simplify and optimize your code

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

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

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

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

Here are some questions to keep in mind:

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

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

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

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

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

8. Write useful comments

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

Stay away from comments such as:

// This is an array. Iterate through it.

// This is a variable

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

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

9. Get feedback through code reviews

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

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

10. Practice, practice, practice

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

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

Thanks Gavin Stark

Written by Valinda Chan

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5 Steps to Solving Programming Problems

We solve issues all the time as people, and developers are no different. Problem-solving-focused classes aren't particularly popular or frequent, and many developers prefer to study tools, languages, and frameworks over learning how to think like a problem solver or a programmer.

Problem solving is a programmer's bread and butter, and while everyone has their own technique, I've discovered five methods that will most certainly help you not only solve issues faster and more efficiently.

What is Problem Solving?

Problem-solving can mean different things for different people or situations so it is good to clarify what this article means when “problem-solving” is mentioned.

When you bring your broken automobile to the shop, they may decide to fix what's broken, replace the broken part, or offer you the option of purchasing a new car. Even though all of these alternatives appear to be “solutions,” only the first one truly addresses the issue. Everything else is an attempt to avoid dealing with the issue.

You solve a problem when given a set of constraints and having to follow some rules you come up with a solution that meets all the constraints and does not break the rules. As programmers, we write a program, a set of instructions that solves the problem.

To Code is different than To Solve Problem

Anyone who invests the effort to learn how to code will eventually be able to program. It's similar to learning a new language to learn to code. It is the ability to provide instructions for a computer to follow using a language that can be understood or compiled by a computer.

Problem-solving is a separate skill set, and we are inherently adept at it as humans. I mean, by solving problem after problem, we constructed the world around us. Connecting these two skill sets is something that many developers struggle with. Solving programming issues improves your ability to solve real-world problems, and if you're excellent at them, programming may come easy to you.

1. Read the problem several times until you can explain it to someone else

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

Here are some questions that run through my mind:

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

2. Manually solve the problem with at least three sets of sample data.

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

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

For example, here are some sample data sets to use:

When you are first starting out, it is easy to gloss over the steps.

Because your brain is already accustomed with even numbers, you may easily glance at a sample set of data and pluck out numbers like 2 , 4 , 6 , and so on in the array without realizing it. If you're having trouble, consider using massive quantities of data, which will overcome your brain's natural ability to answer the problem simply by looking at it.That helps you work through the real algorithm.

Let’s go through the first array [1]

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

Let’s go through the array [1, 2] 1.Look at the first element in array [1, 2]

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

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

3. Simplify and optimize your steps

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

1.Create a function selectEvenNumbers

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

This approach may remind you of Mathematical Induction in that you: 1.Show it is true for n = 1, n = 2, ...

2.Suppose it is true for n = k

3.Prove it is true for n = k + 1

4.Write pseudocode

Even once you've figured out the main processes, developing pseudocode that you can translate into code can help you define your code's structure and make coding a lot easier. Line by line, write pseudocode. You may do this on paper or in your code editor as comments. I recommend doing it on paper if you're just starting off and find blank displays intimidating or distracting.

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

Let's think about the steps needed to write a function that returns a number's squared value.

Now we know exactly what our code is supposed to do, we have one more step.

5. Translate pseudocode into code

When you have your pseudocode ready, translate each line into real code in the language you are working on. We will use JavaScript for this example. If you wrote it out on paper, type this up as comments in your code editor. Then replace each line in your pseudocode. Lets use our square example (very simple for demonstration purposes):

Optimize your code:

If you've reached this point, thank you very much. I hope that this tutorial has been helpful for you and I'll see you all in the next.

If you want to learn more about Web Development don't forget to follow me on Youtube!

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Problem Solving

Foundations course, introduction.

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

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

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

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

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

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

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

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

Lesson overview

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

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

Understand the problem

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

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

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

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

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

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

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

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

Divide and conquer

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

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

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

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

Solving Fizz Buzz

To demonstrate this workflow in action, let’s solve Fizz Buzz

Understanding the problem

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

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

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

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

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

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

Writing the pseudocode

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

Dividing and conquering

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Knowledge check

The following questions are an opportunity to reflect on key topics in this lesson. If you can’t answer a question, click on it to review the material, but keep in mind you are not expected to memorize or master this knowledge.

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

Additional resources

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

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

Support us!

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

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The Beginner Programmer's guide to Problem Solving [With Example]

Have you got this feeling that you are able to grasp the concepts of programming and  you are able to understand what’s a variable, what’s a function, what are data types, etc. yet you find it difficult to solve problems in programming.  Every beginner gets this feeling.  I did too when starting out.

It is important to overcome this feeling at the earliest, otherwise it can form a mental block for you.

How it can be a mental block to you?  Common sense says that the more you practice a certain skill, you get better at that skill as time progresses.  Same goes with problem solving too.  The more problems you solve, the better you become at problem solving.  But when you get a feel that you are trying hard and still unable to solve a problem or find it extremely difficult, your confidence lowers.  At this stage, either you stop solving problems or try to solve lesser number of problems.

The point is your curriculum or your professional work is generally designed in such a manner that the order of difficulty increases as time progresses.  So, you are in a situation where you feel less confident in solving small problems but now tasked with solving bigger problems.  And the cycle continues till it becomes a permanent mental block in you.

Is it too late to start solving problems?

No.  If you have come to the realization that you need to improve your problem solving skills, you have made that good first step.  Quite often our egos don’t let us accept the obvious.  It is good to accept certain truth because that is the only way that we can improve ourselves.

What can I do to become better at solving problems?

Remove the mental block first – exercise your mind.

Your mind is your most powerful weapon.  So you have to think you can actually solve the problem.  So from today, think positively that you can solve any problem.  But you will obviously start with small problems and go on to solve bigger problems.

As with every aspect in life, it starts with conditioning the mind.  So, starting today, tell yourselves the following:

• I can solve any problem that is put at me
• I will commit at least 1-2 hours per day on solving problems alone for the next 30 days
• I will never give up on any problem that is put at me, I will ask for help if required.1

Understand the basic approach to problem solving

Do you know one of the reasons for your struggle with problem solving?  One reason might be due to lack of practice.  But the main reason is because you have not understood the basics of problem solving especially in programming.  Once you understand the approach to problem solving to the smallest of things, you can go ahead and solve bigger and more complex problems with confidence.1

Ever wondered how top tech companies like Google, Amazon solved the internet’s biggest & hardest problems?  The answer is simplicity.  They solved problems at the basic level and then went on to solve bigger and bigger problems.  You can do it too.  But you need to be good at the basics.

What do I need to understand before even trying to solve the problem?

Understand the problem clearly – the power of clarity.

You need to understand your problem clearly before even trying to solve it1.  Lack of clarity at this stage will put you down.  So make a conscious effort in understanding the problem more clearly.  Ask questions like What, Why, When, Where, What if and How.  Not all questions might be applicable to your problem, but it is important to ask questions to yourself at this stage before you go ahead trying to solve the problem.

Visualize – The Power of visualization

I am sure everyone of you is aware of what visualization is.  Trying to picturize your thoughts.  Have you ever imagined how some people can solve extra ordinary problems just by looking into those problems and they will instantly have a solution to it?  And we don’t even understand the problem fully?  It is because they do it with their mind.  They visualize the problem in their minds and they solve it in their minds itself.  Visualization is a powerful tool in your mind.

But in order to get to that state, first you need to visualize the problem externally.  That is where a pen and a paper/notebook (or) a white board comes into play1.  Try to visualize the problem at hand and try to picturize the problem.  That is also one of the steps to make sure that you understand the problem clearly.

There was a situation when I and my dear friend & colleague were discussing about a problem and we were literally going nowhere.  This was actually when we each had around 7 years of experience in the industry.  At that point, my friend said “Let’s put our points in board.  If we don’t put it on the board, we will never get started”.  And we started putting things on board.  Things started to get more clear and raised more questions and ultimately became more clear.

That is the power of visualization.  It really helps us to get started with our thinking. This visual thing works.  Just try it out.

Your next question might be “I kinda get it, but I don’t.  How do I visualize? What exactly do I visualize?”.  Please read on to find out the answers.

What is the basic approach to problem solving

Step 1:  identify small problems.

The major trick in problem solving is to identify and solve the smallest problem and then moving ahead with bigger ones.  So how do you do it?

The answer is division of responsibility.  Simply put, we need to identify parts that can stand on its own and identify a sequence in those responsibilities.  And once you start breaking down the problems into smaller ones, then you can go ahead with the next step.

Step 2:  Solve the smaller problems one at a time

Now that you have identified the smaller problems, try to solve them.  While solving them, make sure that you are focussing only on one problem at a time.  That makes life much simpler for us.  If you feel that this smaller problem is too big to solve on its own, try to break it down further.  You need to iterate steps 1 to step 3 for each smaller problem.  But for now, ignore the bigger problem and solve the rest of the problems.

