What Is Problem Solving? How Software Engineers Approach Complex Challenges

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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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University of Pennsylvania

Computational Thinking for Problem Solving

Taught in English

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Gain insight into a topic and learn the fundamentals

Susan Davidson

Instructor: Susan Davidson

(1,353 reviews)

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Skills you'll gain

  • Simple Algorithm
  • Python Programming
  • Problem Solving
  • Computation

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There are 4 modules in this course

Computational thinking is the process of approaching a problem in a systematic manner and creating and expressing a solution such that it can be carried out by a computer. But you don't need to be a computer scientist to think like a computer scientist! In fact, we encourage students from any field of study to take this course. Many quantitative and data-centric problems can be solved using computational thinking and an understanding of computational thinking will give you a foundation for solving problems that have real-world, social impact.

In this course, you will learn about the pillars of computational thinking, how computer scientists develop and analyze algorithms, and how solutions can be realized on a computer using the Python programming language. By the end of the course, you will be able to develop an algorithm and express it to the computer by writing a simple Python program. This course will introduce you to people from diverse professions who use computational thinking to solve problems. You will engage with a unique community of analytical thinkers and be encouraged to consider how you can make a positive social impact through computational thinking.

Pillars of Computational Thinking

Computational thinking is an approach to solving problems using concepts and ideas from computer science, and expressing solutions to those problems so that they can be run on a computer. As computing becomes more and more prevalent in all aspects of modern society -- not just in software development and engineering, but in business, the humanities, and even everyday life -- understanding how to use computational thinking to solve real-world problems is a key skill in the 21st century. Computational thinking is built on four pillars: decomposition, pattern recognition, data representation and abstraction, and algorithms. This module introduces you to the four pillars of computational thinking and shows how they can be applied as part of the problem solving process.

What's included

6 videos 4 quizzes 2 peer reviews 4 discussion prompts

6 videos • Total 44 minutes

  • 1.1 Introduction • 4 minutes • Preview module
  • 1.2 Decomposition • 6 minutes
  • 1.3 Pattern Recognition • 5 minutes
  • 1.4 Data Representation and Abstraction • 7 minutes
  • 1.5 Algorithms • 8 minutes
  • 1.6 Case Studies • 11 minutes

4 quizzes • Total 50 minutes

  • 1.2 Decomposition • 10 minutes
  • 1.3 Pattern Recognition • 10 minutes
  • 1.4 Data Representation and Abstraction • 15 minutes
  • 1.5 Algorithms • 15 minutes

2 peer reviews • Total 60 minutes

  • Applying Computational Thinking in Your Life • 30 minutes
  • Project Part 1: Applying the Pillars of Computational Thinking • 30 minutes

4 discussion prompts • Total 40 minutes

  • Applying Decomposition in Your Life • 10 minutes
  • Applying Pattern Recognition in Your Life • 10 minutes
  • Applying Data Representation and Abstraction in Your Life • 10 minutes
  • Applying Algorithms in Your Life • 10 minutes

Expressing and Analyzing Algorithms

When we use computational thinking to solve a problem, what we’re really doing is developing an algorithm: a step-by-step series of instructions. Whether it’s a small task like scheduling meetings, or a large task like mapping the planet, the ability to develop and describe algorithms is crucial to the problem-solving process based on computational thinking. This module will introduce you to some common algorithms, as well as some general approaches to developing algorithms yourself. These approaches will be useful when you're looking not just for any answer to a problem, but the best answer. After completing this module, you will be able to evaluate an algorithm and analyze how its performance is affected by the size of the input so that you can choose the best algorithm for the problem you’re trying to solve.

7 videos 6 quizzes 4 peer reviews

7 videos • Total 68 minutes

  • 2.1 Finding the Largest Value • 8 minutes • Preview module
  • 2.2 Linear Search • 5 minutes
  • 2.3 Algorithmic Complexity • 8 minutes
  • 2.4 Binary Search • 11 minutes
  • 2.5 Brute Force Algorithms • 13 minutes
  • 2.6 Greedy Algorithms • 9 minutes
  • 2.7 Case Studies • 12 minutes

6 quizzes • Total 65 minutes

  • 2.1 Finding the Largest Value • 10 minutes
  • 2.2 Linear Search • 10 minutes
  • 2.3 Algorithmic Complexity • 10 minutes
  • 2.4 Binary Search • 10 minutes
  • 2.5 Brute Force Algorithms • 15 minutes
  • 2.6 Greedy Algorithms • 10 minutes

4 peer reviews • Total 115 minutes

  • Finding Minimum Values • 30 minutes
  • Binary Search • 30 minutes
  • Greedy vs. Brute Force Algorithms • 30 minutes
  • Project Part 2: Describing Algorithms Using a Flowchart • 25 minutes

Fundamental Operations of a Modern Computer

Computational thinking is a problem-solving process in which the last step is expressing the solution so that it can be executed on a computer. However, before we are able to write a program to implement an algorithm, we must understand what the computer is capable of doing -- in particular, how it executes instructions and how it uses data. This module describes the inner workings of a modern computer and its fundamental operations. Then it introduces you to a way of expressing algorithms known as pseudocode, which will help you implement your solution using a programming language.

6 videos 5 quizzes 5 peer reviews

6 videos • Total 45 minutes

  • 3.1 A History of the Computer • 7 minutes • Preview module
  • 3.2 Intro to the von Neumann Architecture • 8 minutes
  • 3.3 von Neumann Architecture Data • 6 minutes
  • 3.4 von Neumann Architecture Control Flow • 5 minutes
  • 3.5 Expressing Algorithms in Pseudocode • 8 minutes
  • 3.6 Case Studies • 10 minutes

5 quizzes • Total 50 minutes

  • 3.1 A History of the Computer • 10 minutes
  • 3.2 Intro to the von Neumann Architecture • 10 minutes
  • 3.3 von Neumann Architecture Data • 10 minutes
  • 3.4 von Neumann Architecture Control Flow • 10 minutes
  • 3.5 Expressing Algorithms in Pseudocode • 10 minutes

5 peer reviews • Total 120 minutes

  • von Neumann Architecture Data & Instructions • 30 minutes
  • Reading & Writing Pseudocode • 25 minutes
  • Project Part 3: Writing Pseudocode • 25 minutes
  • (Optional) von Neumann Architecture Control Instructions • 20 minutes
  • (Optional) Understanding Pseudocode • 20 minutes

Applied Computational Thinking Using Python

Writing a program is the last step of the computational thinking process. It’s the act of expressing an algorithm using a syntax that the computer can understand. This module introduces you to the Python programming language and its core features. Even if you have never written a program before -- or never even considered it -- after completing this module, you will be able to write simple Python programs that allow you to express your algorithms to a computer as part of a problem-solving process based on computational thinking.

9 videos 12 readings 12 quizzes

9 videos • Total 90 minutes

  • 4.1 Introduction to Python • 6 minutes • Preview module
  • 4.2 Variables • 13 minutes
  • 4.3 Conditional Statements • 8 minutes
  • 4.4 Lists • 7 minutes
  • 4.5 Iteration • 14 minutes
  • 4.6 Functions • 10 minutes
  • 4.7 Classes and Objects • 9 minutes
  • 4.8 Case Studies • 11 minutes
  • 4.9 Course Conclusion • 8 minutes

12 readings • Total 125 minutes

  • Programming on the Coursera Platform • 10 minutes
  • Python Playground • 0 minutes
  • Variables Programming Activity • 20 minutes
  • Solution to Variables Programming Activity • 10 minutes
  • Conditionals Programming Activity • 20 minutes
  • Solution to Conditionals Programming Activity • 10 minutes
  • Solution to Lists Programming Assignment • 5 minutes
  • Solution to Loops Programming Assignment • 10 minutes
  • Solution to Functions Programming Assignment • 10 minutes
  • Solution to Challenge Programming Assignment • 10 minutes
  • Solution to Classes and Objects Programming Assignment • 10 minutes
  • Solution to Project Part 4 • 10 minutes

12 quizzes • Total 185 minutes

  • (Optional) Challenge Programming Assignment • 20 minutes
  • 4.2 Variables • 10 minutes
  • 4.3 Conditional Statements • 5 minutes
  • 4.4 Lists • 10 minutes
  • Lists Programming Assignment • 15 minutes
  • 4.5 Iteration • 10 minutes
  • Loops Programming Assignment • 30 minutes
  • Functions Programming Assignment • 20 minutes
  • 4.7 Classes and Objects • 10 minutes
  • Classes and Objects Programming Assignment • 20 minutes
  • Project Part 4: Implementing the Solution in Python • 25 minutes

Instructor ratings

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problem solving science computer

The University of Pennsylvania (commonly referred to as Penn) is a private university, located in Philadelphia, Pennsylvania, United States. A member of the Ivy League, Penn is the fourth-oldest institution of higher education in the United States, and considers itself to be the first university in the United States with both undergraduate and graduate studies.

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University of Pennsylvania

Master of Computer and Information Technology

Degree · 16 – 40 months

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1,353 reviews

Reviewed on Nov 17, 2018

Well taught with good examples and exercises that require thinking but still approachable. Very well laid out and taught. Definitely sparked an interest to go learn more.

Reviewed on Jan 17, 2019

Useful course taught at an adequate rate. I recommend it for people who are interested in learning the basics of computational thinking, i.e. a systematic approach to problem-solving.

Reviewed on Aug 3, 2022

Informative but the last assignment on Week 4 is misleading in that you can only submit the search function but the instructions say that you can test your code and the program will test it as well.

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Frequently asked questions

Do i need to know how to program or have studied computer science in order to take this course.

No, definitely not! This course is intended for anyone who has an interest in approaching problems more systematically, developing more efficient solutions, and understanding how computers can be used in the problem solving process. No prior computer science or programming experience is required.

How much math do I need to know to take this course?

Some parts of the course assume familiarity with basic algebra, trigonometry, mathematical functions, exponents, and logarithms. If you don’t remember those concepts or never learned them, don’t worry! As long as you’re comfortable with multiplication, you should still be able to follow along. For everything else, we’ll provide links to references that you can use as a refresher or as supplemental material.

Does this course prepare me for the Master of Computer and Information Technology (MCIT) degree program at the University of Pennsylvania?

This course will help you discover whether you have an aptitude for computational thinking and give you some beginner-level experience with online learning. In this course you will learn several introductory concepts from MCIT instructors produced by the same team that brought the MCIT degree online.

If you have a bachelor's degree and are interested in learning more about computational thinking, we encourage you to apply to MCIT On-campus (http://www.cis.upenn.edu/prospective-students/graduate/mcit.php) or MCIT Online (https://www.coursera.org/degrees/mcit-penn). Please mention that you have completed this course in the application.

Where can I find more information about the Master of Computer and Information Technology (MCIT) degree program at the University of Pennsylvania?

Use these links to learn more about MCIT:

MCIT On-campus: http://www.cis.upenn.edu/prospective-students/graduate/mcit.php

MCIT Online: https://www.coursera.org/degrees/mcit-penn

When will I have access to the lectures and assignments?

Access to lectures and assignments depends on your type of enrollment. If you take a course in audit mode, you will be able to see most course materials for free. To access graded assignments and to earn a Certificate, you will need to purchase the Certificate experience, during or after your audit. If you don't see the audit option:

The course may not offer an audit option. You can try a Free Trial instead, or apply for Financial Aid.

The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.

What will I get if I purchase the Certificate?

When you purchase a Certificate you get access to all course materials, including graded assignments. Upon completing the course, your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.

What is the refund policy?

You will be eligible for a full refund until two weeks after your payment date, or (for courses that have just launched) until two weeks after the first session of the course begins, whichever is later. You cannot receive a refund once you’ve earned a Course Certificate, even if you complete the course within the two-week refund period. See our full refund policy Opens in a new tab .

Is financial aid available?

Yes. In select learning programs, you can apply for financial aid or a scholarship if you can’t afford the enrollment fee. If fin aid or scholarship is available for your learning program selection, you’ll find a link to apply on the description page.

More questions

CS2104: Introduction to Problem Solving in Computer Science

This course introduces the student to a broad range of heuristics for solving problems in a range of settings. Emphasis on problem-solving techniques that aid programmers and computer scientists. Heuristics for solving problems ''in the small'' (classical math and word problems), generating potential solutions to ''real-life'' problems encountered in the profession, and problem solving in teams.

