problem solving and algorithm designing

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A Step-by-Step Guide to Algorithm Design

• Key Takeaways

Gartner reports a 20% increase in demand for skilled algorithm designers in 2024. 

Statista reveals that companies investing in algorithm optimization experience a 30% boost in productivity.

According to SEMrush, websites with well-designed algorithms for search engine optimization (SEO) see a 25% increase in organic traffic. 

Algorithm design is pivotal in programming, impacting code efficiency and performance.

Effective problem analysis, appropriate data structures, and optimization are key components. Regular practice, seeking feedback, and staying updated are vital for improving algorithm design skills.

Are you ready to unlock the secrets of efficient problem-solving in the realm of programming? Algorithm design holds the key to mastering this art. Whether you’re a coding enthusiast or a professional developer, understanding the intricacies of algorithm design is essential for optimizing your code and tackling complex computational challenges. But where do you begin on this journey to algorithmic mastery?

What strategies can you employ to create algorithms that not only solve problems but do so with efficiency and elegance? Join us as we embark on a step-by-step exploration of algorithm design, uncovering the principles and techniques that will empower you to become a proficient algorithm designer.

Introduction to Algorithm Design

• Understanding Algorithms
• Algorithms are sequences of step-by-step instructions for solving problems or performing tasks in computer science.
• They serve as the building blocks for various applications and solutions in programming.
• Examples of algorithms include sorting algorithms, searching algorithms, and optimization algorithms.
• Understanding algorithms is crucial for efficient problem-solving and software development.
• Importance of Algorithm Design
• Algorithm design is the process of creating efficient and effective algorithms to solve specific problems.
• It involves analyzing the problem, devising strategies, and implementing solutions.
• Well-designed algorithms lead to faster execution, reduced resource consumption, and scalable solutions.
• Algorithm design is essential for creating elegant and robust software across different domains of computer science.

Fundamentals of Algorithm Design

• Algorithm Basics

At the core of algorithm design lies the understanding of basic principles. Algorithms consist of a series of well-defined steps that, when followed, lead to the desired outcome. These steps are executed sequentially and can include operations such as arithmetic calculations, comparisons, and data manipulations. Understanding the basics of algorithms is essential before delving into more advanced concepts.

• Algorithm Analysis

When designing algorithms, it’s crucial to analyze their performance to ensure efficiency. Two key aspects of algorithm analysis are time complexity and space complexity.

• Time Complexity: Time complexity measures the amount of time an algorithm takes to complete as a function of the size of its input. It helps us understand how the algorithm’s performance scales with larger inputs.
• Space Complexity: Space complexity measures the amount of memory space an algorithm requires as a function of the size of its input. It helps us understand how much memory the algorithm consumes during execution.
• Algorithm Optimization Techniques

To enhance the efficiency of algorithms, various optimization techniques can be employed. Some common optimization techniques include:

• Greedy Algorithms: Greedy algorithms make simple choices step by step, hoping they lead to the best overall solution. They’re great for solving optimization problems.
• Divide and Conquer: Divide and conquer algorithms break big problems into smaller ones, solve them one by one, and then put their solutions together to solve the original problem.
• Dynamic Programming: Dynamic programming solves problems by breaking them into smaller pieces and remembering the solutions to avoid doing the same work again.
• Backtracking: Backtracking is a methodical way to find solutions to problems by trying out all possible options and giving up on those that won’t lead to a valid answer.

Understanding and using these algorithm tricks can make your programs faster and better at solving problems.

Step-by-Step Guide to Algorithm Design

• Problem Statement

Before diving into algorithm design, it’s essential to clearly define the problem you’re aiming to solve. This involves breaking down the problem statement into manageable components and understanding its scope. 

Ask yourself: What is the specific task or challenge we need to address? What are the inputs, and what should be the desired outputs? By thoroughly analyzing the problem statement, you lay the foundation for creating an effective algorithm.

Understanding Constraints

Every problem comes with its set of constraints—limitations or conditions that must be considered during the algorithm design process. These constraints could be related to time, space, or other resources.

For example, in a real-time application, you may have strict time constraints for processing data. Understanding and incorporating these constraints into your algorithm design ensures that your solution is not only effective but also practical and efficient in real-world scenarios.

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• Identifying Inputs and Outputs

Once you’ve defined the problem and understood its constraints, the next step is to identify the inputs and outputs of your algorithm. Inputs are the data or information that your algorithm will process, while outputs are the results or solutions it will produce.

Clearly defining the inputs and outputs helps in designing algorithms that are precise and focused. It also enables you to anticipate potential edge cases and handle them appropriately within your algorithm.

• Designing the Algorithm

Once you know what the problem is and what you need to achieve, it’s time to make a plan. Think about what tools (like data structures and algorithms) will help you solve the problem best.

Look at things like how fast it needs to work, how much space it needs, and how easy it is to use. If the problem seems big, break it into smaller parts and figure out how to solve each part step by step. This way, you can make strong and flexible solutions for even the toughest problems.

Choosing the Right Approach

• Problem Analysis: Begin by thoroughly understanding the problem statement, including its inputs, outputs, and any constraints.
• Considerations: Take into account factors such as the size of the input data, the desired efficiency of the algorithm, and any specific requirements or limitations.
• Approach Selection: Based on the analysis, choose the most appropriate approach for solving the problem effectively.
• Foundation Setting: Choosing the right approach lays the foundation for a successful algorithm design process.
• Pseudocode Development
• Definition: Pseudocode is a high-level description of the algorithm’s logic, resembling the structure of a programming language.
• Purpose: It helps outline the steps of the algorithm without getting bogged down in syntax details.
• Clarity Check: Developing pseudocode ensures that the algorithm’s logic is accurately captured before proceeding to the coding phase.
• Logic Focus: Focus on the algorithm’s logic rather than specific language syntax during pseudocode development.
• Algorithm Visualization
• Insight Generation: Visualization aids in understanding and analyzing algorithms by providing insights into their behavior.
• Identifying Inefficiencies: Visualizing an algorithm can help identify inefficiencies and areas for optimization.
• Tool Usage: Various tools and techniques, from simple diagrams to interactive simulations, can be used for algorithm visualization.
• Decision Making: Visualization helps make informed decisions during the design and implementation process.
• Coding the Algorithm
• Language Selection: Choose the appropriate programming language based on factors such as syntax, performance, and available libraries.
• Code Structure: Write clean, well-structured code that accurately reflects the logic outlined in the pseudocode.
• Attention to Detail: Pay attention to variable names, comments, and coding conventions to ensure readability and maintainability.
• Translation: Translate the pseudocode into executable code, following best practices for the chosen programming language.
• Implementing the Algorithm
• Functional Decomposition: Break down the algorithm into smaller, manageable functions or modules to promote code reuse and maintainability.
• Testing: Test the implementation with various inputs to ensure correctness and efficiency.
• Refinement: Iteratively refine and optimize the implementation based on performance benchmarks and feedback from testing.
• Performance Considerations: Pay attention to runtime performance and resource usage during implementation.
• Testing and Debugging
• Test Case Generation: Generate test cases that cover a range of input scenarios, including edge cases and corner cases.
• Debugging Techniques: Use debugging tools, print statements, and step-by-step execution to identify and fix errors in the code.
• Error Types: Pay attention to runtime errors, logic errors, and off-by-one errors during testing and debugging.
• Thoroughness: Thorough testing and diligent debugging ensure that the algorithm behaves as expected under various conditions.

Advanced Algorithm Design Concepts

• Graph Algorithms

Graph algorithms are essential in solving problems involving networks or relationships between objects. Among the most commonly used graph algorithms are Breadth-First Search (BFS) and Depth-First Search (DFS). BFS traverses a graph level by level, exploring all neighboring vertices of a given vertex before moving to the next level.

On the other hand, DFS explores as far as possible along each branch before backtracking. These algorithms are fundamental building blocks for solving various graph-related problems efficiently.

Breadth-First Search (BFS)

Breadth-First Search (BFS) is a graph traversal algorithm used to explore a graph systematically. It starts at a selected vertex and explores all of its neighboring vertices before moving on to the next level.