• It is ok to assume that other problems are solved
• It is ok to hardcode when coding a particular problem, but later you will resolve it in step 3.
• Solve the easier problems first, that will give you confidence and momentum until you get the confidence to solve the hardest problem first.

Step 3: Connect the dots (Integration)

You have solved individual problems.  Now it is time to connect the dots by connecting the individual solution.  Identify those steps which will make the solution or the program complete.  Typically in programming, the dots are connected by passing data that is stored in variables.

Step 4: Try to optimize each step & across steps

Once you are completed with a working solution, try to optimize the solution with the best code that you can write.  This comes only with practice.  This trick can make a difference between a good programmer and a great programmer.  But to get to this step, you need to be first good at steps 1 to 3.

Let’s take an example & walkthrough the problem solving approach

Problem:  check if a user given string is a palindrome or not.

I will be using Python for this exercise (Although I have experience in1 C# and JAVA, I am also a Python beginner, so pardon any bad code).  Let’s iterate through our steps:

Let’s call this as Level 1:

Step 1:  Identify smaller problems:

Step 2: Solve the small problems

So each small problem will map to its corresponding solution as below:

Note: When solving the step (3.  Compare the variables), I am doing 2 things:

• I am making an assumption that reversed is the variable name of the reversed string.
• I am hardcoding the variable name reversed to ‘madam’ to avoid compile time error
• If you execute the program at this state, you can input ‘madam’ and check if it is printing ‘The given string is a palindrome’ (And) you can input something else like ‘dog’ and check if it is printing ‘The given string is not a palindrome’

When we are trying to connect the dots, the only thing that is missing now is the variable reversed is hardcoded.  For that to be set to the correct value, we need to break the small problem (Reverse the user input and store in a separate variable) into further smaller problems.  Till that point we need to mark it as incomplete.

2 things still remain unsolved in Level 1:

• Solution for step 2 in the diagram (Reverse the user input and store in a separate variable)
• Connecting the dots once the solution for step 2 is found

Iterating small problem 2 through our problem solving steps:

Let’s call this Level 2:

Step 1: Identify smaller problems

Step 3: Connect the dots

Here, we have already connected the dots.  So we need not do anything extra in this step.

Now we have solved the smaller problems, which means Level 2 is over.  Now we need to come back to Level 1.

If you remember, 2 things remain in Level 1.  One is solution for step 2 which we have found now.  Two is connecting the dots.

Now if we substitute the small problem 2 with the solution that we derived just now, we get something like this:

The thing that remains is connecting the dots.

So if we see what is the missing connection, the variable reversed is set twice.  One to the solution of step 2 and another is hardcoded in step 3.  So we can now remove the hardcoded value in step 3, in which case our code will become like this

If you see, we have actually solved our problem.

We are left with step 4 – Optimize each step and across steps

Step 4: Try to optimize each step and across steps

As you can see, there are many things that needs to be optimized for this code.  I would leave you to optimize the code further.  Come on, put on your thinking cap and try different solutions.

BONUS STEP 5:  Make the code robust

By robust I mean,

• Adding error & exception handling
• Using better variable names
• Adding user defined functions
• Adding comments where necessary

Again, I would leave you to figure out how to do this step.

• We saw just how we can solve problems using a step by step approach
• By solving smaller problems, I get into a momentum for solving bigger & tougher problems
• By focussing one problem at a time, I am eliminating distractions, thus allowing to better direct your efforts for that one problem rather than getting confused with many small problems at hand.
• If you understand this approach and practice, you will definitely go on to solve bigger problems and your confidence will raise.
• Beauty about breaking down the problem is that we can further convert each problem and sub problem into separate functions/modules thus making the code more modularized and maintainable.

Wait, You can’t leave yet:

Now dear beginner programmers, take any problem and try to apply this approach.  See the results for yourselves.  Now, describe the following in the comments section:

• What problem you are solving?
• How did you break it down? (Even a snap of your notebook page or board will do!)
• The final code
• How did you feel and what did you learn from this exercise?

Also remember, I am challenging you for the 30 day problem solving challenge.

If you liked this blog post, please feel free to share it with your circles in social media.

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

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Blog / Time To Code / 6 Ways to Improve Your Programming Problem Solving

6 Ways to Improve Your Programming Problem Solving

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Software development is, at its core, all about problem solving.

Think about it.

First, developers need to find a problem they can solve with software. Then, they have to figure out how humans solve that problem. And then, they have to find a way to effectively translate both the problem and the solution into code that a computer can use to solve the problem as well as (or better than) a person.

And then there are all the problems along the way: Working with teams, finding and fixing bugs, meeting delivery deadlines.

Engineers use problem solving skills constantly .

Because of that, if you want to become a better developer, one place to start might be becoming a better problem solver. But that’s easier said than done, and requires a deep understanding of what problem solving is, why it matters, and what it actually takes to improve those skills.

Ready to dive in? Let’s get started.

What Is Problem Solving, and Why Does It Matter?

Have you ever heard this famous Steve Jobs quote?

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

Jobs was right. Software development is as much about “soft skills” like critical thinking, communication, and problem solving as it is about “hard skills” like writing code.

And so, in the context of software development, problem solving can mean a few different things:

• Creating an application that meets the end user’s goals.
• Communicating effectively with team members to delegate work.
• Finding and fixing bugs in the code.
• Meeting a tight deadline for a client.

There’s only one thing that’s true no matter what problem solving looks like on a given day: It’s an integral part of every step of the software development process.

Why Should Engineers Work On Problem Solving Skills?

Just like any other skill, problem solving takes practice to apply and master.

Many developers think that becoming a better problem solver means being able to solve more problems, faster. But that’s not true — it means being able to find the best solution to a problem, and then put that solution in place.

Learning to do that is a great way to become a better developer overall. And while soft skills can be more difficult to learn and improve upon than hard skills, there are still some tips and tricks that can help you get better at problem solving specifically.

6 Ways to Get Better at Problem Solving

As you’ll see from these learning tools, getting better at problem solving is mostly like getting better at any other skill for work: You need to practice. A lot. And then practice some more.

Solve a Lot of Problems on a Lot of Different Platforms

Step one? Solve as many problems as you can, but try to focus on different types of problems on different platforms.

Here’s why this is so beneficial: It prevents you from getting comfortable with one problem solving method or framework. As we already know, in the world of software development, there is definitely no one-size-fits-all solution for the problems we encounter.

When you regularly practice solving different types of problems in different platforms, it reinforces the fact that you can’t always rely on the same technique to solve every problem. It forces you to learn to be flexible, and to choose the best tool or framework for each job.

Solve Problems in Contexts Other Than Work

Since problem solving is a skill that requires practice, you can (and should) work on it even outside of work hours.

This doesn’t need to be a chore — there are a lot of fun ways to practice problem solving, like by doing math or logic puzzles, solving crosswords, or playing a game like chess. Even many video games can help work on problem solving skills.

There are also many opportunities to practice problem solving just as you live your life from day to day. Broke something around the house? Use your problem solving skills to DIY a fix. Need to solve a conflict with a friend or a family member? You guessed it — time to practice problem solving.

Learn From Past Solutions, and Apply Them to New Problems

As you keep practicing problem solving as much as possible, you’ll start to see patterns emerge in the problems you solve. You’ll build up a sort of toolkit filled with the solutions you’ve found and used in the past, and you’ll be able to apply those to solving new problems.

This part is just as important as finding the solutions in the first place, because the more you practice your growing problem solving skills, the more natural it will become to apply the right solutions to different types of problems, making you able to solve new problems more and more quickly, while still using the best possible solves.

Ask Others for Help and Feedback

Sometimes, finding the best solution to a problem just requires a fresh, new set of eyes. That’s why it’s important to treat growing your problem solving skills not as a totally solo venture, but as a team endeavor where everyone at your organization can support each other and help each other get better.

If you’re stuck on a specific problem, ask for help. Someone else might have a method or framework you aren’t familiar with, that they can teach you. You can then apply that to more problems down the road.

And if you’ve come up with a solve for a problem, ask others for feedback. They might be able to help you refine or further improve your framework, making it even better.

Train the Problem Solving Part of Your Mind

How do you keep muscles from growing weaker over time? You keep exercising them.

The same goes for your brain, and especially for different knowledge-base skills, like problem solving. You’ll stay at the top of your brain if you keep “working out,” or practicing problem solving all the time.

A good move for a developer who wants to invest in their problem solving skills is scheduling time every week (or even every day) to consciously practice problem solving. Remember, this doesn’t necessarily mean solving work problems. You could commit to doing a tricky logic puzzle every day on your lunch break, for example. The important thing is to get in the practice, no matter how that looks.

Practice Other Skills Related to Problem Solving

Problem solving is an important skill on its own. But there are other necessary skills developers need to support their problem solving abilities, and those skills all take practice, too.

Flexibility. Critical thinking. Communication. Teamwork. Focusing on building and practicing all these skills will help you improve your problem solving.