Having successfully completed this course, the student will be able to:

  • Identify skills and personality traits of successful problem solving.
  • Apply standard problem-solving heuristics to aid in problem solving.
  • Apply problem-solving techniques to programming activities.
  • Apply problem-solving techniques to school and personal interactions.
  • Apply pairs and team problem-solving techniques.
  • Generate potential solutions to problems with standard heuristics.
  • Formulate and successfully communicate the solutions to problems.

 Prerequisites:  MATH 1205 or MATH 1225 or MATH 1526.

Taught By:  Alexey Onufriev Dwight Barnette Layne Watson Margaret Ellis Cliff Shaffer William McQuain

problem solving science computer

2.2 Computer Science Fundamentals

Wrap your mind around computational thinking, from everyday tasks to algorithms.

Making Decisions

Computers use decision trees to turn many simple decisions into one big decision.

Searching for Solutions

Sometimes, the right way to solve a computational problem is by “brute force.”

  • Parallelism

When Pierre the baker wants to get lots of things done, it helps to do many things at once.

End of Unit 1

Complete all lessons above to reach this milestone.

0 of 3 lessons complete

Resource Tradeoffs

Computer scientists deal with tradeoffs all the time. So does Farhad when he does his chores.

Order and Search

Information needs to be organized for use by humans or computers, as Tiye the librarian knows well.

Computer systems and people need to be able to reliably find and access people and resources.

Abstraction

Mayor Jing uses abstraction—a critical tool in computer science—to help her run City Hall.

Abstractions have interfaces that explain what they can and cannot do.

End of Unit 2

0 of 5 lessons complete

Algorithms and Implementations

Algorithms are step-by-step processes for achieving an outcome. They can be very specific or quite general.

Divide and Conquer

Problems often get easier when you split them in half, as the 20 Questions guessing game shows.

  • Binary Search

Binary search is a more algorithm-friendly version of the 20 Questions game.

Thinking with Graphs

Graphs are a powerful tool for understanding problems and solving them in clever ways.

Representing Games and Puzzles

Graphs can help us plan solutions to complex problems, like this classic river-crossing puzzle.

Graph Search

Some of the most fundamental algorithms on graphs are designed to get you from point A to point B.

End of Unit 3

0 of 6 lessons complete

Course description

Learn the key ideas of computer science with this interactive course – no coding required! This course is ideal for a high school or college student who wants to learn the fundamentals, or an early professional who wants to strengthen their knowledge of core computer science concepts. Whether you're exploring computer science for the first time or looking to deepen your understanding, this course will allow you to develop the problem-solving techniques you need to think like a computer scientist. Follow librarians, cooks, and mayors to see how computer science problem solving techniques affect their daily lives. Get hands-on with a few specific algorithms, and learn the general principles demonstrated by these algorithms.

Topics covered

  • Brute-Force Search
  • Concurrency
  • Decision Trees
  • Graph Abstractions
  • Greedy Algorithms
  • Programming

Prerequisites and next steps

You don’t need any previous computer science experience to take this course! This course is for anyone excited to actively learn more about how computer scientists think and understand our world.

3.1 Next Steps in Python

Boost your proficiency in Python by learning how to access social media data with public functions.

Classic Computer Science Problems

Essential techniques for practicing programmers, a book series by david kopec, free content.

  • Contact David

Classic Computer Science Problems is a series of books that helps software developers learn several problem solving techniques from the realm of computer science. The series spans three programming languages and nine human languages. The books are written in a tutorial-like, code-centric format. They are appropriate for experienced software developers who want to refresh their skillset, and intermediate programmers who are looking to take their skills to the next level. They can also be helpful when learning some of the more advanced aspects of the programming languages covered by the series.

The three books in the series are Classic Computer Science Problems in Java , Classic Computer Science Problems in Python , and Classic Computer Science Problems in Swift . They are published by Manning . Reading each book does not require a CS degree. In fact, self-taught programmers will get a useful survey of computer science topics they missed by not having a CS education. The books are broad, not deep. Each topic is covered by going over some classic problems, typically taught in a CS undergraduate curriculum, and their solutions in the book's respective language.

These are not textbooks. They are not heavy on mathematical notation, nor do they claim to be replacements for a class in data structures and algorithms. Instead, they aim to excite developers and students about engaging computer science topics by presenting them succinctly with working code in the language of the reader's choice.

The computer science topics touched on through the problems are wide ranging and include:

  • Memoization
  • Bit Manipulation
  • Dynamic Programming
  • Permutation Generation
  • Binary Search
  • Breadth-First Search
  • Depth-First Search
  • Constraint Satisfaction Problems
  • Representing Graphs using Hybrid Adjacency Lists
  • Search in Graphs
  • Finding shortest paths with Dijkstra's Algorithm
  • Finding the minimum-spanning tree with Jarnik's Algorithm (Prim's Algorithm)
  • Genetic Algorithms
  • K-means Clustering
  • Neural Networks
  • Alpha beta pruning (Python, Java books only)

Classic Computer Science Problems in Java

problem solving science computer

  • Requires Java 11+
  • Published in December, 2020
  • Available in English in print from Manning , Amazon , and other fine book sellers.
  • Available in English in PDF, .mobi (Kindle), and .epub (Apple Books & Other E-readers) from Manning
  • Published in German by Rheinwerk Computing and available from Amazon Germany

Classic Computer Science Problems in Python

problem solving science computer

  • Requires Python 3.7+
  • Published in March, 2019
  • Every code example uses type hints
  • Available in English in PDF, .mobi (Kindle), and .epub (Apple Books & Other E-readers) from Manning .
  • Published in Japanese by O'Reilly Japan and available from Amazon Japan .
  • Published in Portuguese by Novatec Editora and available from Amazon Brazil .
  • Published in Russian by Piter
  • Published in Polish by Wydawnictwo Naukowe PWN
  • Published in Korean by Hanbit Media
  • Published in Simplified Chinese by Posts & Telecom Press
  • A Traditional Chinese version is in the works.

Classic Computer Science Problems in Swift

problem solving science computer

  • Written against Swift 4.1 (Xcode 9), all examples compile in Swift 4.2 (Xcode 10)
  • Published in April, 2018
  • Available in Simplified Chinese from Amazon China .

The source code from all of the books is freely available under the terms of the Apache License. This effectively means you can reuse the code in any project you work on, whether personal or commercial, as long as you credit me/the book in an acknowledgement. You can find repositories on GitHub containing the source code for the Java book , the Python book , and the Swift book .

The code has been ported by readers (and in the case of PHP and JavaScript, the German translator) to C++ , Go , PHP , JavaScript , Ruby , and Rust . So, in total, the source code is available in 8 programming languages. Please let me know if you port the book to another language. I would love to link to that here.

The series has been fortunate to receive great reviews from official reviewers and readers alike.

Praise for Classic Computer Science Problems in Python

Praise for classic computer science problems in swift, interviews with david, codexpanse (august, 2020).

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Classic Computer Science Problems in Swift with David Kopec

The Learn Swift Podcast (June, 2018)

29: David Kopec - Assistant Professor @ Champlain College and Author of Classic Computer Science Problems in Swift

  • Article: Constraint-Satisfaction Problems in Python
  • Video: Constraint-Satisfaction Problems in Python
  • Chapter 2: Search Problems (PDF)
  • Chapter 4: Graph Problems (PDF)
  • Article: Solving Mazes with Swift
  • Slideshare: A* Search in Swift: navigating a maze
  • Article: Tic-Tac-Toe (in Swift)

Open Source Projects Related to the Books

The Swift book was based on several (fairly small) open source projects that I had worked on prior to writing it.

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Questions (and Answers)

Are these books suitable for beginning programmers.

Not really: The books in the series assume at least intermediate knowledge of the programming language they are written against. For example, you should be at least an intermediate Python programmer before picking up Classic Computer Science Problems in Python . You do not need to have taken a data structures and algorithms class, though. No data structures and algorithms knowledge is assumed, but programming knowledge is.

Are the books a good way to learn the programming languages that they cover?

Generally, no, but for some readers, yes. I have heard some readers have used them that way, but I think this will only work for programmers who are very experienced in another language prior to picking up the book. There is no "beginners" content about how to use each of the languages in the books. That said, if you are already an intermediate programmer in the given language, reading the book will help you learn some of the language's more advanced constructs. For example, if you have some basic knowledge of Swift and a strong programming background, you will better understand protocol-oriented programming and Swift enums after reading Classic Computer Science Problems in Swift .

Why isn't sorting or some other classic data structures and algorithms topic covered in the series?

These books are not data structures and algorithms textbooks. They don't claim to be that, and they are geared for a slightly different audience. These are broad survey books that cover a large variety of computer science topics in a succinct, friendly, tutorial-like fashion, heavy with a lot of real code. In other words, they are not meant to be academically rigorous, but instead fun while still being educational. Frankly, some of the cliche topics, like sorting, are left out because they will bore many of the self-taught programmers who will pickup the books. The breadth of topics covered in the series actually stretches beyond the gamut of most data structures and algorithms textbooks by covering several topics from artificial intelligence. About half of each book's content can be considered AI. On the other hand, yes, several traditional data structures and algorithms topics are left out.

Will a book in the series in another programming language come out?

It's not likely to happen in the near-term. I think three programming languages is enough for a while. We did three languages in three years (Swift 2018, Python 2019, Java 2020). In the future, depending on the success of the Java book and the publisher's interest, I am open to working with a co-author on a "port" of the book to a language that I am less familiar with. Go is one language the publisher and I have discussed. We've also discussed Rust, Kotlin, JavaScript, C#, and more. However, beyond Java, these books would be looking at release dates of 2022 or later if they happen. If you look at the Code section above though, you can find ports of the books' code to many other programming languages.

Will a book in the series be translated into another human language?

Yes, Classic Computer Science Problems in Python has been translated into Japanese , Polish , Portuguese , German , Russian , Korean , and Simplified Chinese . The rights to translate Classic Computer Science Problems in Python into Traditional Chinese have been acquired as well. Classic Computer Science Problems in Swift is available in Simplified Chinese . Classic Computer Science Problems in Java is available in German . If you are interested in acquiring the rights to translate one of the books into another language, please contact me and I will put you in touch with the appropriate person at the publisher.

How much do the books cost?

The MSRP of the English print editions ranges from $39.99 to $49.99. However, you can often find them cheaper than that from third-party booksellers. Every English print edition copy comes with a way to download the eBook for free from Manning's website. The standalone DRM-free eBooks are available for less from Manning directly. As a bonus for reading this far, here is a promo code: ccspkopec should get you 40% off on Manning.com for any of the books ( links to Manning's website are above). Please let me know if the promo code does not work for you.

I know of a classic problem you didn't include in the book.

Please let me know about it if you think it's just esoteric enough that I haven't heard of it, but it's still fairly classic.

What references did you use when writing the book?

As you can see from footnotes and the More Resources appendix, the two books I relied most heavily upon as references are Algorithms by Sedgewick and Wayne and Artificial Intelligence: A Modern Approach by Russell and Norvig. I also relied on Introduction to Algorithms by Cormen, Leiserson, Rivest, and Stein, The Algorithm Design Manual by Skiena, and Artificial Intelligence in the 21st Century by my late father, Danny Kopec, and Lucci, as further references. I was fortunate to see most of the classic computer science problems in the books during my education at Dartmouth, so I must extend a thank you to the faculty there, especially Tom Cormen and Devin Balkcom. Since, once again (see the earlier question on why certain data structure and algorithms topics are not in the series), these books are not textbooks, if you want a more academically rigorous introduction to the topics covered, I recommend the above mentioned textbooks.

What is the background of the author?

I am an associate professor of Computer Science and Innovation at Champlain College, a small teaching college in Burlington, Vermont, USA . I have worked professionally as a software developer and I am an active contributor to open source projects. I am also the author of Dart for Absolute Beginners (Apress, 2014) but I no longer recommend that book since it is now significantly out-of-date. I hold a bachelor's degree in economics from Dartmouth College and a master's degree in computer science, also from Dartmouth. I live in Burlington with my wife, Rebecca, and my kids. I co-host a podcast about business books and a podcast explaining software for laypeople.