BFS is particularly useful for finding the shortest path in an unweighted graph or for traversing graphs without getting stuck in infinite loops. Its simplicity and efficiency make it a popular choice for a wide range of graph-related problems.

Depth-First Search (DFS)

DFS, or Depth-First Search, is a basic way to move through a graph. It works by going as far as it can along one path before turning back. It doesn’t always find the shortest path, unlike BFS.

But it’s useful for things like sorting, finding cycles, and solving mazes. You can use DFS in different situations and it can be done either by going back or by using a stack. It’s handy for lots of graph problems.

Dijkstra’s Algorithm

Dijkstra’s Algorithm is a well-known graph tool that helps find the shortest route between two points in a weighted graph. It does this by picking the closest point from the starting point and then checking its neighboring points.

This algorithm is great for finding short paths in graphs with positive weights on edges, which is super useful for things like GPS and finding the best routes in networks.

Bellman-Ford Algorithm

The Bellman-Ford Algorithm is a tool used in graphs to find the shortest paths from one starting point to all other points, even when some paths have negative weights. It’s not as fast as Dijkstra’s Algorithm, but it can handle negative weights.

Because of this, it’s useful in many areas like network routing, finding opportunities in finance, and managing resources in computer systems.

• Tree Algorithms

Tree algorithms are essential in algorithm design, offering efficient ways to organize and manipulate data. Among the various types of trees, Binary Search Trees (BST), AVL Trees, and Red-Black Trees stand out as fundamental structures.

Binary Search Trees (BST)

BSTs are binary trees that follow a specific ordering property: for every node, all values in its left subtree are less than the node’s value, and all values in its right subtree are greater. This ordering enables fast searching, insertion, and deletion operations.

However, unbalanced BSTs can degrade into linked lists, leading to inefficient operations. To address this issue, balanced binary search trees like AVL trees and Red-Black trees were developed.

AVL trees are self-balancing binary search trees named after their inventors, Adelson-Velsky and Landis. They maintain balance by enforcing a height difference of at most one between the left and right subtrees of any node.

This balance ensures efficient operations, with worst-case time complexity of O(log n) for search, insert, and delete operations. Although AVL trees require additional bookkeeping to maintain balance, they provide consistent performance across operations.

Red-Black Trees

Red-Black trees are another type of self-balancing binary search tree known for their simpler balancing rules compared to AVL trees. Each node in a Red-Black tree is assigned a color—either red or black—and must adhere to specific rules to ensure balance.

These rules include maintaining the properties of a binary search tree and enforcing constraints on the colors of nodes. Despite being less strictly balanced than AVL trees, Red-Black trees offer better overall performance for insertion and deletion operations due to their simpler balancing mechanisms.

• Sorting Algorithms

Sorting algorithms are essential tools in the toolkit of any algorithm designer. They allow us to arrange data in a specific order, such as numerical or alphabetical. Let’s explore four popular sorting algorithms: Bubble Sort, Merge Sort, Quick Sort, and Heap Sort.

Bubble Sort

Bubble Sort is one of the simplest sorting algorithms to understand and implement. It works by repeatedly stepping through the list, comparing adjacent elements, and swapping them if they are in the wrong order.

The pass through the list is repeated until the list is sorted. While Bubble Sort is easy to grasp, it is not the most efficient sorting algorithm, particularly for large datasets, as it has a time complexity of O(n^2).

Merge Sort is a divide-and-conquer algorithm that works by dividing the input array into smaller sub-arrays, sorting each sub-array recursively, and then merging the sorted sub-arrays to produce the final sorted array.

Merge Sort has a time complexity of O(n log n), making it more efficient than Bubble Sort for large datasets. It is a stable sorting algorithm, meaning it preserves the relative order of equal elements.

Quick Sort is another divide-and-conquer algorithm that works by selecting a pivot element from the array and partitioning the other elements into two sub-arrays according to whether they are less than or greater than the pivot.

The sub-arrays are then sorted recursively. Quick Sort is known for its efficiency and is often faster than other sorting algorithms in practice. However, its worst-case time complexity is O(n^2), although this is rare with proper pivot selection strategies.

Heap Sort is a sorting method that arranges numbers by comparing them. It starts by organizing the numbers into a special structure called a heap. Then, it repeatedly takes out the biggest (or smallest) number from the heap until all numbers are sorted.

Heap Sort works quickly and doesn’t need extra memory. It’s like sorting a deck of cards by picking out the highest card each time and arranging them neatly.

Understanding Algorithm Design

• Problem Analysis

The first step in algorithm design is problem analysis. Before you can design an effective algorithm, you need to clearly understand the problem you’re trying to solve. Take the time to analyze the input, output, and constraints of the problem. Break it down into smaller sub-problems if necessary. This thorough analysis lays the foundation for creating an efficient algorithmic solution.

• Designing Algorithmic Solutions

Once you’ve analyzed the problem, the next step is designing algorithmic solutions. This involves selecting appropriate data structures and algorithms to efficiently solve the problem.

When picking your algorithms, think about things like how long they take to run, how much memory they need, and how easy they are to use. A good algorithm can make your code work better and faster.

• Implementing and Optimizing Algorithms

After designing your algorithm, it’s time to implement it in code. Start by writing pseudocode to outline the logic of your algorithm. Then, translate your pseudocode into the programming language of your choice. Test your implementation with different inputs to ensure it produces the correct output and performs efficiently.

Finally, analyze the performance of your algorithm and make any necessary optimizations. This may involve tweaking your algorithm or selecting different data structures to improve efficiency.

Practical Applications of Algorithm Design

• Software Development

Algorithm design helps developers solve many problems in software development, like sorting and searching, and it also makes software run faster and use less resources, making users happier.

• Data Analysis and Machine Learning

Algorithm design is super important in data analysis and machine learning. It helps process big sets of data and find useful info. When we make good algorithms for things like grouping data, sorting it, or making predictions, we can find patterns and make smart choices based on them.

• Networking and Routing

In networking and routing, algorithm design is essential for optimizing data transmission and routing paths. Efficient routing algorithms ensure that data packets are delivered quickly and reliably, minimizing network congestion and latency.

• Cryptography

Cryptography relies on sophisticated algorithms to secure sensitive information and protect communication channels from unauthorized access. By designing robust encryption and decryption algorithms, cryptographers can safeguard data against cyber threats and ensure confidentiality and integrity.

• Game Development

In video game making, algorithm design helps create lifelike actions, smart enemies, and fun gaming adventures. With algorithms for finding paths, spotting crashes, and deciding how computer characters act, game makers can make exciting games that grab players’ attention.

Tips for Mastering Algorithm Design

• Practice Regularly
• Dedicate consistent time each day to solving algorithmic problems.
• Utilize online platforms like LeetCode, HackerRank, and CodeSignal for practice.
• Start with simple problems and gradually progress to more complex ones.
• Regular practice enhances understanding of different algorithms and problem-solving techniques.
• Collaborate with Peers
• Join online coding communities and participate in coding competitions.
• Engage in peer collaboration to learn from diverse perspectives and approaches.
• Benefit from peer feedback and insights to identify areas for improvement.
• Collaboration accelerates learning and development as an algorithm designer.
• Explore Real-World Problems
• Apply algorithmic skills to solve practical problems in various domains.
• Seek opportunities in fields like finance, healthcare , and logistics.
• Hands-on experience deepens understanding of real-world algorithm usage.
• Tackling real-world problems fosters practical solutions and motivates further skill development.
• Stay Updated with Industry Trends
• Stay informed about the latest advancements in algorithm design.
• Read research papers, attend conferences, and follow industry influencers.
• Incorporate cutting-edge techniques into algorithm designs.
• Networking with professionals provides insights and collaboration opportunities.

Incorporating these tips into your algorithm design practice can lead to mastery in the field, enabling you to confidently tackle complex computational problems.

In summary, learning how to design algorithms is super important for all kinds of programmers. By carefully looking at problems, picking the right tools, and making your solutions better over time, you can solve lots of different computer puzzles. Remember to think about things like how long your code takes to run and how much space it needs. And don’t forget, practicing and not giving up are key to getting really good at it. If you follow the steps we’ve talked about, you’ll be really good at designing algorithms and coding in no time!