Problem solving is one of the most necessary skills for developers to have. With time, practice, and dedication, they can improve it, constantly, and keep becoming better.

Rethinking Timekeeping for Developers:

Turning a timesuck into time well spent.

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

Codility Tests

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

Technical Screening Tools

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

Sharifa Ismail Yusuf

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

dewayne sewell

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

Pakize Bozkurt

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

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

Ipsa iure sed rerum

Excepturi quo volupt

Thanks for this !

Fahil kiima

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

Alan Codinho

Nice overview

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UNIT 1: How to Think Like an Engineer

Learning objectives.

• Explain what we mean by “Computational Thinking”.
• Describe the problem being solved in a computational algorithm.
• Explain the process for generating computational algorithms.
• Generate and test algorithms to solve computational problems.
• Evaluate computational algorithms for exactness, correctness, termination, generalizability and understandability.
• Explain the role of programming in the field of Informatics.

Introduction

The goal of this book is to teach you to solve computational problems and to think like an engineer. Computational problems are problems that can be solved by the use of computations (a computation is what you do when you calculate something). Engineers are people who solve problems – they invent, design, analyze, build and test “things” to fulfill objectives and requirements. The single most important skill for you to learn is problem solving. Problem solving means the ability to formulate problems, think creatively about solutions, and express a solution clearly and accurately. As it turns out, the process of learning to program is an excellent opportunity to practice problem-solving skills.

This book strives to prepare you to write well-designed computer programs that solve interesting problems involving data.

Computational Thinking

Figure 1: “The seven components to computational thinking”(www.ignitemyfutureinschool.org/about)

Computational Thinking is the thought processes involved in understanding a problem and expressing its solution in a way that a computer can effectively carry out. Computational thinking involves solving problems, designing systems, and understanding human behavior (e.g. what the user needs or wants) – thinking like an engineer. Computational thinking is a fundamental skill for everyone, not just for programmers because computational thinking is what comes before any computing technology. [1]

Computer science is the study of computation — what can be computed and how to compute it whereas computational thinking is:

Conceptualizing , not programming. Computer science is not only computer programming. Thinking like a computer scientist means more than being able to program a computer. It requires thinking at multiple levels of abstraction;

Fundamental , not rote skill. A fundamental skill is something every human being must know to function in modern society. Rote means a mechanical routine;

A way that humans, not computers, think . Computational thinking is a way humans solve problems; it is not trying to get humans to think like computers. Computers are dull and boring; humans are clever and imaginative. We humans make computers exciting. Equipped with computing devices, we use our cleverness to tackle problems we would not dare take on before the age of computing and build systems with functionality limited only by our imaginations;

Complements and combines mathematical and engineering thinking . Computer science inherently draws on mathematical thinking, given that, like all sciences, its formal foundations rest on mathematics. Computer science inherently draws on engineering thinking, given that we build systems that interact with the real world;

Ideas , not artifacts. It’s not just the software and hardware artifacts we produce that will be physically present everywhere and touch our lives all the time, it will be the computational concepts we use to approach and solve problems, manage our daily lives, and communicate and interact with other people;

For everyone, everywhere . Computational thinking will be a reality when it is so integral to human endeavors it disappears as an explicit philosophy. [2]

Figure 2 “Are you happy?” by Typcut http://www.typcut.com/headup/are-you-happy

An algorithm specifies a series of steps that perform a particular computation or task. Throughout this book we’ll examine a number of different algorithms to solve a variety of computational problems.

Algorithms resemble recipes. Recipes tell you how to accomplish a task by performing a number of steps. For example, to bake a cake the steps are: preheat the oven; mix flour, sugar, and eggs thoroughly; pour into a baking pan; set the timer and bake until done.

However, “algorithm” is a technical term with a more specific meaning than “recipe”, and calling something an algorithm means that the following properties are all true:

• An algorithm is an unambiguous description that makes clear what has to be implemented in order to solve the problem. In a recipe, a step such as “Bake until done” is ambiguous because it doesn’t explain what “done” means. A more explicit description such as “Bake until the cheese begins to bubble” is better. In a computational algorithm, a step such as “Choose a large number” is vague: what is large? 1 million, 1 billion, or 100? Does the number have to be different each time, or can the same number be used again?
• An algorithm expects a defined set of inputs. For example, it might require two numbers where both numbers are greater than zero. Or it might require a word, or a list customer names.
• An algorithm produces a defined set of outputs. It might output the larger of the two numbers, an all-uppercase version of a word, or a sorted version of the list of names.
• An algorithm is guaranteed to terminate and produce a result, always stopping after a finite time. If an algorithm could potentially run forever, it wouldn’t be very useful because you might never get an answer.
• Must be general for any input it is given. Algorithms solve general problems (determine if a password is valid); they are of little use if they only solve a specific problem (determine if ‘comp15’ is a valid password)
• It is at the right level of detail…..the person or device executing the instruction know how to accomplish the instruction without any extra information.

Once we know it’s possible to solve a problem with an algorithm, a natural question is whether the algorithm is the best possible one. Can the problem be solved more quickly or efficiently?

The first thing you need to do before designing an algorithm is to understand completely the problem given. Read the problem’s description carefully, then read it again. Try sketching out by hand some examples of how the problem can be solved. Finally consider any special cases and design your algorithm to address them.

An algorithm does not solve a problem rather it gives you a series of steps that, if executed correctly, will result in a solution to a problem.

An Example Algorithm

Let us look at a very simple algorithm called find_max.

Problem : Given a list of positive numbers, return the largest number on the list.

Inputs : A list of positive numbers. This list must contain at least one number. (Asking for the largest number in a list of no numbers is not a meaningful question.)

Outputs : A number, which will be the largest number in the list.

Algorithm :

• Accept a list of positive numbers; set to nums_list
• Set max_number to 0.
• If the number is larger, set max_number to the larger number.
• max_number is now set to the largest number in the list of positive numbers, nums_list.

Does this meet the criteria for being an algorithm?

• Is it unambiguous? Yes. Each step of the algorithm consists of uncomplicated operations, and translating each step into programming code is straight forward.
• Does it have defined inputs and outputs? Yes.
• Is it guaranteed to terminate? Yes. The list nums_list is of finite length, so after looking at every element of the list the algorithm will stop.
• Is it general for any input? Yes. A list of any set of positive numbers works.
• Does it produce the correct result? Yes. When tested, the results are what are expected

Figure 3: Example Algorithm

How do we know if an algorithm is unambiguous, correct, comes to an end, is general AND is at the right level of detail? We must test the algorithm. Testing means verifying that the algorithm does what we expect it to do. In our ‘bake a cake’ example we know our algorithm is ‘working’ if, in the end, we get something that looks, smells and tastes like a cake.

Verifying your Algorithm

Figure 3 “ Keyboard ” by Geralt is licensed under CC 2

Your first step should be to carefully read through EACH step of the algorithm to check for ambiguity and if there is any information missing. To ensure that the algorithm is correct, terminates and is general for any input we devise ‘test cases’ for the algorithm.

A test case is a set of inputs, conditions, and expected results developed for a particular computational problem to be solved. A test case is really just a question that you ask of the algorithm (e.g. if my list is the three numbers 2, 14, and 11 does the algorithm return the number 14?). The point of executing the test is to make sure the algorithm is correct, that it terminates and is general for any input.

Good (effective) test cases:

• are easy to understand and execute
• are created with the user in mind (what input mistakes will be made? what are the preconditions?)
• make no assumptions (you already know what it is supposed to do)
• consider the boundaries for a specified range of values.

Let us look at the example algorithm from the previous section. The input for the algorithm is ‘a list of positive numbers’. To make it easy to understand and execute keep the test lists short. The preconditions are that the list only contains numbers and these numbers must be positive so include a test with a ‘non-number’ (i.e. a special character or a letter) and a test with a negative number. The boundaries for the list are zero and the highest positive number so include a test with zero and a large positive number. That is it! Here is an example of three different test cases.

Manually, you should step through your algorithm using each of the three test cases, making sure that the algorithm does indeed terminate and that you get your expected result. As our algorithms and programs become more complex, skilled programmers often break each test case into individual steps of the algorithm/program and indicate what the expected result of each step should be. When you write a detailed test case, you don’t necessarily need to specify the expected result for each test step if the result is obvious.

In computer programming we accept a problem to solve and develop an algorithm that can serve as a general solution. Once we have such a solution, we can use our computer to automate the execution. Programming is a skill that allows a competent programmer to take an algorithm and represent it in a notation (a program) that can be followed by a computer. These programs are written in programming languages (such as Python). Writing a correct and valid algorithm to solve a computational problem is key to writing good code. Learn to Think First and coding will come naturally!

The Process of Computational Problem Solving

Computational problem solving does not simply involve the act of computer programming. It is a process, with programming being only one of the steps. Before a program is written, a design for the program must be developed (the algorithm). And before a design can be developed, the problem to be solved must be well understood. Once written, the program must be thoroughly tested. These steps are outlined in Figure 5.