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Introduction to computers and engineering problem solving, course description.

This course presents the fundamentals of object-oriented software design and development, computational methods and sensing for engineering, and scientific and managerial applications. It cover topics, including design of classes, inheritance, graphical user interfaces, numerical methods, streams, threads, sensors, and data structures. Students use Java ® programming language to complete weekly software assignments.

How is 1.00 different from other intro programming courses offered at MIT?

1.00 is a first course in programming. It assumes no prior experience, and it focuses on the use of computation to solve problems in engineering, science and management. The audience for 1.00 is non-computer science majors. 1.00 does not focus on writing compilers or parsers or computing tools where the computer is the system; it focuses on engineering problems where the computer is part of the system, or is used to model a physical or logical system.

1.00 teaches the Java programming language, and it focuses on the design and development of object-oriented software for technical problems. 1.00 is taught in an active learning style. Lecture segments alternating with laboratory exercises are used in every class to allow students to put concepts into practice immediately; this teaching style generates questions and feedback, and allows the teaching staff and students to interact when concepts are first introduced to ensure that core ideas are understood. Like many MIT classes, 1.00 has weekly assignments, which are programs based on actual engineering, science or management applications. The weekly assignments build on the class material from the previous week, and require students to put the concepts taught in the small in-class labs into a larger program that uses multiple elements of Java together.

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Encyclopedia of Education and Information Technologies pp 1–16 Cite as

Problem-Solving in Computer Science: Learning from a Gifted Peer

  • Bertold Kujath 2 &
  • Andreas Schwill 2  
  • Living reference work entry
  • First Online: 22 August 2019

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A comparative study of individuals with high and low skills in computer science shows that efficient problem-solvers use a significantly different approach while dealing with typical problems of computer science compared to rather weak problem-solvers. It was noteworthy that despite knowing typical tools for informatic problem-solving, such as tree structures or recursion, low performers tended not to utilize them during the problem-solving process. Furthermore, the study revealed that in contrast to high performers, low performers did not heed to many common recommendations for problem-solving, such as splitting the problem into subproblems or performing a problem analysis prior to the actual work on the problem solution. These findings, as well as the efficient strategies used by the high-skilled students, laid the foundation of the concept for an educational video. Its purpose is to allow learners to observe high-skilled problem-solvers while approaching typical informatic problems. The following paper describes the entire development process of an instructional video about informatic problem-solving, from basic research, over the conceptual development to the evaluation of the final video.

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Berk RA (2009) Multimedia teaching with video clips: TV, movies, YouTube and mtvU in the college classroom. Int J Technol Teach Learn 5(1):1–21

Google Scholar  

Friege G (2001) Wissen und Problemlösen. Logos Verlag, Berlin

Fuchs M (2006) Vorgehensweisen mathematisch potentiell begabter Dritt- und Viertklässler beim Problemlösen. LIT Verlag, Berlin

Heller K, Mönks F, Passow A (1993) International handbook of research and development of giftedness and talent. Pergamon, Oxford

Kittelberger R, Freisleben I (1994) Lernen mit Video und Film. Beltz Verlag, Weinheim

Kujath B (2006) Ein Test- und Analyseverfahren zur Kontrastierung von Problemlöseprozessen informatischer Hoch- und Niedrigleister – erste Ergebnisse einer Pilotstudie. In: Schwill A, Schulte C, Thomas M (Hrsg) GI-edition-lecture notes in informatics Band 99, Gesellschaft für Informatik, Bonn, pp 49–69

Kujath B (2007) Vergleichende Analysen zweier Problemlöseprozesse unter dem Aspekt des Problemlöseerfolgs. In: Schubert S (Hrsg) GI-edition-lecture notes in informatics, vol 112. Gesellschaft für Informatik, Bonn, pp 295–306

Kujath B (2008) Anhang zum Workshopbeitrag: Wie können schwache Problemlöser von Hochleistern lernen – Konzeption eines Lehrvideos. http://ddi.cs.uni-potsdam.de/didaktik/kujath/Fachgruppe2008Anhang.pdf

Kujath B (2011a) Keine Angst vor Informatikproblemen. Hochleistern über die Schulter geschaut. Ein Lehrvideo zum informatischen Problemlösen. Universitätsverlag, Potsdam. ISBN 978-3-86956-150-9

Kujath B (2011b) Don’t be afraid of informatics problems – looking over a highflyer’s shoulder. Educational video, 33 minutes. http://mediaup.uni-potsdam.de/Browse/Tag/highflyer

Kujath B, Schütze C (2015) Evaluation der Lernwirksamkeit eines Lehrvideos zum informatischen Problemlösen. HDI 2014: Gestalten und Meistern von Übergängen. Universität, Potsdam. pp 97–104

Lippert H (1987) Rezipienten-orientierte Medienwirkungsforschung. Verlag Josef Lippert, Münster

Mair D (2005) E-Learning – das Drehbuch. Springer, Berlin

Märtin D (2005) Erfolgreich texten. Voltmedia, Paderborn

Mayring P (2014) Qualitative content analysis. Theoretical foundation, basic procedures and software solution. Weinheim, Beltz

Paivio A (1971) Imagery and verbal processes. Lawrence Erlbaum Associates, Inc., Hillsdale

Paivio A (1986) Mental representations: a dual coding approach. Oxford University Press, New York

Sailer M, Figas P (2015) Audiovisuelle Bildungsmedien in der Hochschullehre. Eine Experimentalstudie zu zwei Lernvideotypen in der Statistiklehre. http://bildungsforschung.org , 1 Ausgabe 2015

Schubert S, Schwill A (2004) Didaktik der Informatik. Spektrum Akademie Verlag, Heidelberg

MATH   Google Scholar  

Schütze C (2013) Analyse der Lernwirksamkeit eines Lehrfilms zum problemlösenden Denken im Informatikunterricht, Master Thesis Universität Potsdam. Institut für Informatik

Waldmann MR, Weinert FE (1990) Intelligenz und Denken. Hogrefe, Göttingen

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Kujath, B., Schwill, A. (2019). Problem-Solving in Computer Science: Learning from a Gifted Peer. In: Tatnall, A. (eds) Encyclopedia of Education and Information Technologies. Springer, Cham. https://doi.org/10.1007/978-3-319-60013-0_29-1

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DOI : https://doi.org/10.1007/978-3-319-60013-0_29-1

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One of the most important skills you learn in your computer science courses is how to problem solve. Although we cover some general problem solving paradigms in class, the best way to improve these skills is to get practice, practice, and more practice. Different people have different techniques that work best for them; below are some general tips that work for most people.

Please read these suggestions carefully.

Questions the Helpers May Ask You

When you ask a lab helper for their assistance, they will assume you have tried to solve the problem yourself. They will (reasonably) expect that you have tried out the steps outlined in this document; you should therefore be prepared to answer the following questions:

  • Did you re-read the prelab and lab?
  • Do you understand the problem?
  • Have you tried solving some examples by hand?
  • (For problems designing a solution) What have you tried? What topic from class does this most ressemble?
  • If you can’t solve the problem whole-hog, what small case can you solve?
  • (For syntax errors) What line of your code is causing the error? What do you think the compile error means, and what usually causes this kind of problem?
  • (For logical errors) On what example does your program consistently break? Have you traced through the program? Which line of your program is not doing what it should?

Four Main Problem Solving Steps:

1. understand the problem..

Solving the right problem is the most important part of problem solving. Be sure, absolutely 100% positively sure, that you understand the problem before attempting a solution. This involves:

  • Reading the prelab and lab very carefully (including all bold text, italicized text, and everything else);
  • Reviewing class notes on related topics;
  • Trying some small examples to make sure you understand what is being asked; if examples are given to you, make sure you understand them before continuing, as they are usually there to help clarify some common misconceptions; and
  • Asking someone to help clarify anything that is still confusing.

2. Design a Solution.

Formulate an algorithm to solve your problem. This involves:

  • Understanding what is being asked of you. See step 1.
  • Draw out some examples. Use paper . How would you solve these small cases, by hand? Is there a method to what you are doing? Try to formalize the steps you are taking, and try to think about whether they would work more generally, in bigger cases. Then try some bigger cases and convince yourself.
  • Reread the prelab . Did you already run some examples by hand? Did you have trouble with it then?
  • Write down the stuff you know about the problem and the examples you’ve tried, so that you can more easily find patterns .
  • Might a recent topic from class help? Usually at least some, if not most, of the lab will make use of recently covered material . Go over that topic, make sure you understand it, then try to make connections to lab.
  • Split the problem into smaller (more manageable) chunks, and try to solve the simpler problems. Go as small as you need in order to find some solution. Once you have the smaller problem solved, worry about how to generalize it to a slightly larger problem.
  • Just try something , anything, even if it is completely random and obviously wrong. When/if your attempt doesn’t work, it may still give you insight into what may work. It is not as crazy as it initially sounds!
  • Use a friend, lab helper, puppet, etc. as a sounding board ; sometimes, just voicing your problem will lead you to the “aha!” moment you need.
  • If you are still stuck, step away from the keyboard . Take a walk, go eat dinner or have a coffee. Sleep on it. Not literally. Taking a break is sometimes the most productive thing you can do, trust me.
  • Finally, stay positive . Even when things don’t work, you can still gain a better understanding of the problem. Don’t give up, just go with the flow and see where it takes you. Struggling is part of the process!

3. Implement your Solution.

Write the code to solve your problem. This involves

  • Understanding the problem, and designing a solution on paper. See steps 1 and 2.
  • Translating your design into actual code. Rather than doing this linearly, implement small chunks at a time. Break your code into subroutines, and make sure that each subroutine works before proceeding to the next. Compile and save often .
  • If you run into syntax errors, determine which line of your code is causing the problem. You can do this by systematically commenting out blocks of code until you find the block that causes the problem.
  • If you run into logical errors (as in, the program compiles but does not do what it is supposed to), find some examples on which your problem consistently fails. Trace through the program line by line, with one of these examples, to figure out exactly which line is not doing what you intend it to.
  • If the output doesn’t match what you expect, use print statements to trace through what your program is doing, and compare that to what your program should be doing. Even better, if you know how to use a debugger (in eclipse, for example, use it!)

4. Check your Solution.

This step is often overlooked, but is absolutely crucial. Your program does not necessarily work because it works on the given test cases on the lab. You have to think critically about what you code. This involves

  • Certainly check your program on all test cases given to you on the lab and prelab. The prelab often specifically contains hand-solved test cases precisely for this purpose!
  • Thinking about the “ boundary cases ,” such as, when would this array go out of bounds? For what indices will this for loop start and end?
  • Think: how would this program break ? Then, that failing: how would I convince my skeptical friend it can’t be broken?

Remember: problem solving is a creative process, which cannot be forced. Don’t get angry if you don’t see the answer right away, or you don’t see it as fast as your friend. You will have different strengths, and you can always improve. You will learn from your mistakes, so that’s always a plus!

Last updated July 3rd, 2012 by asharp

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Computational thinking is an interrelated set of skills and practices for solving complex problems, a way to learn topics in many disciplines, and a necessity for fully participating in a computational world.

Many different terms are used when talking about computing, computer science, computational thinking, and programming. Computing encompasses the skills and practices in both computer science and computational thinking. While computer science is an individual academic discipline, computational thinking is a problem-solving approach that integrates across activities, and programming is the practice of developing a set of instructions that a computer can understand and execute, as well as debugging, organizing, and applying that code to appropriate problem-solving contexts. The skills and practices requiring computational thinking are broader, leveraging concepts and skills from computer science and applying them to other contexts, such as core academic disciplines (e.g. arts, English language arts, math, science, social studies) and everyday problem solving. For educators integrating computational thinking into their classrooms, we believe computational thinking is best understood as a series of interrelated skills and competencies.

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Figure 1. The relationship between computer science (CS), computational thinking (CT), programming and computing.

In order to integrate computational thinking into K-12 teaching and learning, educators must define what students need to know and be able to do to be successful computational thinkers. Our recommended framework has three concentric circles.