• Q. How important is algorithm design in programming?

Algorithm design is crucial as it determines the efficiency of code and impacts overall performance. Well-designed algorithms can significantly reduce processing time and resource usage.

• Q. What are the key components of algorithm design?

Understanding problem constraints, selecting appropriate data structures, and optimizing for time and space complexity. Effective problem analysis and algorithmic solution design are fundamental components.

• Q. How can I improve my algorithm design skills?

Practice regularly by solving a variety of problems and analyzing existing algorithms. Seek feedback from peers and experts, and stay updated on the latest trends and techniques.

• Q. Are there any common pitfalls to avoid in algorithm design?

Overcomplicating solutions, neglecting edge cases, and ignoring algorithm efficiency. Lack of proper problem analysis and premature optimization can also hinder algorithm performance.

• Q. Where can I find resources to learn more about algorithm design?

Online courses, textbooks, and programming communities offer valuable resources for mastering algorithm design. Participating in coding competitions and solving algorithmic challenges can also enhance your skills.

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• 1. Micro-Worlds
• 2. Light-Bot in Java
• 3. Jeroos of Santong Island
• 4. Problem Solving and Algorithms
• 5. Creating Jeroo Methods
• 6. Conditionally Executing Actions
• 7. Repeating Actions
• 8. Handling Touch Events
• 9. Adding Text to the Screen

Problem Solving and Algorithms

Learn a basic process for developing a solution to a problem. Nothing in this chapter is unique to using a computer to solve a problem. This process can be used to solve a wide variety of problems, including ones that have nothing to do with computers.

Problems, Solutions, and Tools

I have a problem! I need to thank Aunt Kay for the birthday present she sent me. I could send a thank you note through the mail. I could call her on the telephone. I could send her an email message. I could drive to her house and thank her in person. In fact, there are many ways I could thank her, but that's not the point. The point is that I must decide how I want to solve the problem, and use the appropriate tool to implement (carry out) my plan. The postal service, the telephone, the internet, and my automobile are tools that I can use, but none of these actually solves my problem. In a similar way, a computer does not solve problems, it's just a tool that I can use to implement my plan for solving the problem.

Knowing that Aunt Kay appreciates creative and unusual things, I have decided to hire a singing messenger to deliver my thanks. In this context, the messenger is a tool, but one that needs instructions from me. I have to tell the messenger where Aunt Kay lives, what time I would like the message to be delivered, and what lyrics I want sung. A computer program is similar to my instructions to the messenger.

The story of Aunt Kay uses a familiar context to set the stage for a useful point of view concerning computers and computer programs. The following list summarizes the key aspects of this point of view.

A computer is a tool that can be used to implement a plan for solving a problem.

A computer program is a set of instructions for a computer. These instructions describe the steps that the computer must follow to implement a plan.

An algorithm is a plan for solving a problem.

A person must design an algorithm.

A person must translate an algorithm into a computer program.

This point of view sets the stage for a process that we will use to develop solutions to Jeroo problems. The basic process is important because it can be used to solve a wide variety of problems, including ones where the solution will be written in some other programming language.

An Algorithm Development Process

Every problem solution starts with a plan. That plan is called an algorithm.

There are many ways to write an algorithm. Some are very informal, some are quite formal and mathematical in nature, and some are quite graphical. The instructions for connecting a DVD player to a television are an algorithm. A mathematical formula such as πR 2 is a special case of an algorithm. The form is not particularly important as long as it provides a good way to describe and check the logic of the plan.

The development of an algorithm (a plan) is a key step in solving a problem. Once we have an algorithm, we can translate it into a computer program in some programming language. Our algorithm development process consists of five major steps.

Step 1: Obtain a description of the problem.

Step 2: analyze the problem., step 3: develop a high-level algorithm., step 4: refine the algorithm by adding more detail., step 5: review the algorithm..

This step is much more difficult than it appears. In the following discussion, the word client refers to someone who wants to find a solution to a problem, and the word developer refers to someone who finds a way to solve the problem. The developer must create an algorithm that will solve the client's problem.

The client is responsible for creating a description of the problem, but this is often the weakest part of the process. It's quite common for a problem description to suffer from one or more of the following types of defects: (1) the description relies on unstated assumptions, (2) the description is ambiguous, (3) the description is incomplete, or (4) the description has internal contradictions. These defects are seldom due to carelessness by the client. Instead, they are due to the fact that natural languages (English, French, Korean, etc.) are rather imprecise. Part of the developer's responsibility is to identify defects in the description of a problem, and to work with the client to remedy those defects.

The purpose of this step is to determine both the starting and ending points for solving the problem. This process is analogous to a mathematician determining what is given and what must be proven. A good problem description makes it easier to perform this step.

When determining the starting point, we should start by seeking answers to the following questions:

What data are available?

Where is that data?

What formulas pertain to the problem?

What rules exist for working with the data?

What relationships exist among the data values?

When determining the ending point, we need to describe the characteristics of a solution. In other words, how will we know when we're done? Asking the following questions often helps to determine the ending point.

What new facts will we have?

What items will have changed?

What changes will have been made to those items?

What things will no longer exist?

An algorithm is a plan for solving a problem, but plans come in several levels of detail. It's usually better to start with a high-level algorithm that includes the major part of a solution, but leaves the details until later. We can use an everyday example to demonstrate a high-level algorithm.

Problem: I need a send a birthday card to my brother, Mark.

Analysis: I don't have a card. I prefer to buy a card rather than make one myself.

High-level algorithm:

Go to a store that sells greeting cards Select a card Purchase a card Mail the card

This algorithm is satisfactory for daily use, but it lacks details that would have to be added were a computer to carry out the solution. These details include answers to questions such as the following.

"Which store will I visit?"

"How will I get there: walk, drive, ride my bicycle, take the bus?"

"What kind of card does Mark like: humorous, sentimental, risqué?"

These kinds of details are considered in the next step of our process.

A high-level algorithm shows the major steps that need to be followed to solve a problem. Now we need to add details to these steps, but how much detail should we add? Unfortunately, the answer to this question depends on the situation. We have to consider who (or what) is going to implement the algorithm and how much that person (or thing) already knows how to do. If someone is going to purchase Mark's birthday card on my behalf, my instructions have to be adapted to whether or not that person is familiar with the stores in the community and how well the purchaser known my brother's taste in greeting cards.

When our goal is to develop algorithms that will lead to computer programs, we need to consider the capabilities of the computer and provide enough detail so that someone else could use our algorithm to write a computer program that follows the steps in our algorithm. As with the birthday card problem, we need to adjust the level of detail to match the ability of the programmer. When in doubt, or when you are learning, it is better to have too much detail than to have too little.

Most of our examples will move from a high-level to a detailed algorithm in a single step, but this is not always reasonable. For larger, more complex problems, it is common to go through this process several times, developing intermediate level algorithms as we go. Each time, we add more detail to the previous algorithm, stopping when we see no benefit to further refinement. This technique of gradually working from a high-level to a detailed algorithm is often called stepwise refinement .

The final step is to review the algorithm. What are we looking for? First, we need to work through the algorithm step by step to determine whether or not it will solve the original problem. Once we are satisfied that the algorithm does provide a solution to the problem, we start to look for other things. The following questions are typical of ones that should be asked whenever we review an algorithm. Asking these questions and seeking their answers is a good way to develop skills that can be applied to the next problem.

Does this algorithm solve a very specific problem or does it solve a more general problem ? If it solves a very specific problem, should it be generalized?

For example, an algorithm that computes the area of a circle having radius 5.2 meters (formula π*5.2 2 ) solves a very specific problem, but an algorithm that computes the area of any circle (formula π*R 2 ) solves a more general problem.

Can this algorithm be simplified ?

One formula for computing the perimeter of a rectangle is:

length + width + length + width

A simpler formula would be:

2.0 * ( length + width )

Is this solution similar to the solution to another problem? How are they alike? How are they different?