Figure 5: Process of Computational Problem Solving [footnote]Dierbach, Charles. Introduction to Computer Science Using Python: A Computational Problem-solving Focus. Wiley Publishing, 2012, pp17-18.[/footnote]

Values and Variables

A value is one of the basic things computer programs works with, like a password or a number of errors.

Values belong to different types: 21 is an integer (like the number of errors), and ‘comp15’ is a string of characters (like the password). Python lets you give names to values giving us the ability to generalize our algorithms.

One of the most powerful features of a programming language is the ability to use variables. A variable is simply a name that refers to a value as shown below,

Whenever the variable errors appears in a calculation the current value of the variable is used.

We need some way of storing information (i.e. the number of errors or the password) and manipulate them as well. This is where variables come into the picture. Variables are exactly what the name implies – their value can vary, i.e., you can store anything using a variable. Variables are just parts of your computer’s memory where you store some information. Unlike literal constants, you need some method of accessing these variables and hence you give them names.

Programmers generally choose names for their variables that are meaningful and document what the variable is used for. It is a good idea to begin variable names with a lowercase letter . The underscore character (_) can appear in a name and is often used in names with multiple words.

A program is a sequence of instructions that specifies how to perform a computation. The computation might be something mathematical, such as solving a system of mathematical equations or finding the roots of a polynomial, but it can also be a symbolic computation, such as searching and replacing text in a document or something graphical, like processing user input on an ATM device.

What is a Program?

Figure 6: “ Python Code ” by nyuhuhuu is licensed under CC-BY 2.0

The details look different in different computer programming languages, but there are some low-level conceptual patterns (constructs) that we use to write all programs. These constructs are not just for Python programs, they are a part of every programming language.

input Get data from the “outside world”. This might be reading data from a file, or even some kind of sensor like a microphone or GPS. In our initial algorithms and programs, our input will come from the user typing data on the keyboard.

output Display the results of the program on a screen or store them in a file or perhaps write them to a device like a speaker to play music or speak text.

sequential execution Perform statements one after another in the order they are encountered in the script.

conditional execution Checks for certain conditions and then executes or skips a sequence of statements.

repeated execution Perform some set of statements repeatedly, usually with some variation.

reuse Write a set of instructions once and give them a name and then reuse those instructions as needed throughout your program.

Believe it or not, that’s pretty much all there is to it. Every computer application you’ve ever used, no matter how complicated, is made up of constructs that look pretty much like these. So you can think of programming as the process of breaking a large, complex task into smaller and smaller subtasks until the subtasks are simple enough to be performed with one of these basic constructs. The “art” of writing a program is composing and weaving these basic elements together many times over to produce something that is useful to its users.

Computational Problem Design Using the Basic Programming Constructs

The key to better algorithm design and thus to programming lies in limiting the control structure to only three constructs as shown below.

• The Sequence structure (sequential execution)
• The Decision, Selection or Control structure (conditional execution)
• Repetition or Iteration Structure (repeated execution)

Figure 7: the 3 Programming Constructs

  Let us look at some examples for the sequential control and the selection control.

Sequential Control Example

The following algorithm is an example of sequential control .

Problem : Given two numbers, return the sum and the product of the two numbers.

Inputs : Two numbers.

Outputs : The sum and the product.

• display “Input two numbers”
• sum = number1 + number2
• print “The sum is “, sum
• product = number1 * number2
• print “The product is “, product
• Is it guaranteed to terminate? Yes. Sequential control, by its nature, always ends.
• Is it general for any input? Yes. Any two numbers work in this design.
• Does it produce the correct result? Yes. When tested, the results are what are expected.

Here is an example of three different test cases that are used to verify the algorithm.

Selection Control

The following two algorithms are examples of selection control which uses the ‘IF’ statement in most programming languages.

Problem : Given two numbers, the user chooses to either multiply, add or subtract the two numbers. Return the value of the chosen calculation.

Inputs : Two numbers and calculation option.

Outputs : The value of the chosen calculation.

The relational (or comparison) operators used in selection control are:

= is equal to

> is greater than

< is less than

>= is greater than or equal

<= is less than or equal

<> is not equal to

• display “choose one of the following”
• display “m for multiply”
• display “a for add”
• display “s for subtract”
• accept choice
• display “input two numbers you want to use”
• accept number1, number2
• if choice = m then answer= number1 * number2
• if choice = a then answer= number1 + number2
• if choice = s then answer= number1 -number212. if choice is not m, a, or s then answer is NONE
• display answer
• Is it guaranteed to terminate? Yes. The input is of finite length, so after accepting the user’s choice and the two numbers the algorithm will stop.
• Is it general for any input? Yes. Any two numbers work in this design and only a choice of a’m’, ‘a’, or ‘s’ will result in numeric output.

This example uses an extension of the simple selection control structure we just saw and is referred to as the ‘IF-ELSE’ structure.

Problem : Accept from the user a positive integer value representing a salary amount, return tax due based on the salary amount.

Inputs : One positive integer number.

Outputs : The calculated tax amount.

• accept salary
• If salary < 50000 then
• Tax = 0 Else
• If salary > 50000 AND salary < 100000 then
• Tax = 50000 * 0.05 Else
• Tax = 100000 * 0.30
• display Tax
• Is it guaranteed to terminate? Yes. The input is of finite length, so after accepting the user’s number, even if it is negative, the algorithm will stop.
• Is it general for any input? Yes. Any number entered in this design will work.

Iterative Control Examples

The third programming control is the iterative or, also referred to as, the repetition structure. This control structure causes certain steps to be repeated in a sequence a specified number of times or until a condition is met. This is what is called a ‘loop’ in programming

In all programming languages there are generally two options: an indefinite loop (the Python ‘WHILE’ programming statement) and a definite loop (the Python ‘FOR’ programming statement). We can use these two constructs, WHILE and FOR, for iterations or loops in our algorithms.

Note for Reader: A definite loop is where we know exactly the number of times the loop’s body will be executed. Definite iteration is usually best coded as a Python for loop. An indefinite loop is where we do not know before entering the body of the loop the exact number of iterations the loop will perform. The loop just keeps going until some condition is met. A while statement is used in this case.

The following algorithm is an example of iterative control using WHILE .

Problem : Print each keyboard character the users types in until the user chooses the ‘q’ (for ‘quit’) character.

Inputs : A series of individual characters.

Outputs : Each character typed in by the user.

• initialize (set) letter = ‘a’
• WHILE letter <> ‘q’
• ACCEPT letter
• DISPLAY “The character you typed is”, letter
• Is it guaranteed to terminate? Yes. The input is of finite length, so after accepting the user’s keyboard character, even if it is not a letter, the algorithm will stop.
• Is it general for any input? Yes. Any keyboard character entered in this design will work.

The following algorithm is an example of iterative control using FOR . This statement is used when the number of iterations is known in advance.

Problem : Ask the user how many words they want to enter then print the words entered by the user.

Inputs : Number of words to be entered; this value must be a positive integer greater than zero. Individual words.

Outputs : Each word typed in by the user.

• accept num_words (must be at least one)
• repeat num_words times (FOR 1 to num_words)
• accept word
• DISPLAY “The word you entered is”, word
• Is it guaranteed to terminate? Yes. The input is of finite length, so after accepting the user’s number of words to enter and any characters typed on the keyboard, even if it is not a ‘word’ per say, the algorithm will stop.
• Is it general for any input? Yes. Any positive integer greater than zero and any size ‘word’ will work.

Here is an example of two different test cases that are used to verify the algorithm.

The Role of Programming in the Field of Informatics

Figure8: iPhone apps by Jaap Arriens/NurPhoto via Getty Images (abcnews.go.com)

You see computer programming in use every day. When you use Google or your smartphone, or watch a movie with special effects, there is programing at work. When you order a product over the Internet, there is code in the web site, in the cryptography used to keep your credit card number secure, and in the way that UPS routes their delivery vehicle to get your order to you as quickly as possible.

Programming is indeed important to an informatics professional as they are interested in finding solutions for a wide variety of computational problems involving data.

When you Google the words “pie recipe,” Google reports that it finds approximately 38 million pages, ranked in order of estimated relevance and usefulness. Facebook has approximately 1 billion active users who generate over 3 billion comments and “Likes” each day. GenBank, a national database of DNA sequences used by biologists and medical researchers studying genetic diseases, has over 100 million genetic sequences with over 100 billion DNA base pairs. According to the International Data Corporation, by 2020 the digital universe – the data we create and copy annually – will reach 44 zettabytes, or 44 trillion gigabytes.

Figure 9: The Digital Universe ( www.emc.com/leadership/digital-universe/2014iview/images )

  Doing meaningful things with data is challenging, even if we’re not dealing with millions or billions of things. In this book, we will be working with smaller sets of data. But much of what we’ll do will be applicable to very large amounts of data too.