  • Computational thinking skills , in the outermost circle, are the cognitive processes necessary to engage with computational tools to solve problems. These skills are the foundation to engage in any computational problem solving and should be integrated into early learning opportunities in K-3.
  • Computational thinking practices , in the middle circle, combine multiple computational skills to solve an applied problem. Students in the older grades (4-12) may use these practices to develop artifacts such as a computer program, data visualization, or computational model.
  • Inclusive pedagogies , in the innermost circle, are strategies for engaging all learners in computing, connecting applications to students’ interests and experiences, and providing opportunities to acknowledge, and combat biases and stereotypes within the computing field.

A pie chart extruding from a Venn diagram to illustrate a framework for computational thinking integration.

Figure 2. A framework for computational thinking integration.

What does inclusive computational thinking look like in a classroom? In the image below, we provide examples of inclusive computing pedagogies in the classroom. The pedagogies are divided into three categories to emphasize different pedagogical approaches to inclusivity. Designing Accessible Instruction refers to strategies teachers should use to engage all learners in computing. Connecting to Students’ Interests, Homes, and Communities refers to drawing on the experiences of students to design learning experiences that are connected with their homes, communities, interests and experiences to highlight the relevance of computing in their lives. Acknowledging and Combating Inequity refers to a teacher supporting students to recognize and take a stand against the oppression of marginalized groups in society broadly and specifically in computing. Together these pedagogical approaches promote a more inclusive computational thinking classroom environment, life-relevant learning, and opportunities to critique and counter inequalities. Educators should attend to each of the three approaches as they plan and teach lessons, especially related to computing.

Examples of inclusive pedagogies for teaching computing

Figure 3. Examples of inclusive pedagogies for teaching computing in the classroom adapted from Israel et al., 2017; Kapor Center, 2021; Madkins et al., 2020; National Center for Women & Information Technology, 2021b; Paris & Alim, 2017; Ryoo, 2019; CSTeachingTips, 2021

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A micro-credential is a digital certificate that verifies an individual’s competence in a specific skill or set of skills. To earn a micro-credential, teachers submit evidence of student work from classroom activities, as well as documentation of lesson planning and reflection.

Because the integration of computational thinking is new to most teachers, micro-credentials can be a useful tool for professional learning and/or credentialing pathways. Digital Promise has created micro-credentials for Computational Thinking Practices . These micro-credentials are framed around practices because the degree to which students have built foundational skills cannot be assessed until they are manifested through the applied practices.

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Exploring the Problem Solving Cycle in Computer Science – Strategies, Techniques, and Tools

  • Post author By bicycle-u
  • Post date 08.12.2023

The world of computer science is built on the foundation of problem solving. Whether it’s finding a solution to a complex algorithm or analyzing data to make informed decisions, the problem solving cycle is at the core of every computer science endeavor.

At its essence, problem solving in computer science involves breaking down a complex problem into smaller, more manageable parts. This allows for a systematic approach to finding a solution by analyzing each part individually. The process typically starts with gathering and understanding the data or information related to the problem at hand.

Once the data is collected, computer scientists use various techniques and algorithms to analyze and explore possible solutions. This involves evaluating different approaches and considering factors such as efficiency, accuracy, and scalability. During this analysis phase, it is crucial to think critically and creatively to come up with innovative solutions.

After a thorough analysis, the next step in the problem solving cycle is designing and implementing a solution. This involves creating a detailed plan of action, selecting the appropriate tools and technologies, and writing the necessary code to bring the solution to life. Attention to detail and precision are key in this stage to ensure that the solution functions as intended.

The final step in the problem solving cycle is evaluating the solution and its effectiveness. This includes testing the solution against different scenarios and data sets to ensure its reliability and performance. If any issues or limitations are discovered, adjustments and optimizations are made to improve the solution.

In conclusion, the problem solving cycle is a fundamental process in computer science, involving analysis, data exploration, algorithm development, solution implementation, and evaluation. It is through this cycle that computer scientists are able to tackle complex problems and create innovative solutions that drive progress in the field of computer science.

Understanding the Importance

In computer science, problem solving is a crucial skill that is at the core of the problem solving cycle. The problem solving cycle is a systematic approach to analyzing and solving problems, involving various stages such as problem identification, analysis, algorithm design, implementation, and evaluation. Understanding the importance of this cycle is essential for any computer scientist or programmer.

Data Analysis and Algorithm Design

The first step in the problem solving cycle is problem identification, which involves recognizing and defining the issue at hand. Once the problem is identified, the next crucial step is data analysis. This involves gathering and examining relevant data to gain insights and understand the problem better. Data analysis helps in identifying patterns, trends, and potential solutions.

After data analysis, the next step is algorithm design. An algorithm is a step-by-step procedure or set of rules to solve a problem. Designing an efficient algorithm is crucial as it determines the effectiveness and efficiency of the solution. A well-designed algorithm takes into consideration the constraints, resources, and desired outcomes while implementing the solution.

Implementation and Evaluation

Once the algorithm is designed, the next step in the problem solving cycle is implementation. This involves translating the algorithm into a computer program using a programming language. The implementation phase requires coding skills and expertise in a specific programming language.

After implementation, the solution needs to be evaluated to ensure that it solves the problem effectively. Evaluation involves testing the program and verifying its correctness and efficiency. This step is critical to identify any errors or issues and to make necessary improvements or adjustments.

In conclusion, understanding the importance of the problem solving cycle in computer science is essential for any computer scientist or programmer. It provides a systematic and structured approach to analyze and solve problems, ensuring efficient and effective solutions. By following the problem solving cycle, computer scientists can develop robust algorithms, implement them in efficient programs, and evaluate their solutions to ensure their correctness and efficiency.

Identifying the Problem

In the problem solving cycle in computer science, the first step is to identify the problem that needs to be solved. This step is crucial because without a clear understanding of the problem, it is impossible to find a solution.

Identification of the problem involves a thorough analysis of the given data and understanding the goals of the task at hand. It requires careful examination of the problem statement and any constraints or limitations that may affect the solution.

During the identification phase, the problem is broken down into smaller, more manageable parts. This can involve breaking the problem down into sub-problems or identifying the different aspects or components that need to be addressed.

Identifying the problem also involves considering the resources and tools available for solving it. This may include considering the specific tools and programming languages that are best suited for the problem at hand.

By properly identifying the problem, computer scientists can ensure that they are focused on the right goals and are better equipped to find an effective and efficient solution. It sets the stage for the rest of the problem solving cycle, including the analysis, design, implementation, and evaluation phases.

Gathering the Necessary Data

Before finding a solution to a computer science problem, it is essential to gather the necessary data. Whether it’s writing a program or developing an algorithm, data serves as the backbone of any solution. Without proper data collection and analysis, the problem-solving process can become inefficient and ineffective.

The Importance of Data

In computer science, data is crucial for a variety of reasons. First and foremost, it provides the information needed to understand and define the problem at hand. By analyzing the available data, developers and programmers can gain insights into the nature of the problem and determine the most efficient approach for solving it.

Additionally, data allows for the evaluation of potential solutions. By collecting and organizing relevant data, it becomes possible to compare different algorithms or strategies and select the most suitable one. Data also helps in tracking progress and measuring the effectiveness of the chosen solution.

Data Gathering Process

The process of gathering data involves several steps. Firstly, it is necessary to identify the type of data needed for the particular problem. This may include numerical values, textual information, or other types of data. It is important to determine the sources of data and assess their reliability.

Once the required data has been identified, it needs to be collected. This can be done through various methods, such as surveys, experiments, observations, or by accessing existing data sets. The collected data should be properly organized, ensuring its accuracy and validity.

Data cleaning and preprocessing are vital steps in the data gathering process. This involves removing any irrelevant or erroneous data and transforming it into a suitable format for analysis. Properly cleaned and preprocessed data will help in generating reliable and meaningful insights.

Data Analysis and Interpretation

After gathering and preprocessing the data, the next step is data analysis and interpretation. This involves applying various statistical and analytical methods to uncover patterns, trends, and relationships within the data. By analyzing the data, programmers can gain valuable insights that can inform the development of an effective solution.

During the data analysis process, it is crucial to remain objective and unbiased. The analysis should be based on sound reasoning and logical thinking. It is also important to communicate the findings effectively, using visualizations or summaries to convey the information to stakeholders or fellow developers.

In conclusion, gathering the necessary data is a fundamental step in solving computer science problems. It provides the foundation for understanding the problem, evaluating potential solutions, and tracking progress. By following a systematic and rigorous approach to data gathering and analysis, developers can ensure that their solutions are efficient, effective, and well-informed.

Analyzing the Data

Once you have collected the necessary data, the next step in the problem-solving cycle is to analyze it. Data analysis is a crucial component of computer science, as it helps us understand the problem at hand and develop effective solutions.

To analyze the data, you need to break it down into manageable pieces and examine each piece closely. This process involves identifying patterns, trends, and outliers that may be present in the data. By doing so, you can gain insights into the problem and make informed decisions about the best course of action.

There are several techniques and tools available for data analysis in computer science. Some common methods include statistical analysis, data visualization, and machine learning algorithms. Each approach has its own strengths and limitations, so it’s essential to choose the most appropriate method for the problem you are solving.

Statistical Analysis

Statistical analysis involves using mathematical models and techniques to analyze data. It helps in identifying correlations, distributions, and other statistical properties of the data. By applying statistical tests, you can determine the significance and validity of your findings.

Data Visualization

Data visualization is the process of presenting data in a visual format, such as charts, graphs, or maps. It allows for a better understanding of complex data sets and facilitates the communication of findings. Through data visualization, patterns and trends can become more apparent, making it easier to derive meaningful insights.

Machine Learning Algorithms

Machine learning algorithms are powerful tools for analyzing large and complex data sets. These algorithms can automatically detect patterns and relationships in the data, leading to the development of predictive models and solutions. By training the algorithm on a labeled dataset, it can learn from the data and make accurate predictions or classifications.

In conclusion, analyzing the data is a critical step in the problem-solving cycle in computer science. It helps us gain a deeper understanding of the problem and develop effective solutions. Whether through statistical analysis, data visualization, or machine learning algorithms, data analysis plays a vital role in transforming raw data into actionable insights.

Exploring Possible Solutions

Once you have gathered data and completed the analysis, the next step in the problem-solving cycle is to explore possible solutions. This is where the true power of computer science comes into play. With the use of algorithms and the application of scientific principles, computer scientists can develop innovative solutions to complex problems.

During this stage, it is important to consider a variety of potential solutions. This involves brainstorming different ideas and considering their feasibility and potential effectiveness. It may be helpful to consult with colleagues or experts in the field to gather additional insights and perspectives.

Developing an Algorithm

One key aspect of exploring possible solutions is the development of an algorithm. An algorithm is a step-by-step set of instructions that outlines a specific process or procedure. In the context of problem solving in computer science, an algorithm provides a clear roadmap for implementing a solution.

The development of an algorithm requires careful thought and consideration. It is important to break down the problem into smaller, manageable steps and clearly define the inputs and outputs of each step. This allows for the creation of a logical and efficient solution.

Evaluating the Solutions

Once you have developed potential solutions and corresponding algorithms, the next step is to evaluate them. This involves analyzing each solution to determine its strengths, weaknesses, and potential impact. Consider factors such as efficiency, scalability, and resource requirements.

It may be helpful to conduct experiments or simulations to further assess the effectiveness of each solution. This can provide valuable insights and data to support the decision-making process.

Ultimately, the goal of exploring possible solutions is to find the most effective and efficient solution to the problem at hand. By leveraging the power of data, analysis, algorithms, and scientific principles, computer scientists can develop innovative solutions that drive progress and solve complex problems in the world of technology.

Evaluating the Options

Once you have identified potential solutions and algorithms for a problem, the next step in the problem-solving cycle in computer science is to evaluate the options. This evaluation process involves analyzing the potential solutions and algorithms based on various criteria to determine the best course of action.

Consider the Problem

Before evaluating the options, it is important to take a step back and consider the problem at hand. Understand the requirements, constraints, and desired outcomes of the problem. This analysis will help guide the evaluation process.

Analyze the Options

Next, it is crucial to analyze each solution or algorithm option individually. Look at factors such as efficiency, accuracy, ease of implementation, and scalability. Consider whether the solution or algorithm meets the specific requirements of the problem, and if it can be applied to related problems in the future.