For example, consider the following two formulae:

Rectangle area = length * width Triangle area = 0.5 * base * height

Similarities: Each computes an area. Each multiplies two measurements.

Differences: Different measurements are used. The triangle formula contains 0.5.

Hypothesis: Perhaps every area formula involves multiplying two measurements.

Example 4.1: Pick and Plant

This section contains an extended example that demonstrates the algorithm development process. To complete the algorithm, we need to know that every Jeroo can hop forward, turn left and right, pick a flower from its current location, and plant a flower at its current location.

Problem Statement (Step 1)

A Jeroo starts at (0, 0) facing East with no flowers in its pouch. There is a flower at location (3, 0). Write a program that directs the Jeroo to pick the flower and plant it at location (3, 2). After planting the flower, the Jeroo should hop one space East and stop. There are no other nets, flowers, or Jeroos on the island.

Analysis of the Problem (Step 2)

The flower is exactly three spaces ahead of the jeroo.

The flower is to be planted exactly two spaces South of its current location.

The Jeroo is to finish facing East one space East of the planted flower.

There are no nets to worry about.

High-level Algorithm (Step 3)

Let's name the Jeroo Bobby. Bobby should do the following:

Get the flower Put the flower Hop East

Detailed Algorithm (Step 4)

Get the flower Hop 3 times Pick the flower Put the flower Turn right Hop 2 times Plant a flower Hop East Turn left Hop once

Review the Algorithm (Step 5)

The high-level algorithm partitioned the problem into three rather easy subproblems. This seems like a good technique.

This algorithm solves a very specific problem because the Jeroo and the flower are in very specific locations.

This algorithm is actually a solution to a slightly more general problem in which the Jeroo starts anywhere, and the flower is 3 spaces directly ahead of the Jeroo.

Java Code for "Pick and Plant"

A good programmer doesn't write a program all at once. Instead, the programmer will write and test the program in a series of builds. Each build adds to the previous one. The high-level algorithm will guide us in this process.

FIRST BUILD

To see this solution in action, create a new Greenfoot4Sofia scenario and use the Edit Palettes Jeroo menu command to make the Jeroo classes visible. Right-click on the Island class and create a new subclass with the name of your choice. This subclass will hold your new code.

The recommended first build contains three things:

The main method (here myProgram() in your island subclass).

Declaration and instantiation of every Jeroo that will be used.

The high-level algorithm in the form of comments.

The instantiation at the beginning of myProgram() places bobby at (0, 0), facing East, with no flowers.

Once the first build is working correctly, we can proceed to the others. In this case, each build will correspond to one step in the high-level algorithm. It may seem like a lot of work to use four builds for such a simple program, but doing so helps establish habits that will become invaluable as the programs become more complex.

SECOND BUILD

This build adds the logic to "get the flower", which in the detailed algorithm (step 4 above) consists of hopping 3 times and then picking the flower. The new code is indicated by comments that wouldn't appear in the original (they are just here to call attention to the additions). The blank lines help show the organization of the logic.

By taking a moment to run the work so far, you can confirm whether or not this step in the planned algorithm works as expected.

THIRD BUILD

This build adds the logic to "put the flower". New code is indicated by the comments that are provided here to mark the additions.

FOURTH BUILD (final)

Example 4.2: replace net with flower.

This section contains a second example that demonstrates the algorithm development process.

There are two Jeroos. One Jeroo starts at (0, 0) facing North with one flower in its pouch. The second starts at (0, 2) facing East with one flower in its pouch. There is a net at location (3, 2). Write a program that directs the first Jeroo to give its flower to the second one. After receiving the flower, the second Jeroo must disable the net, and plant a flower in its place. After planting the flower, the Jeroo must turn and face South. There are no other nets, flowers, or Jeroos on the island.

Jeroo_2 is exactly two spaces behind Jeroo_1.

The only net is exactly three spaces ahead of Jeroo_2.

Each Jeroo has exactly one flower.

Jeroo_2 will have two flowers after receiving one from Jeroo_1. One flower must be used to disable the net. The other flower must be planted at the location of the net, i.e. (3, 2).

Jeroo_1 will finish at (0, 1) facing South.

Jeroo_2 is to finish at (3, 2) facing South.

Each Jeroo will finish with 0 flowers in its pouch. One flower was used to disable the net, and the other was planted.

Let's name the first Jeroo Ann and the second one Andy.

Ann should do the following: Find Andy (but don't collide with him) Give a flower to Andy (he will be straight ahead) After receiving the flower, Andy should do the following: Find the net (but don't hop onto it) Disable the net Plant a flower at the location of the net Face South

Ann should do the following: Find Andy Turn around (either left or right twice) Hop (to location (0, 1)) Give a flower to Andy Give ahead Now Andy should do the following: Find the net Hop twice (to location (2, 2)) Disable the net Toss Plant a flower at the location of the net Hop (to location (3, 2)) Plant a flower Face South Turn right

The high-level algorithm helps manage the details.

This algorithm solves a very specific problem, but the specific locations are not important. The only thing that is important is the starting location of the Jeroos relative to one another and the location of the net relative to the second Jeroo's location and direction.

Java Code for "Replace Net with Flower"

As before, the code should be written incrementally as a series of builds. Four builds will be suitable for this problem. As usual, the first build will contain the main method, the declaration and instantiation of the Jeroo objects, and the high-level algorithm in the form of comments. The second build will have Ann give her flower to Andy. The third build will have Andy locate and disable the net. In the final build, Andy will place the flower and turn East.

This build creates the main method, instantiates the Jeroos, and outlines the high-level algorithm. In this example, the main method would be myProgram() contained within a subclass of Island .

This build adds the logic for Ann to locate Andy and give him a flower.

This build adds the logic for Andy to locate and disable the net.

This build adds the logic for Andy to place a flower at (3, 2) and turn South.

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Understanding Algorithms: The Key to Problem-Solving Mastery

The world of computer science is a fascinating realm, where intricate concepts and technologies continuously shape the way we interact with machines. Among the vast array of ideas and principles, few are as fundamental and essential as algorithms. These powerful tools serve as the building blocks of computation, enabling computers to solve problems, make decisions, and process vast amounts of data efficiently.

An algorithm can be thought of as a step-by-step procedure or a set of instructions designed to solve a specific problem or accomplish a particular task. It represents a systematic approach to finding solutions and provides a structured way to tackle complex computational challenges. Algorithms are at the heart of various applications, from simple calculations to sophisticated machine learning models and complex data analysis.

Understanding algorithms and their inner workings is crucial for anyone interested in computer science. They serve as the backbone of software development, powering the creation of innovative applications across numerous domains. By comprehending the concept of algorithms, aspiring computer science enthusiasts gain a powerful toolset to approach problem-solving and gain insight into the efficiency and performance of different computational methods.

In this article, we aim to provide a clear and accessible introduction to algorithms, focusing on their importance in problem-solving and exploring common types such as searching, sorting, and recursion. By delving into these topics, readers will gain a solid foundation in algorithmic thinking and discover the underlying principles that drive the functioning of modern computing systems. Whether you’re a beginner in the world of computer science or seeking to deepen your understanding, this article will equip you with the knowledge to navigate the fascinating world of algorithms.

What are Algorithms?

At its core, an algorithm is a systematic, step-by-step procedure or set of rules designed to solve a problem or perform a specific task. It provides clear instructions that, when followed meticulously, lead to the desired outcome.

Consider an algorithm to be akin to a recipe for your favorite dish. When you decide to cook, the recipe is your go-to guide. It lists out the ingredients you need, their exact quantities, and a detailed, step-by-step explanation of the process, from how to prepare the ingredients to how to mix them, and finally, the cooking process. It even provides an order for adding the ingredients and specific times for cooking to ensure the dish turns out perfect.

In the same vein, an algorithm, within the realm of computer science, provides an explicit series of instructions to accomplish a goal. This could be a simple goal like sorting a list of numbers in ascending order, a more complex task such as searching for a specific data point in a massive dataset, or even a highly complicated task like determining the shortest path between two points on a map (think Google Maps). No matter the complexity of the problem at hand, there’s always an algorithm working tirelessly behind the scenes to solve it.