Unit Summary

Computational Thinking is the thought processes involved in formulating a problem and expressing its solution in a way that a computer—human or machine—can effectively carry out.

Computational Thinking is what comes before any computing technology—thought of by a human, knowing full well the power of automation.

Writing a correct and valid algorithm to solve a computational problem is key to writing good code.

• What are the inputs?
• What are the outputs (or results)?
• Can we break the problem into parts?
• Think about the connections between the input & output.
• Consider designing ‘backwards’.
• Have you seen the problem before? In a slightly different form?
• Can you solve part of the problem?
• Did you use all the inputs?
• Can you test it on a variety of inputs?
• Can you think of how you might write the algorithm differently if you had to start again?
• Does it solve the problem? Does it meet all the requirements? Is the output correct?
• Does it terminate?
• Is it general for all cases?

Practice Problems

• Write about a process in your life (e.g. driving to the mall, walking to class, etc.) and estimate the number of steps necessary to complete the task. Would you consider this a complex or simple task? What happens if you scale that task (e.g. driving two states away to the mall)? Is your method the most efficient? Can you come up with a more efficient way?

• Write an algorithm to find the average of 25 test grades out of a possible 100 points.
• If you are given three sticks, you may or may not be able to arrange them in a triangle. For example, if one of the sticks is 12 inches long and the other two are one inch long, it is clear that you will not be able to get the short sticks to meet in the middle. For any three lengths, there is a simple test to see if it is possible to form a triangle: “If any of the three lengths is greater than the sum of the other two, then you cannot form a triangle. Otherwise, you can.”Write an algorithm that accepts three integers as arguments, and that displays either “Yes” or “No,” depending on whether you can or cannot form a triangle from sticks with the given lengths.
• ROT13 is a weak form of encryption that involves “rotating” each letter in a word by 13 places. To rotate a letter means to shift it through the alphabet, wrapping around to the beginning if necessary, so ‘A’ shifted by 3 is ‘D’ and ‘Z’ shifted by 1 is ‘A’. Write an algorithm that accepts a word and an integer from the user, and that prints a new encrypted word that contains the letters from the original word “rotated” by the given amount (the integer input). For example, “cheer” rotated by 7 is “jolly” and “melon” rotated by −10 is “cubed.”
• Write an algorithm which repeatedly accepts numbers until the user enters “done”. Once “done” is entered, display the total sum of all the numbers, the count of numbers entered, and the average of all the numbers.
• Write an algorithm that sums a series of ten positive integers entered by the user excluding all numbers greater than 100. Display the final sum.
• Wing, Jeannette M. "Computational thinking." Communications of the ACM 49.3 (2006): 33-35. ↵

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Expert advice

Dynamic Programming: An Approach to Solving Computing Problems

Sometimes in computer science, you will run into problems. You can divide these into subproblems, which can, in turn, be divided into smaller subproblems. If the smaller subproblems overlap, then you can save the result in memory for future reference. This way, you don’t need to compute the same result multiple times, thus increasing the efficiency of the program substantially. This way of solving these problems is referred to as dynamic programming.

In this article, you will learn what dynamic programming is. I will also show how to compute Fibonacci numbers, which is a simple problem that dynamic programming can solve. I will compare the dynamic programming solutions to the naive solution that uses recursion. These examples are written in Python syntax. Finally, I’ll also give some general pointers to keep in mind when attempting to solve problems using dynamic programming

Dynamic programming

More From Artturi Jalli: Python Cheat Sheet: A Handy Guide to Python

What Types of Problems Can Dynamic Programming Solve?

Dynamic programming is typically a way to optimize solutions to certain problems that use recursion. If a recursive solution to a problem has to compute solutions for subproblems with the same inputs repeatedly, then you can optimize it through dynamic programming. As mentioned earlier, in this case, you would simply save the result of the computation for use later if and when it’s needed. This optimization can reduce the time complexity of an algorithm from exponential time to polynomial time. This means that the number of computations n scales like a polynomial expression instead of scaling like an exponential expression as n increases. In general, polynomial expressions grow much slower than exponential expressions.

There are two conditions that need to be satisfied to use dynamic programming:

• Overlapping subproblems
• Optimal substructure property

What Are Overlapping Subproblems?

I alluded to the overlapping subproblems condition earlier. It simply means that when solving the problem in question, the solutions for the same subproblems are repeatedly necessary. In this case, the solutions to these subproblems can be stored for later use to skip recomputation.

Another way to think about this condition is to turn it upside down. If there are no overlapping subproblems, then there’s no point in saving the solutions for the subproblems, and you can’t use dynamic programming.

There are two different ways of storing the solutions to the overlapping subproblems:

• Memoization (top-down)
• Tabulation (bottom-up)

What Is Memoization?

The memoization approach to dynamic programming is very similar to the naive recursion approach, with only a small change. The difference is that we use a lookup table to store solutions to the subproblems, and then use this table to check whether that solution already exists.

If the solution for a certain subproblem already exists in the lookup table, then that solution is returned from the lookup table. If it does not, then it needs to be computed (through recursion) and added to the lookup table.

For the sake of clarity, let’s define a solution for a subproblem in our dynamic programming problem to be DP[X] ., with DP[N] being the desired solution and DP[0] being the base solution. In the memoization approach, the program starts from DP[N] and asks for the solutions from which DP[N] can be reached (these should be subproblems of lower order DP[n<N]) . Then, from these states, the same process is repeated recursively, until reaching the base solution DP[0] .

If this feels a little too abstract, don’t worry. The examples introduced later in this article should clarify what I mean.

Memoization is known as a top-down approach to dynamic programming since the program will start from the desired, last (top) state and work its way down recursively.

What Is Tabulation?

The tabulation approach to dynamic programming works in a reverse manner compared to the memoization approach. The program will start from the base (or bottom) solution for the subproblem and work its way up, solving the subproblems one by one until reaching the desired solution.

In terms of solutions to subproblems, the tabulation approach starts from the base solution DP[0] and then calculates DP[1], DP[2], … DP[N] until reaching the desired solution for the subproblem DP[N] . Since we started from the base solution DP[0] and worked towards the desired solution DP[N] , the tabulation approach is also known as a bottom-up approach.

Again, the examples below should make this easier to understand.

What Is Optimal Substructure Property?

If the optimal solution to a problem can be obtained using the optimal solution to its subproblems, then the problem is said to have optimal substructure property .

As an example, let’s consider the problem of finding the shortest path between ‘Start’ and ‘Goal’ nodes in the graph below. The nodes are connected to other nodes via edges, and the distance between two connected nodes is marked with a number next to the edge.

The shortest path from the Start node to the Goal node is through nodes three and four.

This problem clearly has optimal substructure property. Since the shortest path from the Start node to the Goal node goes through Node Four, it clearly follows that this path is a combination of the shortest path from the Start node to Node Four and the shortest path from Node Four to the Goal node.

Many problems do not have optimal substructure property. For example, the problem of finding the longest path (with no cycles) between the Start node and the Goal node in the above graph doesn’t. Here’s how you can see this:

The longest path is: Start - Node Three - Node Two - Node One - Node Four - Goal. However, this does not imply that the longest path from the Start node to Node Two is Start - Node Three - Node Two. The longest path from the Start node to Node Two is actually Start - Node One - Node Four - Node Three - Node Two (and Start - Node One - Node Four - Goal - Node Two, which has equal length to the first one).

Dynamic Programming Example: Calculating Fibonacci Numbers

One of the simplests examples of dynamic programming is the computation of Fibonacci numbers, which are numbers from the Fibonacci sequence. The first Fibonacci number is zero, the second is one, and the subsequent numbers are the sum of the previous two Fibonacci numbers. The 10 first Fibonacci numbers are  zero, one, one, two, three, five, eight, 13, 21, and 34.

Let’s first start with the naive, recursive solution. Here’s a Python function to calculate the nth Fibonacci number (indexing starts from zero):

From this example it is easy to see that this problem satisfies the overlapping subproblems condition since the function clearly has to calculate the previous Fibonacci numbers multiple times (when n > three). The smallest Fibonacci numbers are computed most often, when this function is called for a large n.

This problem also clearly has optimal substructure since there is only a single solution for the subproblems, which are used to compute the solution to the desired problem.

Due to the recursion, this function runs in exponential time.

Let’s next look at how this could be solved using dynamic programming. Let’s start with a top-down solution using memoization. Here’s a Python function that calculates the nth Fibonacci number that implements dynamic programming through memoization:

This approach is quite similar to the recursive approach since it starts from calculating the nth Fibonacci number and, in order to calculate it, goes onto calculating the n-1st and n-2nd Fibonacci numbers. The difference is in the lookup table, where the smaller Fibonacci numbers will be saved as they are calculated, so that they do not need to be calculated again and again.

This makes this function actually run in linear time instead of exponential time.