Additionally, evaluate the potential risks and drawbacks associated with each option. Consider factors such as cost, time, and resources required for implementation. Assess any potential limitations or trade-offs that may impact the overall effectiveness of the solution or algorithm.

Select the Best Option

Based on the analysis, select the best option that aligns with the specific problem-solving goals. This may involve prioritizing certain criteria or making compromises based on the limitations identified during the evaluation process.

Remember that the best option may not always be the most technically complex or advanced solution. Consider the practicality and feasibility of implementation, as well as the potential impact on the overall system or project.

In conclusion, evaluating the options is a critical step in the problem-solving cycle in computer science. By carefully analyzing the potential solutions and algorithms, considering the problem requirements, and considering the limitations and trade-offs, you can select the best option to solve the problem at hand.

Making a Decision

Decision-making is a critical component in the problem-solving process in computer science. Once you have analyzed the problem, identified the relevant data, and generated a potential solution, it is important to evaluate your options and choose the best course of action.

Consider All Factors

When making a decision, it is important to consider all relevant factors. This includes evaluating the potential benefits and drawbacks of each option, as well as understanding any constraints or limitations that may impact your choice.

In computer science, this may involve analyzing the efficiency of different algorithms or considering the scalability of a proposed solution. It is important to take into account both the short-term and long-term impacts of your decision.

Weigh the Options

Once you have considered all the factors, it is important to weigh the options and determine the best approach. This may involve assigning weights or priorities to different factors based on their importance.

Using techniques such as decision matrices or cost-benefit analysis can help you systematically compare and evaluate different options. By quantifying and assessing the potential risks and rewards, you can make a more informed decision.

Remember: Decision-making in computer science is not purely subjective or based on personal preference. It is crucial to use analytical and logical thinking to select the most optimal solution.

In conclusion, making a decision is a crucial step in the problem-solving process in computer science. By considering all relevant factors and weighing the options using logical analysis, you can choose the best possible solution to a given problem.

Implementing the Solution

Once the problem has been analyzed and a solution has been proposed, the next step in the problem-solving cycle in computer science is implementing the solution. This involves turning the proposed solution into an actual computer program or algorithm that can solve the problem.

In order to implement the solution, computer science professionals need to have a strong understanding of various programming languages and data structures. They need to be able to write code that can manipulate and process data in order to solve the problem at hand.

During the implementation phase, the proposed solution is translated into a series of steps or instructions that a computer can understand and execute. This involves breaking down the problem into smaller sub-problems and designing algorithms to solve each sub-problem.

Computer scientists also need to consider the efficiency of their solution during the implementation phase. They need to ensure that the algorithm they design is able to handle large amounts of data and solve the problem in a reasonable amount of time. This often requires optimization techniques and careful consideration of the data structures used.

Once the code has been written and the algorithm has been implemented, it is important to test and debug the solution. This involves running test cases and checking the output to ensure that the program is working correctly. If any errors or bugs are found, they need to be fixed before the solution can be considered complete.

In conclusion, implementing the solution is a crucial step in the problem-solving cycle in computer science. It requires strong programming skills and a deep understanding of algorithms and data structures. By carefully designing and implementing the solution, computer scientists can solve problems efficiently and effectively.

Testing and Debugging

In computer science, testing and debugging are critical steps in the problem-solving cycle. Testing helps ensure that a program or algorithm is functioning correctly, while debugging analyzes and resolves any issues or bugs that may arise.

Testing involves running a program with specific input data to evaluate its output. This process helps verify that the program produces the expected results and handles different scenarios correctly. It is important to test both the normal and edge cases to ensure the program’s reliability.

Debugging is the process of identifying and fixing errors or bugs in a program. When a program does not produce the expected results or crashes, it is necessary to go through the code to find and fix the problem. This can involve analyzing the program’s logic, checking for syntax errors, and using debugging tools to trace the flow of data and identify the source of the issue.

Data analysis plays a crucial role in both testing and debugging. It helps to identify patterns, anomalies, or inconsistencies in the program’s behavior. By analyzing the data, developers can gain insights into potential issues and make informed decisions on how to improve the program’s performance.

In conclusion, testing and debugging are integral parts of the problem-solving cycle in computer science. Through testing and data analysis, developers can verify the correctness of their programs and identify and resolve any issues that may arise. This ensures that the algorithms and programs developed in computer science are robust, reliable, and efficient.

Iterating for Improvement

In computer science, problem solving often involves iterating through multiple cycles of analysis, solution development, and evaluation. This iterative process allows for continuous improvement in finding the most effective solution to a given problem.

The problem solving cycle starts with problem analysis, where the specific problem is identified and its requirements are understood. This step involves examining the problem from various angles and gathering all relevant information.

Once the problem is properly understood, the next step is to develop an algorithm or a step-by-step plan to solve the problem. This algorithm is a set of instructions that, when followed correctly, will lead to the solution.

After the algorithm is developed, it is implemented in a computer program. This step involves translating the algorithm into a programming language that a computer can understand and execute.

Once the program is implemented, it is then tested and evaluated to ensure that it produces the correct solution. This evaluation step is crucial in identifying any errors or inefficiencies in the program and allows for further improvement.

If any issues or problems are found during testing, the cycle iterates, starting from problem analysis again. This iterative process allows for refinement and improvement of the solution until the desired results are achieved.

Iterating for improvement is a fundamental concept in computer science problem solving. By continually analyzing, developing, and evaluating solutions, computer scientists are able to find the most optimal and efficient approaches to solving problems.

Documenting the Process

Documenting the problem-solving process in computer science is an essential step to ensure that the cycle is repeated successfully. The process involves gathering information, analyzing the problem, and designing a solution.

During the analysis phase, it is crucial to identify the specific problem at hand and break it down into smaller components. This allows for a more targeted approach to finding the solution. Additionally, analyzing the data involved in the problem can provide valuable insights and help in designing an effective solution.

Once the analysis is complete, it is important to document the findings. This documentation can take various forms, such as written reports, diagrams, or even code comments. The goal is to create a record that captures the problem, the analysis, and the proposed solution.

Documenting the process serves several purposes. Firstly, it allows for easy communication and collaboration between team members or future developers. By documenting the problem, analysis, and solution, others can easily understand the thought process behind the solution and potentially build upon it.

Secondly, documenting the process provides an opportunity for reflection and improvement. By reviewing the documentation, developers can identify areas where the problem-solving cycle can be strengthened or optimized. This continuous improvement is crucial in the field of computer science, as new challenges and technologies emerge rapidly.

In conclusion, documenting the problem-solving process is an integral part of the computer science cycle. It allows for effective communication, collaboration, and reflection on the solutions devised. By taking the time to document the process, developers can ensure a more efficient and successful problem-solving experience.

Communicating the Solution

Once the problem solving cycle is complete, it is important to effectively communicate the solution. This involves explaining the analysis, data, and steps taken to arrive at the solution.

Analyzing the Problem

During the problem solving cycle, a thorough analysis of the problem is conducted. This includes understanding the problem statement, gathering relevant data, and identifying any constraints or limitations. It is important to clearly communicate this analysis to ensure that others understand the problem at hand.

Presenting the Solution

The next step in communicating the solution is presenting the actual solution. This should include a detailed explanation of the steps taken to solve the problem, as well as any algorithms or data structures used. It is important to provide clear and concise descriptions of the solution, so that others can understand and reproduce the results.

Overall, effective communication of the solution in computer science is essential to ensure that others can understand and replicate the problem solving process. By clearly explaining the analysis, data, and steps taken, the solution can be communicated in a way that promotes understanding and collaboration within the field of computer science.

Reflecting and Learning

Reflecting and learning are crucial steps in the problem solving cycle in computer science. Once a problem has been solved, it is essential to reflect on the entire process and learn from the experience. This allows for continuous improvement and growth in the field of computer science.

During the reflecting phase, one must analyze and evaluate the problem solving process. This involves reviewing the initial problem statement, understanding the constraints and requirements, and assessing the effectiveness of the chosen algorithm and solution. It is important to consider the efficiency and accuracy of the solution, as well as any potential limitations or areas for optimization.

By reflecting on the problem solving cycle, computer scientists can gain valuable insights into their own strengths and weaknesses. They can identify areas where they excelled and areas where improvement is needed. This self-analysis helps in honing problem solving skills and becoming a better problem solver.

Learning from Mistakes

Mistakes are an integral part of the problem solving cycle, and they provide valuable learning opportunities. When a problem is not successfully solved, it is essential to analyze the reasons behind the failure and learn from them. This involves identifying errors in the algorithm or solution, understanding the underlying concepts or principles that were misunderstood, and finding alternative approaches or strategies.

Failure should not be seen as a setback, but rather as an opportunity for growth. By learning from mistakes, computer scientists can improve their problem solving abilities and expand their knowledge and understanding of computer science. It is through these failures and the subsequent learning process that new ideas and innovations are often born.

Continuous Improvement

Reflecting and learning should not be limited to individual problem solving experiences, but should be an ongoing practice. As computer science is a rapidly evolving field, it is crucial to stay updated with new technologies, algorithms, and problem solving techniques. Continuous learning and improvement contribute to staying competitive and relevant in the field.

Computer scientists can engage in continuous improvement by seeking feedback from peers, participating in research and development activities, attending conferences and workshops, and actively seeking new challenges and problem solving opportunities. This dedication to learning and improvement ensures that one’s problem solving skills remain sharp and effective.

In conclusion, reflecting and learning are integral parts of the problem solving cycle in computer science. They enable computer scientists to refine their problem solving abilities, learn from mistakes, and continuously improve their skills and knowledge. By embracing these steps, computer scientists can stay at the forefront of the ever-changing world of computer science and contribute to its advancements.

Applying Problem Solving in Real Life

In computer science, problem solving is not limited to the realm of programming and algorithms. It is a skill that can be applied to various aspects of our daily lives, helping us to solve problems efficiently and effectively. By using the problem-solving cycle and applying the principles of analysis, data, solution, algorithm, and cycle, we can tackle real-life challenges with confidence and success.

The first step in problem-solving is to analyze the problem at hand. This involves breaking it down into smaller, more manageable parts and identifying the key issues or goals. By understanding the problem thoroughly, we can gain insights into its root causes and potential solutions.

For example, let’s say you’re facing a recurring issue in your daily commute – traffic congestion. By analyzing the problem, you may discover that the main causes are a lack of alternative routes and a lack of communication between drivers. This analysis helps you identify potential solutions such as using navigation apps to find alternate routes or promoting carpooling to reduce the number of vehicles on the road.

Gathering and Analyzing Data

Once we have identified the problem, it is important to gather relevant data to support our analysis. This may involve conducting surveys, collecting statistics, or reviewing existing research. By gathering data, we can make informed decisions and prioritize potential solutions based on their impact and feasibility.

Continuing with the traffic congestion example, you may gather data on the average commute time, the number of vehicles on the road, and the impact of carpooling on congestion levels. This data can help you analyze the problem more accurately and determine the most effective solutions.

Generating and Evaluating Solutions

After analyzing the problem and gathering data, the next step is to generate potential solutions. This can be done through brainstorming, researching best practices, or seeking input from experts. It is important to consider multiple options and think outside the box to find innovative and effective solutions.

For our traffic congestion problem, potential solutions can include implementing a smart traffic management system that optimizes traffic flow or investing in public transportation to incentivize people to leave their cars at home. By evaluating each solution’s potential impact, cost, and feasibility, you can make an informed decision on the best course of action.

Implementing and Iterating

Once a solution has been chosen, it is time to implement it in real life. This may involve developing a plan, allocating resources, and executing the solution. It is important to monitor the progress and collect feedback to learn from the implementation and make necessary adjustments.

For example, if the chosen solution to address traffic congestion is implementing a smart traffic management system, you would work with engineers and transportation authorities to develop and deploy the system. Regular evaluation and iteration of the system’s performance would ensure that it is effective and making a positive impact on reducing congestion.

By applying the problem-solving cycle derived from computer science to real-life situations, we can approach challenges with a systematic and analytical mindset. This can help us make better decisions, improve our problem-solving skills, and ultimately achieve more efficient and effective solutions.

Building Problem Solving Skills

In the field of computer science, problem-solving is a fundamental skill that is crucial for success. Whether you are a computer scientist, programmer, or student, developing strong problem-solving skills will greatly benefit your work and studies. It allows you to approach challenges with a logical and systematic approach, leading to efficient and effective problem resolution.