Furthermore, algorithms aren’t limited to specific programming languages. They are universal and can be implemented in any language. This is why understanding the fundamental concept of algorithms can empower you to solve problems across various programming languages.

The Importance of Algorithms

Algorithms are indisputably the backbone of all computational operations. They’re a fundamental part of the digital world that we interact with daily. When you search for something on the web, an algorithm is tirelessly working behind the scenes to sift through millions, possibly billions, of web pages to bring you the most relevant results. When you use a GPS to find the fastest route to a location, an algorithm is computing all possible paths, factoring in variables like traffic and road conditions, to provide you the optimal route.

Consider the world of social media, where algorithms curate personalized feeds based on our previous interactions, or in streaming platforms where they recommend shows and movies based on our viewing habits. Every click, every like, every search, and every interaction is processed by algorithms to serve you a seamless digital experience.

In the realm of computer science and beyond, everything revolves around problem-solving, and algorithms are our most reliable problem-solving tools. They provide a structured approach to problem-solving, breaking down complex problems into manageable steps and ensuring that every eventuality is accounted for.

Moreover, an algorithm’s efficiency is not just a matter of preference but a necessity. Given that computers have finite resources — time, memory, and computational power — the algorithms we use need to be optimized to make the best possible use of these resources. Efficient algorithms are the ones that can perform tasks more quickly, using less memory, and provide solutions to complex problems that might be infeasible with less efficient alternatives.

In the context of massive datasets (the likes of which are common in our data-driven world), the difference between a poorly designed algorithm and an efficient one could be the difference between a solution that takes years to compute and one that takes mere seconds. Therefore, understanding, designing, and implementing efficient algorithms is a critical skill for any computer scientist or software engineer.

Hence, as a computer science beginner, you are starting a journey where algorithms will be your best allies — universal keys capable of unlocking solutions to a myriad of problems, big or small.

Common Types of Algorithms: Searching and Sorting

Two of the most ubiquitous types of algorithms that beginners often encounter are searching and sorting algorithms.

Searching algorithms are designed to retrieve specific information from a data structure, like an array or a database. A simple example is the linear search, which works by checking each element in the array until it finds the one it’s looking for. Although easy to understand, this method isn’t efficient for large datasets, which is where more complex algorithms like binary search come in.

Binary search, on the other hand, is like looking up a word in the dictionary. Instead of checking each word from beginning to end, you open the dictionary in the middle and see if the word you’re looking for should be on the left or right side, thereby reducing the search space by half with each step.

Sorting algorithms, meanwhile, are designed to arrange elements in a particular order. A simple sorting algorithm is bubble sort, which works by repeatedly swapping adjacent elements if they’re in the wrong order. Again, while straightforward, it’s not efficient for larger datasets. More advanced sorting algorithms, such as quicksort or mergesort, have been designed to sort large data collections more efficiently.

Diving Deeper: Graph and Dynamic Programming Algorithms

Building upon our understanding of searching and sorting algorithms, let’s delve into two other families of algorithms often encountered in computer science: graph algorithms and dynamic programming algorithms.

A graph is a mathematical structure that models the relationship between pairs of objects. Graphs consist of vertices (or nodes) and edges (where each edge connects a pair of vertices). Graphs are commonly used to represent real-world systems such as social networks, web pages, biological networks, and more.

Graph algorithms are designed to solve problems centered around these structures. Some common graph algorithms include:

Dynamic programming is a powerful method used in optimization problems, where the main problem is broken down into simpler, overlapping subproblems. The solutions to these subproblems are stored and reused to build up the solution to the main problem, saving computational effort.

Here are two common dynamic programming problems:

Understanding these algorithm families — searching, sorting, graph, and dynamic programming algorithms — not only equips you with powerful tools to solve a variety of complex problems but also serves as a springboard to dive deeper into the rich ocean of algorithms and computer science.

Recursion: A Powerful Technique

While searching and sorting represent specific problem domains, recursion is a broad technique used in a wide range of algorithms. Recursion involves breaking down a problem into smaller, more manageable parts, and a function calling itself to solve these smaller parts.

To visualize recursion, consider the task of calculating factorial of a number. The factorial of a number n (denoted as n! ) is the product of all positive integers less than or equal to n . For instance, the factorial of 5 ( 5! ) is 5 x 4 x 3 x 2 x 1 = 120 . A recursive algorithm for finding factorial of n would involve multiplying n by the factorial of n-1 . The function keeps calling itself with a smaller value of n each time until it reaches a point where n is equal to 1, at which point it starts returning values back up the chain.

Algorithms are truly the heart of computer science, transforming raw data into valuable information and insight. Understanding their functionality and purpose is key to progressing in your computer science journey. As you continue your exploration, remember that each algorithm you encounter, no matter how complex it may seem, is simply a step-by-step procedure to solve a problem.

We’ve just scratched the surface of the fascinating world of algorithms. With time, patience, and practice, you will learn to create your own algorithms and start solving problems with confidence and efficiency.

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Three Elegant Algorithms Every Computer Science Beginner Should Know

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1.1: Activity 1 - Overview of Algorithm Design and Analysis

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• Page ID 49341

• Godfry Justo
• University of Dar es Salaam via African Virtual University

Introduction

There are compelling reasons to study algorithms. To put it simply, computer programs would not exist without algorithms. And with computer applications becoming indispensable in almost all aspects of our professional and personal lives, studying algorithms becomes a necessity for more and more people.

Another reason for studying algorithms is their usefulness in developing analytical skills. After all, algorithms can be seen as special kinds of solutions to problems, not answers but precisely defined procedures for getting answers. Consequently, specific algorithm design techniques can be interpreted as problem solving strategies that can be useful regardless of whether a computer is involved.

Activity Details

The term algorithm can be defined using any of the following statements:

• An algorithm is a set of rules for carrying out calculation either by hand or on a machine.
• An algorithm is a finite step-by-step procedure to achieve a required result.
• An algorithm is a sequence of computational steps that transform the input into the output.
• An algorithm is a sequence of operations performed on data that have to be organized in data structures.
• An algorithm is an abstraction of a program to be executed on a physical machine (model of Computation).

The most famous algorithm in history dates well before the time of the ancient Greeks: this is the Euclid’s algorithm for calculating the greatest common divisor of two integers.

The Classic Multiplication Algorithm

Multiplication, the American way:

Multiply the multiplicand one after another by each digit of the multiplier taken from right to left.

Multiplication, the English way:

Multiply the multiplicand one after another by each digit of the multiplier taken from left to right.

Algorithmics is a branch of computer science that consists of designing and analyzing computer algorithms.

The “design” concern to:

• The description of algorithm at an abstract level by means of a pseudo language, and
• Proof of correctness that is, the algorithm solves the given problem in all cases.

The “analysis” deals with performance evaluation (complexity analysis).

We start with defining the model of computation, which is usually the Random Access Machine (RAM) model, but other models of computations can be use such as PRAM. Once the model of computation has been defined, an algorithm can be describe using a simple language (or pseudo language) whose syntax is close to programming language such as C or java.

Algorithm’s Performance

Two important ways to characterize the effectiveness of an algorithm are its space complexity and time complexity. Time complexity of an algorithm concerns with determining an expression of the number of steps needed as a function of the problem size. Since the step count measure is somewhat rough, one does not aim at obtaining an exact step count. Instead, one attempts only to get asymptotic bounds on the step count.

Asymptotic analysis makes use of the O (Big Oh) notation. Two other notational constructs used by computer scientists in the analysis of algorithms are Θ (Big Theta) notation and Ω (Big Omega) notation. The performance evaluation of an algorithm is obtained by tallying the number of occurrences of each operation when running the algorithm. The performance of an algorithm is evaluated as a function of the input size n and is to be considered modulo a multiplicative constant.

The following notations are commonly use notations in performance analysis and used to characterize the complexity of an algorithm.

Θ-Notation (Same order)

This notation bounds a function to within constant factors. We say f(n) = Θ(g(n)) if there exist positive constants n0, c1 and c2 such that to the right of n0 the value of f(n) always lies between c1 g(n) and c2 g(n) inclusive.