For the sake of an example, let’s also look at a Python function that solves the same problem in a bottom-up manner with dynamic programming using tabulation:

In this solution, the nth Fibonacci number is calculated in a bottom-up manner, starting by calculating the first Fibonacci number, then the second, third and so on until reaching the nth Fibonacci number. This function also runs in linear time.

More in Software Engineering: Glob Module in Python: Explained

How to Solve Problems Using Dynamic Programming

The first step to solving a problem using dynamic programming is to identify it as a dynamic programming problem. If you can validate that the problem has overlapping subproblems and that it satisfies the optimal substructure property, you can be sure that you can solve it with dynamic programming.

The second step is to decide on a state expression. This state is the set of parameters that uniquely identifies the different subproblems.

In the Fibonacci numbers example, the parameter identifying the state would just be the serial number of a certain Fibonacci number.

There can be more than one parameter identifying a state. You should always use as few parameters as possible, however.

The third — and probably hardest — step in solving problems using dynamic programming is formulating the relation between the different states.

In the Fibonacci number case this is simple, however, since the nth Fibonacci number is the sum of the n-1st and n-2nd Fibonacci numbers. So F[n] = F[n-1] + F[n-2].

The fourth step is to implement memoization or tabulation for the states that you decided upon, using the relation you discovered between the states. This means simply saving the state (or in other words the solution to a certain subproblem) so it can be recovered from memory without recomputation when it is needed again. This should be fairly simple, if you did steps one to three well

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• Interview Problems on DP
• Practice DP
• Tutorial on Dynamic Programming
• Optimal Substructure
• Overlapping Subproblem
• Memoization
• Tabulation vs Memoization
• 0/1 Knapsack
• Unbounded Knapsack
• Coin Change
• Egg Dropping Puzzle
• Matrix Chain Multiplication
• Palindrome Partitioning
• DP on Arrays
• DP with Bitmasking
• DP on Trees
• DP on Graph
• Dynamic Programming or DP
• What is memoization? A Complete tutorial

Dynamic Programming (DP) Tutorial with Problems

• Optimal Substructure Property in Dynamic Programming | DP-2
• Overlapping Subproblems Property in Dynamic Programming | DP-1
• Steps for how to solve a Dynamic Programming Problem

Advanced Topics

• Bitmasking and Dynamic Programming | Set 1 (Count ways to assign unique cap to every person)
• Digit DP | Introduction
• Sum over Subsets | Dynamic Programming

Easy problems in Dynamic programming

• Count all combinations of coins to make a given value sum (Coin Change II)
• Subset Sum Problem
• Introduction and Dynamic Programming solution to compute nCr%p
• Cutting a Rod | DP-13
• Painting Fence Algorithm
• Longest Common Subsequence (LCS)
• Longest Increasing Subsequence (LIS)
• Longest subsequence such that difference between adjacents is one
• Maximum size square sub-matrix with all 1s
• Min Cost Path | DP-6
• Longest Common Substring (Space optimized DP solution)
• Count ways to reach the nth stair using step 1, 2 or 3
• Count Unique Paths in matrix
• Unique paths in a Grid with Obstacles

Medium problems on Dynamic programming

• 0/1 Knapsack Problem
• Printing Items in 0/1 Knapsack
• Unbounded Knapsack (Repetition of items allowed)
• Egg Dropping Puzzle | DP-11
• Word Break Problem | DP-32
• Vertex Cover Problem (Dynamic Programming Solution for Tree)
• Tile Stacking Problem
• Box Stacking Problem | DP-22
• Partition problem | DP-18
• Travelling Salesman Problem using Dynamic Programming
• Longest Palindromic Subsequence (LPS)
• Longest Common Increasing Subsequence (LCS + LIS)
• Find all distinct subset (or subsequence) sums of an array
• Weighted Job Scheduling
• Count Derangements (Permutation such that no element appears in its original position)
• Minimum insertions to form a palindrome | DP-28
• Ways to arrange Balls such that adjacent balls are of different types

Hard problems on Dynamic programming

• Word Wrap Problem
• The Painter's Partition Problem
• Program for Bridge and Torch problem
• Matrix Chain Multiplication | DP-8
• Printing brackets in Matrix Chain Multiplication Problem
• Maximum sum rectangle in a 2D matrix | DP-27
• Maximum profit by buying and selling a share at most k times
• Minimum cost to sort strings using reversal operations of different costs
• Count of AP (Arithmetic Progression) Subsequences in an array
• Introduction to Dynamic Programming on Trees
• Maximum height of Tree when any Node can be considered as Root
• Longest repeating and non-overlapping substring
• Top 20 Dynamic Programming Interview Questions

Dynamic Programming (DP) is defined as a technique that solves some particular type of problems in Polynomial Time. Dynamic Programming solutions are faster than the exponential brute method and can be easily proved their correctness.

Important Topics in Dynamic Programming Tutorial

Characteristics of dynamic programming algorithm:, what is the difference between a dynamic programming algorithm and recursion, techniques to solve dynamic programming problems:.

• Tabulation(Dynamic Programming) vs Memoization:
• How to solve a Dynamic Programming Problem?

How to solve Dynamic Programming problems through Example?

Greedy approach vs dynamic programming, some commonly asked problems in dynamic programming:, faqs about dynamic programming algorithm:.

Dynamic Programming is mainly an optimization over plain recursion . Wherever we see a recursive solution that has repeated calls for the same inputs, we can optimize it using Dynamic Programming. The idea is to simply store the results of subproblems so that we do not have to re-compute them when needed later. This simple optimization reduces time complexities from exponential to polynomial.

Introduction to Dynamic Programming – Data Structures and Algorithm Tutorials

• In general, dynamic programming (DP) is one of the most powerful techniques for solving a certain class of problems. 
• There is an elegant way to formulate the approach and a very simple thinking process, and the coding part is very easy. 
• Essentially, it is a simple idea, after solving a problem with a given input, save the result as a reference for future use, so you won’t have to re-solve it.. briefly ‘Remember your Past’ :). 
• It is a big hint for DP if the given problem can be broken up into smaller sub-problems, and these smaller subproblems can be divided into still smaller ones, and in this process, you see some overlapping subproblems. 
• Additionally, the optimal solutions to the subproblems contribute to the optimal solution of the given problem (referred to as the Optimal Substructure Property ).
•  The solutions to the subproblems are stored in a table or array (memoization) or in a bottom-up manner (tabulation) to avoid redundant computation.
• The solution to the problem can be constructed from the solutions to the subproblems.
• Dynamic programming can be implemented using a recursive algorithm, where the solutions to subproblems are found recursively, or using an iterative algorithm, where the solutions are found by working through the subproblems in a specific order.

Dynamic programming works on following principles: 

• Characterize structure of optimal solution, i.e. build a mathematical model of the solution.
• Recursively define the value of the optimal solution. 
• Using bottom-up approach, compute the value of the optimal solution for each possible subproblems.
•  Construct optimal solution for the original problem using information computed in the previous step.

Applications:

Dynamic programming is used to solve optimization problems. It is used to solve many real-life problems such as,

(i) Make a change problem

 (ii) Knapsack problem

(iii) Optimal binary search tree

• In dynamic programming , problems are solved by breaking them down into smaller ones to solve the larger ones, while recursion is when a function is called and executed by itself. While dynamic programming can function without making use of recursion techniques, since the purpose of dynamic programming is to optimize and accelerate the process, programmers usually make use of recursion techniques to accelerate and turn the process efficiently.
• When a function can execute a specific task by calling itself, receive the name of the recursive function. In order to perform and accomplish the work, this function calls itself when it has to be executed.
• Using dynamic programming , you can break a problem into smaller parts, called subproblems, to solve it. Dynamic programming involves solving the problem for the first time, then using memoization to store the solutions.
• Therefore, the main difference between the two techniques is their intended use; recursion is used to automate a function, whereas dynamic programming is an optimization technique used to solve problems.
• Recursive functions recognize when they are needed, execute themselves, then stop working. When the function identifies the moment it is needed, it calls itself and is executed; this is called a recursive case. As a result, the function must stop once the task is completed, known as the base case.
• By establishing states, dynamic programming recognizes the problem and divides it into sub-problems in order to solve the whole scene. After solving these sub-problems, or variables, the programmer must establish a mathematical relationship between them. Last but not least, these solutions and results are stored as algorithms, so they can be accessed in the future without having to solve the whole problem again.

1. Top-Down(Memoization):

Break down the given problem in order to begin solving it. If you see that the problem has already been solved, return the saved answer. If it hasn’t been solved, solve it and save it. This is usually easy to think of and very intuitive, This is referred to as Memoization .

2. Bottom-Up(Tabulation):

Analyze the problem and see in what order the subproblems are solved, and work your way up from the trivial subproblem to the given problem. This process ensures that the subproblems are solved before the main problem. This is referred to as Dynamic Programming .