The Problem Solving Cycle

Problem-solving in computer science involves a cyclical process known as the problem-solving cycle. This cycle consists of several stages, including problem identification, data analysis, solution development, implementation, and evaluation. By following this cycle, computer scientists are able to tackle complex problems and arrive at optimal solutions.

Importance of Data Analysis

Data analysis is a critical step in the problem-solving cycle. It involves gathering and examining relevant data to gain insights and identify patterns that can inform the development of a solution. Without proper data analysis, computer scientists may overlook important information or make unfounded assumptions, leading to subpar solutions.

To effectively analyze data, computer scientists can employ various techniques such as data visualization, statistical analysis, and machine learning algorithms. These tools enable them to extract meaningful information from large datasets and make informed decisions during the problem-solving process.

Developing Effective Solutions

Developing effective solutions requires creativity, critical thinking, and logical reasoning. Computer scientists must evaluate multiple approaches, consider various factors, and assess the feasibility of different solutions. They should also consider potential limitations and trade-offs to ensure that the chosen solution addresses the problem effectively.

Furthermore, collaboration and communication skills are vital when building problem-solving skills. Computer scientists often work in teams and need to effectively communicate their ideas, propose solutions, and address any challenges that arise during the problem-solving process. Strong interpersonal skills facilitate collaboration and enhance problem-solving outcomes.

  • Mastering programming languages and algorithms
  • Staying updated with technological advancements in the field
  • Practicing problem solving through coding challenges and projects
  • Seeking feedback and learning from mistakes
  • Continuing to learn and improve problem-solving skills

By following these strategies, individuals can strengthen their problem-solving abilities and become more effective computer scientists or programmers. Problem-solving is an essential skill in computer science and plays a central role in driving innovation and advancing the field.

Questions and answers:

What is the problem solving cycle in computer science.

The problem solving cycle in computer science refers to a systematic approach that programmers use to solve problems. It involves several steps, including problem definition, algorithm design, implementation, testing, and debugging.

How important is the problem solving cycle in computer science?

The problem solving cycle is extremely important in computer science as it allows programmers to effectively tackle complex problems and develop efficient solutions. It helps in organizing the thought process and ensures that the problem is approached in a logical and systematic manner.

What are the steps involved in the problem solving cycle?

The problem solving cycle typically consists of the following steps: problem definition and analysis, algorithm design, implementation, testing, and debugging. These steps are repeated as necessary until a satisfactory solution is achieved.

Can you explain the problem definition and analysis step in the problem solving cycle?

During the problem definition and analysis step, the programmer identifies and thoroughly understands the problem that needs to be solved. This involves analyzing the requirements, constraints, and possible inputs and outputs. It is important to have a clear understanding of the problem before proceeding to the next steps.

Why is testing and debugging an important step in the problem solving cycle?

Testing and debugging are important steps in the problem solving cycle because they ensure that the implemented solution functions as intended and is free from errors. Through testing, the programmer can identify and fix any issues or bugs in the code, thereby improving the quality and reliability of the solution.

What is the problem-solving cycle in computer science?

The problem-solving cycle in computer science refers to the systematic approach that computer scientists use to solve problems. It involves various steps, including problem analysis, algorithm design, coding, testing, and debugging.

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The 50-year-old problem that eludes theoretical computer science

A solution to P vs NP could unlock countless computational problems—or keep them forever out of reach.

The Steiner tree problem:  Connect a set of points with line segments of minimum total length.

  • Siobhan Roberts archive page

1. On Monday, July 19, 2021, in the middle of another strange pandemic summer, a leading computer scientist in the field of complexity theory tweeted out a public service message about an administrative snafu at a journal. He signed off with a very loaded 

“Happy Monday.”

In a parallel universe, it might have been a very happy Monday indeed. A proof had appeared online at the esteemed journal ACM Transactions on Computational Theory, which trades in “outstanding original research exploring the limits of feasible computation.” The result purported to solve the problem of all problems—the Holy Grail of theoretical computer science, worth a $1 million prize and fame rivaling Aristotle’s forevermore.

This treasured problem—known as “P versus NP”—is considered at once the most important in theoretical computer science and mathematics and completely out of reach. It addresses questions central to the promise, limits, and ambitions of computation, asking: 

Why are some problems harder than others? 

Which problems can computers realistically solve? 

How much time will it take? 

And it’s a quest with big philosophical and practical payoffs. 

“Look, this P versus NP question, what can I say?” Scott Aaronson, a computer scientist at the University of Texas at Austin, wrote in his memoir of ideas , Quantum Computing Since Democritus . “People like to describe it as ‘probably the central unsolved problem of theoretical computer science.’ That’s a comical understatement. P vs NP is one of the deepest questions that human beings have ever asked.” 

One way to think of this story’s protagonists is as follows:

“P” represents problems that a computer can handily solve. 

“NP” represents problems that, once solved, are easy to check—like jigsaw puzzles, or Sudoku. Many NP problems correspond to some of the most stubborn and urgent problems society faces. 

The million-dollar question posed by P vs. NP is this: Are these two classes of problems one and the same? Which is to say, could the problems that seem so difficult in fact be solved with an algorithm in a reasonable amount of time, if only the right, devilishly fast algorithm could be found? If so, many hard problems are suddenly solvable. And their algorithmic solutions could bring about societal changes of utopian proportions—in medicine and engineering and economics, biology and ecology, neuroscience and social science, industry, the arts, even politics and beyond. 

Sometimes the classifications evolve—hard problems are revealed to be easy when researchers find more efficient solutions. Testing whether a number is prime, for instance, has been known to be in the class NP since the mid-1970s. But in 2002, three computer scientists at the Indian Institute of Technology Kanpur devised an unconditional proof and a clever algorithm that finally confirmed the problem was also in P. 

If all the tricky problems could be transformed with such algorithmic sleight of hand, the consequences for society—for humanity and our planet—would be enormous. 

For starters, encryption systems, most of which are based on NP problems, would be cracked. We’d need to find a completely different approach to sending secure communications. Protein folding, a 50-year-old grand challenge in biology, would become more tractable, unlocking newfound abilities to design drugs that cure or treat disease and discover enzymes that break down industrial waste. It would also mean finding optimal solutions to everyday hard problems, such as mapping out a road trip to hit all destinations with minimal driving, or seating wedding guests so that only friends share the same dinner table. 

Since the P vs. NP problem’s inception 50 years ago—emerging from the momentous intersection of mathematical logic and electronic computing technology—researchers around the world have made Herculean attempts at a solution. Some computer scientists have suggested that the efforts might be better likened to those of Sisyphus, who labored without resolution. But while those who first explored the problem are running out of time to see a solution, the newer generations are happily taking up the quest.

For Manuel Sabin, a computer scientist just finishing a PhD at UC Berkeley, the allure is in probing the impossibility of problems where “you won’t know the answer until the sun engulfs the earth.” The search might be quixotic, but Sabin would regret not tilting at these windmills. 

Timothy Gowers, a mathematician at the University of Cambridge, calls it “one of my personal mathematical diseases.” He lost the summer of 2013 to the pursuit, after he asked students for an essay about the subject on a test. As he recounted on his blog: “After marking the essays in June, I thought I would just spend an hour or two thinking about the problem again, and that hour or two accidentally turned into about three months.” 

stanchions

The quest has even stumped the University of Toronto computer scientist Stephen Cook, who framed the problem and launched the field of computational complexity with a seminal paper in 1971. For this work, he won the Turing Award, computer science’s equivalent of the Nobel Prize. But he’s had no luck finding a solution. Cook says he never had any good ideas—“It’s just too difficult.”

2. Michael Sipser, an MIT computer scientist, estimates he’s spent, all told, as much as a decade on the problem. He got interested during grad school in the 1970s, and he bet his fellow student Len Adleman an ounce of gold that it would be solved by the end of the century (Sipser paid up). 

In the 1980s, he achieved a nice result solving a version of the problem with a “restricted” computational model—leading to an exciting period in the field with several beautiful results, giving cause for hope that a solution might not be too far off. 

Sipser still returns to the problem every now and then, and he’s a steadfast ambassador, delivering countless talks on the subject. 

The way he inches into an accessible explanation of P vs. NP is with a basic multiplication problem: 7 × 13 = ?

The answer, 91, is easy enough to compute in your head. Though multiplying bigger numbers isn’t as easy, it would still take a computer practically no time at all. 

But flipping those problems around is another matter. Consider, for example, finding the two 97-digit prime numbers that multiply to produce this very large number: 

310 7418240490 0437213507 5003588856 7930037346 0228427275 4572016194 8823206440 5180815045 5634682967 1723286782 4379162728 3803341547 1073108501 9195485290 0733772482 2783525742 3864540146 9173660247 7652346609 

This factoring problem was part of a challenge assessing the difficulty of cracking the RSA keys used in cryptography. Solving it took 80 processors five months of continuous computing, Sipser explains—which works out to roughly 33 years with only a single processor. Factoring is a hard problem because all current methods seek the answer via “brute force,” checking the astronomical number of possibilities one by one by one. Even for a computer, this is a slow process. 

“The interesting question here is, do you really need to search?” Sipser says. “Or is there some way of solving the factoring problem that zooms in on the answer quickly without searching? We don’t know the answer to that question.”

Questions like this one get at the heart of computational complexity—a field full of beastly problems that researchers are trying to understand. Aaronson has assembled a “Complexity Zoo,” an online catalogue with 545 classes of problems (and counting). Each is classified according to its complexity, or difficulty, and the resources—time, memory, energy—required to find solutions. P and NP are the main attractions. 

As scientific serendipity would have it, a Soviet mathematician, Leonid Levin, converged on a result equivalent to Cook's at more or less the same time.

P is “the class that started it all.” It is the class of problems that can be solved by a computer in a reasonable amount of time. More specifically, P problems are those for which the time it takes to find a solution can be described by a polynomial function, such as n ^2. In polynomial-­time algorithms, n is the size of the input, and growth against that input occurs at a reasonable rate (in this case, to the power of two).

By contrast, some hard NP problems might only be solvable by algorithms with run times defined by an exponential function, such as 2^n—producing an exponential growth rate (as with the spread of covid). NP, as Aaronson describes it, is “the class of dashed hopes and idle dreams.” He is, though, quick to clarify a common misconception: not all NP problems are difficult. The class NP in fact contains the class P—because problems with easy solutions are, of course, also easy to check.

NP’s more challenging problems often have momentous practical applications. For these problems, an exhaustive brute-force search for a solution would likely go on for an impractically long time—geologic time—before producing an answer. If a brute-force search algorithm is the best algorithm possible, then P does not equal NP. 

And among the cognoscenti, that’s apparently the consensus, which some liken more to religious belief: P ≠ NP. Most allow only a sliver of hope that the opposite will prove true. “I’d give it a 2 to 3% chance that P equals NP,” Aaronson says. “Those are the betting odds that I’d take.”

The result published in July presented a proof of exactly that long shot. But it was only the latest in a long tradition of proofs that don’t pass muster. Within a day of publication, in a turn of events worthy of Monty Python, the paper was removed from the online journal; then it seemed to reappear briefly before disappearing permanently. It was the most recent version of a paper that the author had posted more than 60 times to the arXiv preprint server over the last decade. The journal’s editor in chief explained on Twitter that the result had been rejected, but in a case of human error, the paper’s disposition had somehow changed from “reject” to “accept” and the proof had found its way to publication. 

3. In early August, when I met Steve Cook at his office on campus, he’d neither seen nor heard of that latest P vs. NP proof snafu. Now 81, he’d only recently retired, since his memory was failing. “That’s why we have James here,” he said—his son James, 36, also a computer scientist, had joined us for my visit. Steve was in the midst of clearing out his office. A giant recycling bin stood in the middle of the room, filling up with old yellowing issues of the Journal of Symbolic Logic, a stack of super-fat Toronto telephone books waiting nearby.

Over the years, Cook has seen many proofs purporting to solve the P vs. NP problem. In 2000, after the Clay Mathematics Institute named it one of the seven unsolved “Millennium Problems” (each worth a $1 million prize), he was inundated with messages from people who thought they’d triumphed. All the results were wrong, if not plainly bogus. About half claimed to have proved that P equals NP; the other half went in the opposite direction. Not too long ago, one person claimed to have proved both.