In the set notation, we write as follows:

Θ ( g(n)) = {f(n) : there exist positive constants c1, c2, and n0 such that 0 ≤ c1 g(n) ≤ f(n) ≤ c2 g(n) for all n ≥ n0}

We say that g(n) is an asymptotically tight bound for f(n)

As shown in Figure 1.1.1 , graphically, for all values of n to the right of n0, the value of f(n) lies at or above c1 g(n) and at or below c2 g(n). In other words, for all n ≥ n0, the function f(n) is equal to g(n) to within a constant factor. We say that g(n) is an asymptotically tight bound for f(n).

In the set terminology, f(n) is said to be a member of the set Θ(g(n)) of functions. In other words, because O(g(n)) is a set, we could write

f(n) ∈ Θ(g(n))

to indicate that f(n) is a member of Θ(g(n)). Instead, we write

f(n) = Θ(g(n))

to express the same notation.

Historically, this notation is “f(n) = Θ(g(n))” although the idea that f(n) is equal to something called Θ(g(n)) is misleading.

Example: n2/2 − 2n = Θ(n2), with c1 = 1/4, c2 = 1/2, and n0 = 8.

Ο -Notation (Upper Bound)

This notation gives an upper bound for a function to within a constant factor. We write f(n) = O(g(n)) if there are positive constants n0 and c such that to the right of n0, the value of f(n) always lies on or below c g(n).

In the set notation, we write as follows: For a given function g(n), the set of functions

Ο(g(n)) = {f(n): there exist positive constants c and n0 such that 0 ≤ f(n) ≤ c g(n) for all n ≥ n0}

We say that the function g(n) is an asymptotic upper bound for the function f(n). We use Ο-notation to give an upper bound on a function, to within a constant factor.

As shown in Figure 1.1.2 , graphically, for all values of n to the right of n0, the value of the function f(n) is on or below g(n). We write f(n) = O(g(n)) to indicate that a function f(n) is a member of the set Ο(g(n)) i.e.

f(n) ∈ Ο(g(n))

Note that f(n) = Θ(g(n)) implies f(n) = Ο(g(n)), since Θ-notation is a stronger notation than Ο-notation.

Example: 2n2 = Ο(n3), with c = 1 and n0 = 2.

Equivalently, we may also define f is of order g as follows:

If f(n) and g(n) are functions defined on the positive integers, then f(n) is Ο(g(n)) if and only if there is a c > 0 and an n0 > 0 such that

| f(n) | ≤ | g(n) | for all n ≥ n0

Ω-Notation (Lower Bound)

This notation gives a lower bound for a function to within a constant factor. We write f(n) = Ω(g(n)) if there are positive constants n0 and c such that to the right of n0, the value of f(n) always lies on or above c g(n).

Ω(g(n)) = {f(n) : there exist positive constants c and n0 such that 0 ≤ c g(n) ≤ f(n) for all n ≥ n0}

We say that the function g(n) is an asymptotic lower bound for the function f(n).

Figure 1.1.3 provides an insight behind Ω-notation. For example, √n = (lg n), with c = 1 and n0 = 16.

Algorithm’s Analysis

The complexity of an algorithm is a function g(n) that gives the upper bound of the number of operation (or running time) performed by an algorithm when the input size is n.

There are two interpretations of upper bound.

• Worst-case Complexity: the running time for any given size input will be lower than the upper bound except possibly for some values of the input where the maximum is reached.
• Average-case Complexity: the running time for any given size input will be the average number of operations over all problem instances for a given size.

Because it is quite difficult to estimate the statistical behaviour of the input, most of the time we content ourselves to a worst case behaviour. Most of the time, the complexity of g(n) is approximated by its family O(f(n)) where f(n) is one of the following functions: n (linear complexity), log n (logarithmic complexity), na where a ≥ 2 (polynomial complexity), an (exponential complexity).

Once the complexity of an algorithm has been estimated, the question arises whether this algorithm is optimal. An algorithm for a given problem is optimal if its complexity reaches the lower bound over all the algorithms solving this problem. For example, any algorithm solving “the intersection of n segments” problem will execute at least n2 operations in the worst case even if it does nothing but print the output. This is abbreviated by saying that the problem has Ω(n2) complexity. If one finds an O(n2) algorithm that solves this problem, it will be optimal and of complexity Θ(n2).

Another technique for estimating the complexity of a problem is the transformation of problems, also called problem reduction. As an example, suppose we know a lower bound for a problem A, and that we would like to estimate a lower bound for a problem B. If we can transform A into B by a transformation step whose cost is less than that for solving A, then B has the same bound as A.

The Convex hull problem nicely illustrates “reduction” technique. A lower bound of Convex-hull problem is established by reducing the sorting problem (complexity: Θ(n log n)) to the Convex hull problem.

This activity introduced the basic concepts of algorithm design and analysis. The need for analysing the time and space complexity of algorithms was articulated and the notations for describing algorithm complexity were presented.

• Distinguish between space and time complexity.
• Briefly explain the commonly used notations in performance analysis.

What is Algorithm Design and How is it Used?

What is an algorithm? An algorithm is a set of instructions. You follow these instructions when solving a particular problem. Steps within an algorithm are in order for a reason. You must follow the series of instructions or list of rules to complete a desired task. If you skip a step, your end result won’t be the one you desire.

You use algorithms when you follow a recipe to bake a cake or do a load of laundry. You don’t put the soap in the dryer, now do you? Instead, you follow a series of steps or a set of instructions until you complete the task.

You also use algorithms in math and computers. Sure, they’re a bit more complicated than washing your clothes. But they carry you through a series of steps and lead you to an end result.

So, what is algorithm design and what’s important about designing algorithms? This article digs into the algorithm definition in computer science. Read on to find out what is algorithm design and how to design algorithms.

Algorithm Basics

There are many different types of algorithms. But at their core, they are all the same. Even in computer programming and science.

The algorithm definition computer science states that an algorithm is a list or set of rules used to perform tasks or solve problems. It has the same meaning in CS that it does in the kitchen while baking a cake. You’re given a set of variables and a list of steps. It’s up to you to follow them.

Types of Algorithms

Now that we’ve answered the question: What is an algorithm in computer science? Let’s look at the different algorithm types.

Brute force algorithms

These are computer algorithms that try all possible solutions until you find the right one. Algorithms work by computing and problem solving. Because of the way they work, this algorithm is widely used.

Divide and conquer algorithms

This algorithm divides the problem into smaller problems (subproblems) of the same type. You then solve the smaller problems and combine the solutions to solve the original problem.

Dynamic programming algorithms

This is a lot like the algorithm that divides and conquers. It breaks a complex problem into a series of smaller subproblems. Then it solves each of the subproblems once. It stores the solutions for future use.

Greedy algorithms

Greedy algorithms are used to find the best solution at the local level, but with the intent on locating a solution for the entire problem. Of the many algorithms out there, this one is good for solving optimization issues.

Randomized algorithms

A good example of an algorithm that uses random numbers for computation problems is randomized algorithms. They use random numbers once to find a viable solution.

Recursive algorithms

You use a recursive algorithm to solve the simplest version of a problem to then solve more complicated versions of the problem. You do this until you find a solution for the original problem.

Search algorithms

A search algorithm solves a search problem. It retrieves stored information within a particular data structure. It locates where it is stored.

Sorting algorithms

You use sorting algorithms to rearrange a well defined list of elements into an order. Quicksort is one of the most efficient algorithms of this kind.

Algorithm Design Techniques

Now that you know what is a computer algorithm, you should learn about the algorithm design definition. Because you use algorithm design when you solve problems.

Algorithm design refers to a method or process of solving a problem. It is the design of algorithms that is part of many solution theories. In short, your design is what you use to solve the problem. Algorithms get you to the solution you desire.

Your design techniques are the algorithms you use. They can be any of the different types of algorithms, from sorting to dynamic programming.

Algorithms Design and Analysis

Algorithms are a set of rules or instructions needed to complete a task. Long before the computer age, people established set routines for how to carry out their daily tasks. People listed the steps needed to accomplish a goal. Lists help you reduce the risk of forgetting something important.