Types of the approach of dynamic programming algorithm

Tabulation vs Memoization:

There are two different ways to store the values so that the values of a sub-problem can be reused. Here, will discuss two patterns of solving dynamic programming (DP) problems: 

• Tabulation: Bottom Up
• Memoization: Top Down

Before getting to the definitions of the above two terms consider the following statements:

• Version 1 : I will study the theory of DP from GeeksforGeeks, then I will practice some problems on classic DP and hence I will master DP.
• Version 2 : To Master DP, I would have to practice Dynamic problems and practice problems – Firstly, I would have to study some theories of DP from GeeksforGeeks

Both versions say the same thing, the difference simply lies in the way of conveying the message and that’s exactly what Bottom-Up and Top-Down DP do. Version 1 can be related to Bottom-Up DP and Version-2 can be related to Top-Down DP.

To dynamically solve a problem, we need to check two necessary conditions: 

• Overlapping Subproblems : When the solutions to the same subproblems are needed repetitively for solving the actual problem. The problem is said to have overlapping subproblems property.  

N-th Fibonacci Series as Overlapping Subproblems

• Optimal Substructure Property : If the optimal solution of the given problem can be obtained by using optimal solutions of its subproblems then the problem is said to have Optimal Substructure Property.

Steps to solve a Dynamic programming problem:

• Identify if it is a Dynamic programming problem.
• Decide a state expression with the Least parameters.
• Formulate state and transition relationships.
• Do tabulation (or memorization).

1) How to classify a problem as a Dynamic Programming algorithm Problem?

• Typically, all the problems that require maximizing or minimizing certain quantities or counting problems that say to count the arrangements under certain conditions or certain probability problems can be solved by using Dynamic Programming.
• All dynamic programming problems satisfy the overlapping subproblems property and most of the classic Dynamic programming problems also satisfy the optimal substructure property. Once we observe these properties in a given problem be sure that it can be solved using Dynamic Programming.

2) Deciding the state:

Problems with dynamic programming are mostly concerned with the state and its transition. The most fundamental phase must be carried out with extreme care because the state transition depends on the state definition you select.

A state is a collection of characteristics that can be used to specifically describe a given position or standing in a given challenge. To minimise state space, this set of parameters has to be as compact as feasible.

3) Formulating a relation among the states:

The hardest part of a Dynamic Programming challenge is this step, which calls for a lot of intuition, observation, and training.

Given 3 numbers {1, 3, 5}, the task is to tell the total number of ways we can form a number N using the sum of the given three numbers. (allowing repetitions and different arrangements).

The total number of ways to form 6 is: 8 1+1+1+1+1+1 1+1+1+3 1+1+3+1 1+3+1+1 3+1+1+1 3+3 1+5 5+1

Following are the steps to solve the problem:

• We choose a state for the given problem.
• N will be used as the determining factor for the state because it can be used to identify any subproblem.
• The DP state will resemble state(N), where the state(N) is the total number of arrangements required to create N using the elements 1, 3, and 5. Identify the relationship of the transition between any two states.
• We must now calculate the state (N).

3.1) How to Compute the state?

As we can only use 1, 3, or 5 to form a given number N. Let us assume that we know the result for N = 1, 2, 3, 4, 5, 6 

Let us say we know the result for: state (n = 1), state (n = 2), state (n = 3) ……… state (n = 6)  Now, we wish to know the result of the state (n = 7). See, we can only add 1, 3, and 5. Now we can get a sum total of 7 in the following 3 ways:

1) Adding 1 to all possible combinations of state (n = 6)  Eg: [ (1+1+1+1+1+1) + 1]  [ (1+1+1+3) + 1]  [ (1+1+3+1) + 1]  [ (1+3+1+1) + 1]  [ (3+1+1+1) + 1]  [ (3+3) + 1]  [ (1+5) + 1]  [ (5+1) + 1] 2) Adding 3 to all possible combinations of state (n = 4); [(1+1+1+1) + 3]  [(1+3) + 3]  [(3+1) + 3] 3) Adding 5 to all possible combinations of state(n = 2)  [ (1+1) + 5] (Note how it sufficient to add only on the right-side – all the add-from-left-side cases are covered, either in the same state, or another, e.g. [ 1+(1+1+1+3)]  is not needed in state (n=6) because it’s covered by state (n = 4) [(1+1+1+1) + 3]) Now, think carefully and satisfy yourself that the above three cases are covering all possible ways to form a sum total of 7; Therefore, we can say that result for  state(7) = state (6) + state (4) + state (2)  OR state(7) = state (7-1) + state (7-3) + state (7-5) In general,  state(n) = state(n-1) + state(n-3) + state(n-5)

Below is the implementation for the above approach:

Time Complexity: O(3 n ), As at every stage we need to take three decisions and the height of the tree will be of the order of n. Auxiliary Space: O(n), The extra space is used due to the recursion call stack.

The above code seems exponential as it is calculating the same state again and again. So, we just need to add memoization .

4) Adding memoization or tabulation for the state

The simplest portion of a solution based on dynamic programming is this. Simply storing the state solution will allow us to access it from memory the next time that state is needed.

Adding memoization to the above code:

Time Complexity: O(n), As we just need to make 3n function calls and there will be no repetitive calculations as we are returning previously calculated results. Auxiliary Space: O(n), The extra space is used due to the recursion call stack.

Problem: Let’s find the Fibonacci sequence up to the nth term . A Fibonacci series is the sequence of numbers in which each number is the sum of the two preceding ones. For example, 0, 1, 1, 2, 3, and so on. Here, each number is the sum of the two preceding numbers.

Naive Approach: The basic way to find the nth Fibonacci number is to use recursion .

Complexity Analysis: 

Time Complexity: O(2 n )

• Here, for every n, we are required to make a recursive call to fib(n – 1) and fib(n – 2). For fib(n – 1), we will again make the recursive call to fib(n – 2) and fib(n – 3). Similarly, for fib(n – 2), recursive calls are made on fib(n – 3) and fib(n – 4) until we reach the base case.
• During each recursive call, we perform constant work(k) (adding previous outputs to obtain the current output). We perform 2nK work at every level (where n = 0, 1, 2, …). Since n is the number of calls needed to reach 1, we are performing 2n-1k at the final level. Total work can be calculated as:
• If we draw the recursion tree of the Fibonacci recursion then we found the maximum height of the tree will be n and hence the space complexity of the Fibonacci recursion will be O(n).

Efficient approach: As it is a very terrible complexity(Exponential), thus we need to optimize it with an efficient method. (Memoization)

Let’s look at the example below for finding the 5th Fibonacci number.

Representation of 5th Fibonacci number

Observations:

The entire program repeats recursive calls. As in the above figure, for calculating fib(4), we need the value of fib(3) (first recursive call over fib(3)), and for calculating fib(5), we again need the value of fib(3)(second similar recursive call over fib(3)).  Both of these recursive calls are shown above in the outlining circle.  Similarly, there are many others for which we are repeating the recursive calls.  Recursion generally involves repeated recursive calls, which increases the program’s time complexity.  By storing the output of previously encountered values (preferably in arrays, as these can be traversed and extracted most efficiently), we can overcome this problem. The next time we make a recursive call over these values, we will use their already stored outputs instead of calculating them all over again.  In this way, we can improve the performance of our code. Memoization is the process of storing each recursive call’s output for later use, preventing the code from calculating it again.  Way to memoize: To achieve this in our example we will simply take an answer array initialized to -1. As we make a recursive call, we will first check if the value stored in the answer array corresponding to that position is -1. The value -1 indicates that we haven’t calculated it yet and have to recursively compute it. The output must be stored in the answer array so that, next time, if the same value is encountered, it can be directly used from the answer array.   

Now in this process of memoization, considering the above Fibonacci numbers example, it can be observed that the total number of unique calls will be at most (n + 1) only.

Complexity analysis:

• Time complexity: O(n)
• Auxiliary Space: O(n)

Optimized approach: Following a bottom-up approach to reach the desired index. This approach of converting recursion into iteration is known as Dynamic programming(DP).

Finally, what we do is recursively call each response index field and calculate its value using previously saved outputs.  Recursive calls terminate via the base case, which means we are already aware of the answers which should be stored in the base case indexes.  In the case of Fibonacci numbers, these indices are 0 and 1 as f(ib0) = 0 and f(ib1) = 1. So we can directly assign these two values ​​into our answer array and then use them to calculate f(ib2), which is f(ib1) + f(ib0), and so on for each subsequent index.  This can easily be done iteratively by running a loop from i = (2 to n). Finally, we get our answer at the 5th index of the array because we already know that the ith index contains the answer to the ith value. Simply, we first try to find out the dependence of the current value on previous values ​​and then use them to calculate our new value. Now, we are looking for those values which do not depend on other values, which means they are independent(base case values, since these, are the smallest problems which we are already aware of).

Complexity analysis: 

Optimization of above method

in above code we can see that the current state of any fibonacci number depend only on prev two number so using this observation we can conclude that we did not need to store the whole table of size n but instead of that we can only store the prev two values so this way we can optimize the space complexity in the above code O(n) to O(1)

1) Is dynamic programming just recursion?