Cook, in his 1971 paper, conjectured that P does not equal NP (he phrased it using different terminology common at the time). He’s since invested a significant if indeterminate amount of time working to establish that that’s the case. “I don’t have a good memory of toiling away,” he says, but his colleagues recall that whenever they went into the department on the weekend, Steve was there in his office. 

Unless he’s racing sailboats, Cook is not one to rush; he likes to give an idea time. And his former students remember a distinct lack of swagger. The computer scientist Anna Lubiw, at the University of Waterloo, says that when he taught Cook’s theorem—part of that pioneering paper—he never referred to it as such and never even gave any hints that he was the person who proved it. Maria Klawe, a mathematician and computer scientist and the president of Harvey Mudd College, says she would regularly correct Cook when he lost his way teaching proofs that he knew inside out: “He’d get stuck and say, ‘Okay. Tell me how the proof goes.’” Cook was also famously modest in grant applications and reports pertaining to his research—he’d confess: “Honestly, I have made little progress …”

He did make headway, however, in recruiting James to take up the cause. Early on, James displayed an interest in mathematics and computing—at age nine, he urged his dad to teach him Boolean algebra and logic. A couple of years ago, after earning a PhD at Berkeley and doing a stint at Google, he set off as an independent researcher focusing on miscellaneous projects, some of them indirectly connected to P vs. NP. And despite the track record, James, who bears a striking resemblance to his father, is undaunted at having inherited such a seemingly interminable quest. He regards it as he would any mathematical endeavor: it’s a fun puzzle. “There’s got to be an answer to these questions,” he says. “And it’s like, come on, somebody’s got to solve it. Let’s just get this figured out. It’s been a long time. It’s embarrassing that we don’t know the answer yet.” 

The lack of progress hasn’t stopped this community of happy Sisypheans from celebrating computational complexity’s 50th anniversary. The festivities began in 2019, when devotees from around the world gathered at the Fields Institute for Research in Mathematical Sciences, at the University of Toronto, for a symposium in Cook’s honor. Christos Papadimitriou, a computer scientist at Columbia University who has spent much of his career working on P vs. NP, opened the event with a public lecture, looking back not a half-century but millennia. 

He began by describing age-old quests for solutions—using algebraic tools or straightedge and compass, which he considered rudimentary forms of computation. Papadimitriou’s tale eventually arrived at Alan Turing, the British mathematician whose 1936 paper “On Computable Numbers” formalized the notions of “algorithm” and “computation.” Turing also showed—with his idea of a “universal computing machine”—that there is no “mechanical” way (that is, performed by a machine) to prove the truth or falsehood of mathematical statements; no systematic way to distinguish the provable from the unprovable. 

Papadimitriou said he considers Turing’s paper the birth certificate of computer science—“and the birth certificate says that computer science was born with a stark understanding of its own limitations.” He reckoned computer science is the only known field of scientific discourse born with such an awareness—“as opposed to other sciences, which understand their own limitations, like the rest of us, in late middle age.”

It wasn’t long after Turing’s  ideas (and similar ideas from others) found embodiment in the first computers that scientists confronted questions about the machines’ inherent capabilities and limitations. In the early 1950s, John von Neumann, the Hungarian-American pioneer of the modern computer, “bragged about an algorithm of his being polynomial, compared to the exponential incumbent,” as Papadimitriou recalled—he’d outwitted a slow algorithm with a fast one. This was the dawn of a new theory: computational complexity theory. The crux of it was that only polynomial algorithms are in any sense good or practical or worth aiming at a problem, whereas an exponential algorithm, Papadimitriou said, “is the algorithmic equivalent of death.”

Cook first started thinking about complexity in the mid-1960s. While working on his PhD at Harvard, he contemplated whether it is possible to prove, given certain computational models, that multiplication is harder than addition (it remains an open problem). 

In 1967, according to a book about Cook forthcoming from the Association for Computing Machinery (ACM), while a postdoc at Berkeley, he drafted course notes that contained the seed of his big result. He’d worked out a formulation of the complexity classes that came to be known as P and NP, and he posed the question of whether P was equal to NP. (At around the same time, others, including the computer scientist Jack Edmonds, now retired from the University of Waterloo, were circling around the same ideas.)

But the field of computer science was only just beginning, and to most scientists and mathematicians such ideas were unfamiliar if not downright strange. After four years at Berkeley’s mathematics department, Cook was considered for tenure but not offered a position. He had advocates in the university’s new department of computer science, and they lobbied for him to be granted a position in their ranks, but the dean wasn’t inclined to give tenure to someone whom the illustrious mathematicians had denied. 

Most complexity theorists dream a little smaller, opting instead for indirect approaches.

In 1970, Cook moved to the University of Toronto. The following year he published his breakthrough. Submitted to a symposium of the ACM held that May in Shaker Heights, Ohio, the paper sharpened the concept of complexity and defined a way to characterize the hardest problems in NP. It proved, in a flash of algorithmic alchemy, that one problem, known as the satisfiability problem (seeking a solution for a formula given a set of constraints), was in a sense the hardest problem in NP, and that all the other NP problems could be reduced to it. 

This was a crucial theorem: If there is a polynomial-time algorithm that solves the satisfiability problem, then that algorithm will serve as a skeleton key, unlocking solutions to all the problems in NP. And if there exists a polynomial-time solution for all the problems in NP, then P = NP. 

Among computer scientists, Cook’s theorem is iconic. Leslie Valiant, of Harvard, recalled at the 2019 symposium precisely where and when he first heard of it. After finishing undergraduate studies in math, he’d started a PhD in computer science. While there were courses and degrees in this fledgling field, he said, it felt ephemeral, perhaps lacking in deep intellectual content. “It was a serious worry for people doing computer science at the time,” he said. They asked, ‘Is this a field? Where is it going?’ One day, Valiant came upon Cook’s paper. He read it overnight. “I was transformed,” he said. “In an instant, my concerns about computer science were very much reduced. This paper—for me, it really made the field. I think it made computer science—made it into something of substance.”

And then, as the story goes, after Cook’s theorem came a deluge.

In 1972, Dick Karp, a computer scientist at Berkeley, having read Cook’s esoteric paper, demonstrated that many of the classic computational problems with which he was intimately acquainted—essentially every problem he didn’t know how to solve, drawn from mathematical programming, operations research, graph theory, combinatorics, and computational logic—possessed the same transformational property that Cook had found with the satisfiability problem. In total, Karp found 21 problems, including the knapsack problem (seeking the optimal way to pack a constrained space with the most valuable items), the traveling-­salesman problem (finding the shortest possible route that visits each city once and returns to the city of origin), and the Steiner tree problem (seeking to optimally connect a set of points with line segments of minimum total length). 

Karp showed that this special collection of problems were all equivalent, which in turn demonstrated that the pattern identified by Cook was not an isolated phenomenon, but rather a classification methodology of surprising power and reach. It was a litmus test of sorts, identifying the class of what became known as “NP-complete” problems: a solution to any would crack them all. 

Papadimitriou thinks of NP-completeness as a versatile tool. “If you cannot solve a problem, try to prove it is NP-complete, because this will maybe save you a lot of time,” he said at the public lecture—you can give up on an exact solution and move on to solving an approximation or variation of the problem instead. 

In the grand sweep of history, Papadimitriou sees the phenomenon of NP-completeness and the P vs. NP quest as computer science’s destiny. Because as scientific serendipity would have it, a Soviet mathematician, Leonid Levin, converged on a result equivalent to Cook’s at more or less the same time. Levin, now at Boston University, did his work behind the Iron Curtain. After it received wider attention (he immigrated to America in 1978), the result became known as the Cook-Levin theorem.

And in a further coda a decade or so later, a “lost letter” was discovered in the Princeton archives of the Austrian logician Kurt Gödel. In 1956, he’d written to von Neumann asking whether a logic problem—which in modern parlance would be called NP-complete—could be solved in polynomial time. He opined that “this would have consequences of the greatest magnitude.”

billiard balls

4. While a half-century of work hasn’t yielded anything close to a solution, some results at least capture the imagination: a paper in 2004 claimed a proof for P = NP using soap bubbles as a mechanism of analog computation (soap film, naturally aligning in the minimum-­energy configuration, solves the NP-complete Steiner tree problem in a fashion). 

These days it’s a rare bird of a computer scientist—for example, Ron Fagin, an IBM fellow—who tackles the problem head on. In the 1970s, he produced Fagin’s theorem, which characterized the class NP in terms of mathematical logic. And he’s solved the problem more than once, but the results never stood for more than a few days before he found a bug. Fagin recently got funding for a P vs. NP project from IBM’s Exploratory Challenges program supporting adventurous research. In explaining why he keeps at it, he likes to quote Theodore Roosevelt, who said that it is far better to “dare mighty things” than to rank among those who “live in a gray twilight that knows neither victory nor defeat.”

But most complexity theorists dream a little smaller, opting instead for indirect approaches—tilting the problem, reshaping or reframing it, exploring related environs, and further whittling down the arsenal of tools that could be deployed against it (many are now known to be useless). 

Ryan Williams, a computer scientist at MIT, is trying to illuminate the problem both from above and from below—investigating the nature of “upper bounds” and “lower bounds” on core computational problems. An upper bound, in simple terms, is a specific mathematical claim that there exists a concrete algorithm that solves a particular problem without exceeding a certain amount of resources (time, memory, energy). A lower bound is the intangible opposite: it’s a general claim of impossibility, showing that no such algorithm exists universally. One focus of Williams’s research is to make lower bounds constructive and concrete—mathematical objects with describable features. He believes that more constructive approaches to lower bounds are “precisely what we are missing from current approaches in complexity theory.”

Williams has pegged the likelihood that P ≠ NP at a fairly moderate 80%. But lately some researchers in the field are expressing doubts about even that level of certainty. “More and more, I’m starting to wonder whether P equals NP,” Toniann Pitassi, a computer scientist at the University of Toronto and a former PhD student of Cook’s, says. Her approach in circling around the problem is to study both scaled-up and scaled-down analogues, harder and easier models. “Sometimes generalizing the question makes it clearer,” she says. But overall, she hasn’t achieved clarity: “Most people think P doesn’t equal NP. And I don’t know. Maybe it’s just me, but I feel like it’s become less and less clear that that’s the truth.” 

Historically, Pitassi points out, surprising results have occasionally come out of nowhere—seeming impossibilities proved possible by smart algorithm designers. The same could happen with P vs. NP, maybe in another 50 years or a century. One of the most important results in all of complexity theory, for instance, was achieved by David Barrington, of the University of Massachusetts, Amherst, in 1989. The gist of it (for our purposes) is that he devised a clever algorithm, which set out to do something that seemingly should’ve required an unbounded amount of memory but in fact used an astonishingly small amount—just five bits of information, enough to specify a number between one and 32 (inclusive) or a two-­letter word.

A more recent and related result, from 2014, took James Cook by surprise. Drawing from Barrington’s theorem, it uses memory in a wonderfully weird way. As hinted in the title of the paper, by the University of Amsterdam’s Harry Buhrman and collaborators, it’s about “computing with a full memory.” James can rattle off the paper’s introductory paragraph practically verbatim:

Imagine the following scenario. You want to perform a computation that requires more memory than you currently have available on your computer. One way of dealing with this problem is by installing a new hard drive. As it turns out you have a hard drive but it is full with data, pictures, movies, files, etc. You don’t need to access that data at the moment but you also don’t want to erase it. Can you use the hard drive for your computation, possibly altering its contents temporarily, guaranteeing that when the computation is completed, the hard drive is back in its original state with all the data intact? 

The answer, counterintuitively, is yes. 

James thinks of it as “borrowed memory.” After the shock of this result sank in, he had fun figuring out how to apply it to a particular problem—picking up where his dad had left off. 

A couple of decades ago, Steve Cook moved on to other related problems in complexity theory. With one problem, he made a conjecture about the amount of memory an algorithm would need to solve the problem—honing it to the absolute minimum. In 2019, James, together with Ian Mertz, one of Pitassi’s PhD students, deployed the poetic idea of borrowing memory and proved that even less memory was needed. The result didn’t go all the way to refuting his dad’s conjecture, but it’s a bit of progress in the grand complexity quest nonetheless.