Designers take a similar approach to the development of algorithms for computational purposes. They first look at a problem. Next, they outline the steps required to resolve it. They develop a series of mathematical operations to accomplish those steps. You call this development algorithm design.

When to Use Algorithm Design

You use algorithms when you want to solve problems. Developers use them in programming languages and machines. Machines, such as a search engine, use search algorithms to find information. The point is you use algorithm design to solve a problem.

Other uses include:

• Automate reasoning through a finite number of steps
• Computer program storage issues
• Data processing
• Find a solution

Jobs in Computers that Use Algorithms

You now understand what is algorithm in computer science. You’ve also learned how it’s used. But did you know different jobs use algorithms? Below are some of the occupations where you use algorithms on the job.

Computer Design Engineers

When you conduct engineering tasks in a programming language you use algorithms. Computer engineers receive a list of instructions so they can find a solution to a primary problem. They use algorithm designs to solve the problem.

Data Scientists

With the large number of data science algorithms available, it’s no wonder that data scientists use them to do their job. They use algorithms to solve the following kinds of problems:

• Classification problems
• Regression problems

Since the job entails working with data structures, you should have experience with useful algorithms.

Machine Learning Developers

This field uses algorithms. Developers examine huge data sets and find patterns within that data. They make predictions based on the patterns they find. All of this is possible because of algorithms.

Efficiency in Solving Complex Problems

You can use algorithms to complete the simplest of tasks. But you can also use them to solve complex problems. For centuries, mathematicians have solved complicated problems using algorithms. But they did the work with no computers.

Time’s have changed.

Computer scientists and developers have it easier today thanks to modern computers. From cyber security to big data, solving problems using algorithms is easier with the use of computers. Computers make finding a solution more efficient. Instead of sorting through large sets of data by hand, a computer processes the information within seconds.

Algorithm Engineering

Algorithm engineering is a field of engineering that focuses on:

• Implementation
• Optimization

Algorithm engineers work for large employers, such as Amazon and Google. These companies create specialized algorithms. They come up with specialized ways of collecting data.

Some companies refer to their algorithm engineers as algorithm developers. Their job is to design and integrate algorithms to find solutions to problems. Developers also use algorithms to extrapolate data. They then use the new algorithm created to install in software or in the computer environment.

Education and Skills for Algorithm Engineers

To become an algorithm engineer or developer, you should first earn a bachelor’s degree in computer science, software engineering, or a related field. A four-year degree is the foundation you need to get your foot in the door. To advance, you need more training and experience.

Some aspiring algorithm engineers earn a master’s degree in a related field. Popular graduate degrees include:

• Computer technology or science
• Information technology
• Software development
• Software engineering

Because algorithm engineers use specialized skills to find solutions in data sets, you need training. To qualify for a job as an algorithm engineer, you need the following skills.

Advanced coding skills

You need the ability to code algorithms to assess data sets. It is helpful to know different languages in computers like C++ and Python.

Algorithm deployment skills

Since the job includes creating and implementing algorithms to solve problems that improve AI functionality, you need strong algorithm development skills.

Analytical skills

The word algorithm means process. To process, you must be analytical. It should come as no surprise that you need strong analytical skills to work as an algorithm engineer. Your work includes creating an algorithm that will comb through data sets. Your job is to solve problems with the algorithms you create. To do this, you must be analytical.

Communication skills

Good communication and reporting skills are a must when working as an algorithm engineer. In this role, you provide real-time algorithm results to company administration and executives. You should know how to speak clearly, sharing complex information to a wide audience.

Signal processing skills

Signal processing skills help you analyze and synthesize signals. These skills also help improve efficiency of data quality. You use your processing skills to help improve storage and transmissions. You need these skills to succeed on the job.

Team management skills

Most algorithm design work is team-oriented. It takes a village, they say. And this is no different when working with algorithms. You should be able to assist other algorithm engineers and help team members fulfill their project schedules.

Now that you know what skills and education you need to work with algorithms, are you ready to take the plunge?

November 2022

Related Resources:

• 30 Most Affordable Online Bachelor’s Degrees in Computer Science
• Do I Have to Be Good at Algorithms to Get a Computer Science Degree?
• Top 10 Best Computer Science Online Degree Programs
• What Does an Algorithm Specialist Do?

This concludes our article on what is algorithm design and how is it used.

Algorithms, design and problem-solving

Designing and understanding algorithms.

• Program development life cycle
• Decomposition and sub-systems
• Methods of designing a solution
• Explain the purpose of an algorithm

Common algorithms

• Standard solutions

Validation and verification

• Data validation
• Data verification

Testing and fixing programs

• Suggest and apply suitable test data
• Using trace tables
• Identify errors in algorithms and suggest corrections

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Ideas Made to Matter

How to use algorithms to solve everyday problems

Kara Baskin

May 8, 2017

How can I navigate the grocery store quickly? Why doesn’t anyone like my Facebook status? How can I alphabetize my bookshelves in a hurry? Apple data visualizer and MIT System Design and Management graduate Ali Almossawi solves these common dilemmas and more in his new book, “ Bad Choices: How Algorithms Can Help You Think Smarter and Live Happier ,” a quirky, illustrated guide to algorithmic thinking. 

For the uninitiated: What is an algorithm? And how can algorithms help us to think smarter?

An algorithm is a process with unambiguous steps that has a beginning and an end, and does something useful.

Algorithmic thinking is taking a step back and asking, “If it’s the case that algorithms are so useful in computing to achieve predictability, might they also be useful in everyday life, when it comes to, say, deciding between alternative ways of solving a problem or completing a task?” In all cases, we optimize for efficiency: We care about time or space.

Note the mention of “deciding between.” Computer scientists do that all the time, and I was convinced that the tools they use to evaluate competing algorithms would be of interest to a broad audience.

Why did you write this book, and who can benefit from it?

All the books I came across that tried to introduce computer science involved coding. My approach to making algorithms compelling was focusing on comparisons. I take algorithms and put them in a scene from everyday life, such as matching socks from a pile, putting books on a shelf, remembering things, driving from one point to another, or cutting an onion. These activities can be mapped to one or more fundamental algorithms, which form the basis for the field of computing and have far-reaching applications and uses.

I wrote the book with two audiences in mind. One, anyone, be it a learner or an educator, who is interested in computer science and wants an engaging and lighthearted, but not a dumbed-down, introduction to the field. Two, anyone who is already familiar with the field and wants to experience a way of explaining some of the fundamental concepts in computer science differently than how they’re taught.

I’m going to the grocery store and only have 15 minutes. What do I do?

Do you know what the grocery store looks like ahead of time? If you know what it looks like, it determines your list. How do you prioritize things on your list? Order the items in a way that allows you to avoid walking down the same aisles twice.

For me, the intriguing thing is that the grocery store is a scene from everyday life that I can use as a launch pad to talk about various related topics, like priority queues and graphs and hashing. For instance, what is the most efficient way for a machine to store a prioritized list, and what happens when the equivalent of you scratching an item from a list happens in the machine’s list? How is a store analogous to a graph (an abstraction in computer science and mathematics that defines how things are connected), and how is navigating the aisles in a store analogous to traversing a graph?

Nobody follows me on Instagram. How do I get more followers?

The concept of links and networks, which I cover in Chapter 6, is relevant here. It’s much easier to get to people whom you might be interested in and who might be interested in you if you can start within the ball of links that connects those people, rather than starting at a random spot.

You mention Instagram: There, the hashtag is one way to enter that ball of links. Tag your photos, engage with users who tag their photos with the same hashtags, and you should be on your way to stardom.

What are the secret ingredients of a successful Facebook post?

I’ve posted things on social media that have died a sad death and then posted the same thing at a later date that somehow did great. Again, if we think of it in terms that are relevant to algorithms, we’d say that the challenge with making something go viral is really getting that first spark. And to get that first spark, a person who is connected to the largest number of people who are likely to engage with that post, needs to share it.

With [my first book], “Bad Arguments,” I spent a month pouring close to $5,000 into advertising for that project with moderate results. And then one science journalist with a large audience wrote about it, and the project took off and hasn’t stopped since.