Dynamic programming and recursion are things completely different. While dynamic programming can use recursion techniques, recursion itself doesn’t have anything similar to dynamic programming. . Dynamic programming involves breaking down a problem into smaller subproblems, storing the solutions to these subproblems to avoid redundant computation, and using these solutions to construct the overall solution. Recursion, on the other hand, is a technique for solving problems by breaking them down into smaller subproblems and solving them recursively.

2) How does dynamic programming works?

Dynamic Programming (DP) is a technique that solves some particular type of problems in Polynomial Time. Dynamic Programming solutions are faster than the exponential brute method and can be easily proved their correctness. Dynamic programming works by breaking down a problem into smaller subproblems, solving each subproblem independently, and using the solutions to these subproblems to construct the overall solution. The solutions to the subproblems are stored in a table or array (memoization) or in a bottom-up manner (tabulation) to avoid redundant computation.

3) How greedy algorithms are similar to Dynamic programming?

Greedy Algorithms are similar to dynamic programming in the sense that they are both tools for optimization. Both dynamic programming and greedy algorithms are used for optimization problems. However, while dynamic programming breaks down a problem into smaller subproblems and solves them independently, greedy algorithms make a locally optimal choice at each step with the hope of finding a globally optimal solution.

4) What are the basics of Dynamic programming?

You can solve subproblems faster by using dynamic programming, which is nothing more than recursion and memoization, thereby reducing the complexity of your code and making it faster. Following are the basic points:

• Breaking down a problem into smaller subproblems.
• Solving each subproblem independently.
• Storing the solutions to subproblems to avoid redundant computation.
• Using the solutions to the subproblems to construct the overall solution.
• Using the principle of optimality to ensure that the solution is optimal.

5) What are the advantages of Dynamic programming?

Dynamic programming has the advantage of being able to find both a local and a global optimal solution. Additionally, practical experience can be exploited to benefit from dynamic programming’s better efficiency. However, there isn’t a single, accepted paradigm for dynamic programming, and other conditions could show up as the problem is being solved. Dynamic programming algorithms are guaranteed to find the optimal solution among a set of possible solutions, provided that the problem satisfies the principle of optimality. The solutions to subproblems can be stored in a table, which can be reused for similar problems. Dynamic programming can be applied to a wide range of problems, including optimization, sequence alignment, and resource allocation.

Conclusion:

In conclusion, dynamic programming is a powerful problem-solving technique that is used for optimization problems. Dynamic programming is a superior form of recursion that overcomes its limitations. It involves breaking down a problem into smaller subproblems, solving each subproblem independently, and using the solutions to these subproblems to construct the overall solution. The key characteristics of a dynamic programming algorithm include overlapping subproblems, optimal substructure, memoization or tabulation, and the use of either iterative or recursive methods.

Dynamic programming has several advantages over other problem-solving techniques, including efficiency, simplicity, flexibility, optimality, clarity, and code reusability. It is not just recursion, although it can be implemented using a recursive algorithm. Dynamic programming is different from greedy algorithms in that it breaks down the problem into smaller subproblems, solves each subproblem independently, and uses the solutions to the subproblems to construct the overall solution.

The basics of dynamic programming include breaking down a problem into smaller subproblems, solving each subproblem independently, storing the solutions to subproblems to avoid redundant computation, using the solutions to the subproblems to construct the overall solution and using the principle of optimality to ensure that the solution is optimal.  However, DP can occasionally be challenging to comprehend, making it a well-liked option for coding interviews. Understanding how DP functions work can be useful to everyone, whether they are a professional or a student getting ready for the placements. 

Overall, dynamic programming is a valuable tool for solving complex optimization problems and can lead to more efficient and effective solutions.

Some important links:

• Top 20 Dynamic programming interview questions
• Dynamic programming
• Practice Problems on Dynamic Programming
• Interview series

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Generative AI is transforming the software development industry. AI-powered coding tools are assisting programmers in their workflows, while jobs in AI continue to increase. But the shift is also evident in academia—one of the major avenues through which the next generation of software engineers learn how to code.

Computer science students are embracing the technology, using generative AI to help them understand complex concepts, summarize complicated research papers, brainstorm ways to solve a problem, come up with new research directions, and, of course, learn how to code.

“Students are early adopters and have been actively testing these tools,” says Johnny Chang , a teaching assistant at Stanford University pursuing a master’s degree in computer science. He also founded the AI x Education conference in 2023, a virtual gathering of students and educators to discuss the impact of AI on education.

So as not to be left behind, educators are also experimenting with generative AI. But they’re grappling with techniques to adopt the technology while still ensuring students learn the foundations of computer science.

“It’s a difficult balancing act,” says Ooi Wei Tsang , an associate professor in the School of Computing at the National University of Singapore . “Given that large language models are evolving rapidly, we are still learning how to do this.”

Less Emphasis on Syntax, More on Problem Solving

The fundamentals and skills themselves are evolving. Most introductory computer science courses focus on code syntax and getting programs to run, and while knowing how to read and write code is still essential, testing and debugging—which aren’t commonly part of the syllabus—now need to be taught more explicitly.

“We’re seeing a little upping of that skill, where students are getting code snippets from generative AI that they need to test for correctness,” says Jeanna Matthews , a professor of computer science at Clarkson University in Potsdam, N.Y.

Another vital expertise is problem decomposition. “This is a skill to know early on because you need to break a large problem into smaller pieces that an LLM can solve,” says Leo Porter , an associate teaching professor of computer science at the University of California, San Diego . “It’s hard to find where in the curriculum that’s taught—maybe in an algorithms or software engineering class, but those are advanced classes. Now, it becomes a priority in introductory classes.”

“Given that large language models are evolving rapidly, we are still learning how to do this.” —Ooi Wei Tsang, National University of Singapore

As a result, educators are modifying their teaching strategies. “I used to have this singular focus on students writing code that they submit, and then I run test cases on the code to determine what their grade is,” says Daniel Zingaro , an associate professor of computer science at the University of Toronto Mississauga . “This is such a narrow view of what it means to be a software engineer, and I just felt that with generative AI, I’ve managed to overcome that restrictive view.”

Zingaro, who coauthored a book on AI-assisted Python programming with Porter, now has his students work in groups and submit a video explaining how their code works. Through these walk-throughs, he gets a sense of how students use AI to generate code, what they struggle with, and how they approach design, testing, and teamwork.

“It’s an opportunity for me to assess their learning process of the whole software development [life cycle]—not just code,” Zingaro says. “And I feel like my courses have opened up more and they’re much broader than they used to be. I can make students work on larger and more advanced projects.”

Ooi echoes that sentiment, noting that generative AI tools “will free up time for us to teach higher-level thinking—for example, how to design software, what is the right problem to solve, and what are the solutions. Students can spend more time on optimization, ethical issues, and the user-friendliness of a system rather than focusing on the syntax of the code.”

Avoiding AI’s Coding Pitfalls

But educators are cautious given an LLM’s tendency to hallucinate . “We need to be teaching students to be skeptical of the results and take ownership of verifying and validating them,” says Matthews.

Matthews adds that generative AI “can short-circuit the learning process of students relying on it too much.” Chang agrees that this overreliance can be a pitfall and advises his fellow students to explore possible solutions to problems by themselves so they don’t lose out on that critical thinking or effective learning process. “We should be making AI a copilot—not the autopilot—for learning,” he says.

“We should be making AI a copilot—not the autopilot—for learning.” —Johnny Chang, Stanford University

Other drawbacks include copyright and bias. “I teach my students about the ethical constraints—that this is a model built off other people’s code and we’d recognize the ownership of that,” Porter says. “We also have to recognize that models are going to represent the bias that’s already in society.”

Adapting to the rise of generative AI involves students and educators working together and learning from each other. For her colleagues, Matthews’s advice is to “try to foster an environment where you encourage students to tell you when and how they’re using these tools. Ultimately, we are preparing our students for the real world, and the real world is shifting, so sticking with what you’ve always done may not be the recipe that best serves students in this transition.”

Porter is optimistic that the changes they’re applying now will serve students well in the future. “There’s this long history of a gap between what we teach in academia and what’s actually needed as skills when students arrive in the industry,” he says. “There’s hope on my part that we might help close the gap if we embrace LLMs.”

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Rina Diane Caballar is a writer covering tech and its intersections with science, society, and the environment. An IEEE Spectrum Contributing Editor, she's a former software engineer based in Wellington, New Zealand.

Yes! Great summary of how things are evolving with AI. I’m a retired coder (BS comp sci) and understand the fundamentals of developing systems. Learning the lastest systems is now the greatest challenge. I was intrigued by Ansible to help me manage my homelab cluster, but who wants to learn one more scripting language? Turns out ChatGPT4 knows the syntax, semantics, and work flow of Ansible and all I do is tell is to “install log2ram on all my proxmox servers” and I get a playbook that does just that. The same with Docker Compose scripts. Wow.

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