And problems in complexity theory, James observes, sometimes have a domino effect—if there’s a proof in one critical corner, then all the dominoes fall. The breakthrough results, the most important ones, come from a long line of work, by a lot of different people, making incremental progress and establishing connections between different questions, until finally a big result emerges.

He also mentions a caveat: while a truly devilishly fast P = NP algorithm would be earth-shattering, there is also a scenario in which P = NP might be a letdown. It might turn out that a P algorithm capable of solving the NP-complete problem is on a time scale of, say, n ^100. “Technically that falls under P: it’s a polynomial,” says James. “But n ^100 is still very impractical”—it would mean any sizable problems would still be out of reach on human time scales. 

That is, of course, assuming we can find the algorithm in the first place. Donald Knuth, an algorithmist at Stanford, in recent years changed his mind—he “flipped the bit.” His intuition is that P does indeed equal NP, but that we’ll probably never be able to make use of that fact, practically speaking—because we won’t actually know any of the algorithms that happen to work. There are mind-boggling numbers of algorithms out there, he explains, but most of them are beyond our ken. So whereas some researchers might insist that no P = NP algorithm exists, Knuth contends that “it’s more likely that no polynomial-time algorithm will ever be embodied—actually written down as a program—by mere mortals.” 

For Papadimitriou, any answer would quench a lifelong obsession. He believes the P vs. NP problem belongs in the realm of fundamental scientific conundrums such as the origin of life and the unification of nature’s force fields. It’s the kind of profound, consequential puzzle, “concrete yet universal,” he said, “that adds meaning not only to science, but to human life itself.”

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Problem solving - Eduqas Computational thinking

Computers can be used to help solve complex problems using computational thinking. This means that before a problem can be tackled, it must first have been through decomposition and abstraction. This will result in a modular programmed solution with subroutines and clear interfaces.

Computational thinking

Computers can be used to help solve problems. However, before a problem can be tackled, the problem itself - and the ways in which it could be solved - needs to be understood.

Computational thinking close computational thinking A problem-solving method using computer science techniques, where possible solutions are developed and presented in a way that can be understood by humans and computers. helps with this. It allows us to take a complex problem, understand what the problem is and develop possible solutions. These solutions can then be presented in a way that a computer, a human, or both, can understand.

Two important elements of computational thinking are:

  • decomposition close decomposition Breaking down a complex problem or system into smaller parts that are more manageable and easier to understand.
  • abstraction close abstraction The process of extracting or withdrawing something.

Complex problems

A complex problem is one that, at first glance, does not have an obvious, immediate solution.

Computational thinking involves taking that complex problem and breaking it down into a series of small, more manageable problems. Each of these smaller problems can then be looked at individually.

Next, simple steps to solve each of the smaller problems can be designed. Finally, these simple steps are used to program a computer to help solve the complex problem in the best way.

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Problem Solving Techniques in Computer Science

problem solving science computer

Problem-solving is the process of identifying a problem and finding the best solution for it. Problem-solving is a technique that can be developed by following a well-organized approach. Every day we encounter many problems and solve them.

Every problem is different. Some problems are very difficult and are needed more attention to recognize the solution.

A problem may be solved by multiple methods. One solution may be faster, cheaper, and more reliable than others. It is important to choose a suitable worthy solution.

Different strategies, techniques, and tools are used to solve a problem. Computers are used as a tool to solve complex problems by developing computer programs.

Computer programs contain different instructions for computers. A programmer writes instructions and the computer executes these instructions to solve a problem. A person can be a good programmer if he has the skill of solving problems.

Table of Contents

Problem-Solving Techniques.

There are three different types of problem-solving techniques.

A set of instructions given to a computer to solve a problem is called a program.

A computer works according to the given instructions in the program. Computer programs are written in programming languages. A person who develops a program is called a programmer.

The programmer develops programs to instruct the computer on how to process data into information. The programmer uses programming languages or tools to write programs.

 Advantages of Computer Program

Different advantages of computer programs are as follows:

  • A computer program can solve many problems by giving instructions to the computer.
  • A computer program can be used to perform a task again and again and fastly.
  • A program can process a large amount of data easily.
  • It can display the results in different styles.
  • The processing of a program is more efficient and less time-consuming.
  • Different types of programs are used in different fields to perform certain tasks.

   Algorithms & Pseudo Code

An algorithm is a step-by-step procedure to solve a problem. The process of solving

problem becomes simpler and easier with help of algorithm. It is better to write an algorithm

before writing the actual computer program.

Properties of Algorithm

Following are some properties of an algorithm:

  • The given problem should be broken down into simple and meaningful steps.
  • The steps should be numbered sequentially.
  • The steps should be descriptive and written in simple English. 

Algorithms are written in a language that is similar to simple English called pseudocode. There is no standard to write pseudo code. It is used to specify program logic in an English-like manner that is independent of any particular programming language.

Pseudocode simplifies program development by separating it into two main parts.

Logic Design

In this part, the logic of the program is designed. We specify different steps required to solve the problem and the sequence of these steps.

In this part, the algorithm is converted into a program. The steps of the algorithm are

translated into instructions of any programming language.

The use of pseudo-code allows the programmer to focus on the planning of the program. After the planning is final, it can be written in any programming language.

The following algorithm inputs two numbers calculate the sum and then displays the result on the screen.

4. Total A+B

5. Display Total

The following algorithm inputs the radius from the user and calculates the area of a circle.

Hint: Area 3.14* radius* radius)

2. Input radius in r

3. area = 3.14* r* r

4. Print area

Advantages of Algorithm

There are many advantages of an algorithm

Reduce complexity

Writing algorithm and program separately simplifies the overall task by dividing it into two simpler tasks. While writing the algorithm, we can focus on solving the problem instead of concentrating on a particular language.

Increased Flexibility

An algorithm is written so that the code may be written in any language. Using an algorithm, the program could be written in Visual Basic, Java or C++, etc.

Ease of Understanding

It is not necessary to understand a particular programming language to understand an algorithm. It is written in an English-like manner.

A flowchart is a combination of two words flow and chart. A chart consists of different symbols to display information about any program. Flow indicates the direction processing that takes place in the program.

Flowchart is a graphical representation of an algorithm. It is a way of visually presenting the flow of data, operations performed on data, and the sequence of these operations.

Flowchart is similar to the layout plan of a building. A designer draws the layout plan of the building before constructing it. Similarly, a programmer prefers to design the flowchart before writing the computer program. Flowchart is designed according to the defined rule.

Uses of Logic Flowchart

Flowchart is used for the following reasons

  • Flowchart is used to represent an algorithm in a simple graphical manner.
  • Flowchart is used to show the steps of an algorithm easily.
  • Flowchart is used to understand the flow of the program.
  • Flowchart is used to improve the logic for solving a problem.
  • Programs can be reviewed and debugged easily.
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Computer Science > Computation and Language

Title: sola: solver-layer adaption of llm for better logic reasoning.

Abstract: Considering the challenges faced by large language models (LLMs) on logical reasoning, prior efforts have sought to transform problem-solving through tool learning. While progress has been made on small-scale problems, solving industrial cases remains difficult due to their large scale and intricate expressions. In this paper, we propose a novel solver-layer adaptation (SoLA) method, where we introduce a solver as a new layer of the LLM to differentially guide solutions towards satisfiability. In SoLA, LLM aims to comprehend the search space described in natural language and identify local solutions of the highest quality, while the solver layer focuses solely on constraints not satisfied by the initial solution. Leveraging MaxSAT as a bridge, we define forward and backward transfer gradients, enabling the final model to converge to a satisfied solution or prove unsatisfiability. The backdoor theory ensures that SoLA can obtain accurate solutions within polynomial loops. We evaluate the performance of SoLA on various datasets and empirically demonstrate its consistent outperformance against existing symbolic solvers (including Z3 and Kissat) and tool-learning methods in terms of efficiency in large-scale problem-solving.

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Welcome to the daily solving of our PROBLEM OF THE DAY with Yash Dwivedi . We will discuss the entire problem step-by-step and work towards developing an optimized solution. This will not only help you brush up on your concepts of Strings but also build up problem-solving skills.

In this problem, we are given a string A and a dictionary of n words B, to find out if A can be segmented into a space-separated sequence of dictionary words. Return 1 if it is possible to break A into a sequence of dictionary words, else return 0.

Note: From the dictionary B each word can be taken any number of times and in any order.

Input: n = 6 B = { "i", "like", "sam", "sung", "samsung", "mobile"} A = "ilike" Output: 1 Explanation: The string can be segmented as "i like".

Give the problem a try before going through the video. All the best!!! Problem Link: https://www.geeksforgeeks.org/problems/word-break1352/1

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AI has a large and growing carbon footprint, but there are potential solutions on the horizon

world outline with dark background and AI

Image: Getty.

Given the huge problem-solving potential of artificial intelligence (AI), it wouldn’t be far-fetched to think that AI could also help us in tackling the climate crisis. However, when we consider the energy needs of AI models, it becomes clear that the technology is as much a part of the climate problem as a solution.

The emissions come from the infrastructure associated with AI, such as building and running the data centres that handle the large amounts of information required to sustain these systems.

But different technological approaches to how we build AI systems could help reduce its carbon footprint. Two technologies in particular hold promise for doing this:   spiking neural networks   and lifelong learning.

The lifetime of an AI system can be split into two phases: training and inference. During training, a relevant dataset is used to build and tune – improve – the system. In inference, the trained system generates predictions on previously unseen data.

For example, training an AI that’s to be used in self-driving cars would require a dataset of many different driving scenarios and decisions taken by human drivers.

After the training phase, the AI system will predict effective manoeuvres for a self-driving car.   Artificial neural networks (ANN) , are an underlying technology used in most current AI systems.

They have many different elements to them, called parameters, whose values are adjusted during the training phase of the AI system. These parameters can run to more than 100 billion in total.

While large numbers of parameters improve the capabilities of ANNs, they also make training and inference resource-intensive processes. To put things in perspective, training GPT-3 (the precursor AI system to the current ChatGPT) generated 502 metric tonnes of carbon, which is equivalent to driving 112 petrol powered cars for a year.

GPT-3 further emits   8.4 tonnes of CO₂ annually   due to inference. Since the AI boom started in the early 2010s, the energy requirements of AI systems known as large language models (LLMs) – the type of technology that’s behind ChatGPT – have gone up   by a factor of 300,000 .

With the increasing ubiquity and complexity of AI models, this trend is going to continue, potentially making AI a significant contributor of CO₂ emissions. In fact, our current estimates   could be lower than AI’s actual carbon footprint   due to a lack of standard and accurate techniques for measuring AI-related emissions.

Spiking neural networks

The previously mentioned new technologies, spiking neural networks (SNNs) and lifelong learning (L2), have the potential to lower AI’s ever-increasing carbon footprint, with SNNs acting as an energy-efficient alternative to ANNs.

ANNs work by processing and learning patterns from data, enabling them to make predictions. They work with decimal numbers. To make accurate calculations, especially when multiplying numbers with decimal points together, the computer needs to be very precise. It is because of these decimal numbers that ANNs require lots of computing power, memory and time.

This means ANNs become more energy-intensive as the networks get larger and more complex. Both ANNs and SNNs are inspired by the brain, which contains billions of neurons (nerve cells) connected to each other via synapses.

Like the brain, ANNs and SNNs also have components which researchers call neurons, although these are artificial, not biological ones. The key difference between the two types of neural networks is in the way individual neurons transmit information to each other.

Neurons in the human brain communicate with each other by transmitting intermittent electrical signals called spikes. The spikes themselves do not contain information. Instead, the information lies in the timing of these spikes. This binary, all-or-none characteristic of spikes (usually represented as 0 or 1) implies that neurons are active when they spike and inactive otherwise.

This is one of the reasons for   energy efficient processing in the brain .

Just as Morse code uses specific sequences of dots and dashes to convey messages, SNNs use patterns or timings of spikes to process and transmit information... 

Continues…

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The full article - by   Dr Shirin Dora , of Loughborough University's   Department of Computer Science - can be  read on the Conversation website. 

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