What problems do you wish you could solve via algorithm but can’t?

When we care about efficiency, thinking in terms of algorithms is useful. There are cases when that’s not the quality we want to optimize for — for instance, learning or love. I walk for several miles every day, all throughout the city, as I find it relaxing. I’ve never asked myself, “What’s the most efficient way I can traverse the streets of San Francisco?” It’s not relevant to my objective.

Algorithms are a great way of thinking about efficiency, but the question has to be, “What approach can you optimize for that objective?” That’s what worries me about self-help: Books give you a silver bullet for doing everything “right” but leave out all the nuances that make us different. What works for you might not work for me.

Which companies use algorithms well?

When you read that the overwhelming majority of the shows that users of, say, Netflix, watch are due to Netflix’s recommendation engine, you know they’re doing something right.

Related Articles

Chapter: Introduction to the Design and Analysis of Algorithms

Fundamentals of Algorithmic Problem Solving

Let us start by reiterating an important point made in the introduction to this chapter:

We can consider algorithms to be procedural solutions to problems.

These solutions are not answers but specific instructions for getting answers. It is this emphasis on precisely defined constructive procedures that makes computer science distinct from other disciplines. In particular, this distinguishes it from the-oretical mathematics, whose practitioners are typically satisfied with just proving the existence of a solution to a problem and, possibly, investigating the solution’s properties.

We now list and briefly discuss a sequence of steps one typically goes through in designing and analyzing an algorithm (Figure 1.2).

Understanding the Problem

From a practical perspective, the first thing you need to do before designing an algorithm is to understand completely the problem given. Read the problem’s description carefully and ask questions if you have any doubts about the problem, do a few small examples by hand, think about special cases, and ask questions again if needed.

There are a few types of problems that arise in computing applications quite often. We review them in the next section. If the problem in question is one of them, you might be able to use a known algorithm for solving it. Of course, it helps to understand how such an algorithm works and to know its strengths and weaknesses, especially if you have to choose among several available algorithms. But often you will not find a readily available algorithm and will have to design your own. The sequence of steps outlined in this section should help you in this exciting but not always easy task.

An input to an algorithm specifies an instance of the problem the algorithm solves. It is very important to specify exactly the set of instances the algorithm needs to handle. (As an example, recall the variations in the set of instances for the three greatest common divisor algorithms discussed in the previous section.) If you fail to do this, your algorithm may work correctly for a majority of inputs but crash on some “boundary” value. Remember that a correct algorithm is not one that works most of the time, but one that works correctly for all legitimate inputs.

Do not skimp on this first step of the algorithmic problem-solving process; otherwise, you will run the risk of unnecessary rework.

Ascertaining the Capabilities of the Computational Device

Once you completely understand a problem, you need to ascertain the capabilities of the computational device the algorithm is intended for. The vast majority of 

algorithms in use today are still destined to be programmed for a computer closely resembling the von Neumann machine—a computer architecture outlined by the prominent Hungarian-American mathematician John von Neumann (1903– 1957), in collaboration with A. Burks and H. Goldstine, in 1946. The essence of this architecture is captured by the so-called random-access machine ( RAM ). Its central assumption is that instructions are executed one after another, one operation at a time. Accordingly, algorithms designed to be executed on such machines are called sequential algorithms .

The central assumption of the RAM model does not hold for some newer computers that can execute operations concurrently, i.e., in parallel. Algorithms that take advantage of this capability are called parallel algorithms . Still, studying the classic techniques for design and analysis of algorithms under the RAM model remains the cornerstone of algorithmics for the foreseeable future.

Should you worry about the speed and amount of memory of a computer at your disposal? If you are designing an algorithm as a scientific exercise, the answer is a qualified no. As you will see in Section 2.1, most computer scientists prefer to study algorithms in terms independent of specification parameters for a particular computer. If you are designing an algorithm as a practical tool, the answer may depend on a problem you need to solve. Even the “slow” computers of today are almost unimaginably fast. Consequently, in many situations you need not worry about a computer being too slow for the task. There are important problems, however, that are very complex by their nature, or have to process huge volumes of data, or deal with applications where the time is critical. In such situations, it is imperative to be aware of the speed and memory available on a particular computer system.

Choosing between Exact and Approximate Problem Solving

The next principal decision is to choose between solving the problem exactly or solving it approximately. In the former case, an algorithm is called an exact algo-rithm ; in the latter case, an algorithm is called an approximation algorithm . Why would one opt for an approximation algorithm? First, there are important prob-lems that simply cannot be solved exactly for most of their instances; examples include extracting square roots, solving nonlinear equations, and evaluating def-inite integrals. Second, available algorithms for solving a problem exactly can be unacceptably slow because of the problem’s intrinsic complexity. This happens, in particular, for many problems involving a very large number of choices; you will see examples of such difficult problems in Chapters 3, 11, and 12. Third, an ap-proximation algorithm can be a part of a more sophisticated algorithm that solves a problem exactly.

Algorithm Design Techniques

Now, with all the components of the algorithmic problem solving in place, how do you design an algorithm to solve a given problem? This is the main question this book seeks to answer by teaching you several general design techniques.

What is an algorithm design technique?

An algorithm design technique (or “strategy” or “paradigm”) is a general approach to solving problems algorithmically that is applicable to a variety of problems from different areas of computing.

Check this book’s table of contents and you will see that a majority of its chapters are devoted to individual design techniques. They distill a few key ideas that have proven to be useful in designing algorithms. Learning these techniques is of utmost importance for the following reasons.

First, they provide guidance for designing algorithms for new problems, i.e., problems for which there is no known satisfactory algorithm. Therefore—to use the language of a famous proverb—learning such techniques is akin to learning to fish as opposed to being given a fish caught by somebody else. It is not true, of course, that each of these general techniques will be necessarily applicable to every problem you may encounter. But taken together, they do constitute a powerful collection of tools that you will find quite handy in your studies and work.

Second, algorithms are the cornerstone of computer science. Every science is interested in classifying its principal subject, and computer science is no exception. Algorithm design techniques make it possible to classify algorithms according to an underlying design idea; therefore, they can serve as a natural way to both categorize and study algorithms.

Designing an Algorithm and Data Structures

While the algorithm design techniques do provide a powerful set of general ap-proaches to algorithmic problem solving, designing an algorithm for a particular problem may still be a challenging task. Some design techniques can be simply inapplicable to the problem in question. Sometimes, several techniques need to be combined, and there are algorithms that are hard to pinpoint as applications of the known design techniques. Even when a particular design technique is ap-plicable, getting an algorithm often requires a nontrivial ingenuity on the part of the algorithm designer. With practice, both tasks—choosing among the general techniques and applying them—get easier, but they are rarely easy.

Of course, one should pay close attention to choosing data structures appro-priate for the operations performed by the algorithm. For example, the sieve of Eratosthenes introduced in Section 1.1 would run longer if we used a linked list instead of an array in its implementation (why?). Also note that some of the al-gorithm design techniques discussed in Chapters 6 and 7 depend intimately on structuring or restructuring data specifying a problem’s instance. Many years ago, an influential textbook proclaimed the fundamental importance of both algo-rithms and data structures for computer programming by its very title: Algorithms + Data Structures = Programs [Wir76]. In the new world of object-oriented programming, data structures remain crucially important for both design and analysis of algorithms. We review basic data structures in Section 1.4.

Methods of Specifying an Algorithm

Once you have designed an algorithm, you need to specify it in some fashion. In Section 1.1, to give you an example, Euclid’s algorithm is described in words (in a free and also a step-by-step form) and in pseudocode. These are the two options that are most widely used nowadays for specifying algorithms.

Using a natural language has an obvious appeal; however, the inherent ambi-guity of any natural language makes a succinct and clear description of algorithms surprisingly difficult. Nevertheless, being able to do this is an important skill that you should strive to develop in the process of learning algorithms.

Pseudocode is a mixture of a natural language and programming language-like constructs. Pseudocode is usually more precise than natural language, and its usage often yields more succinct algorithm descriptions. Surprisingly, computer scientists have never agreed on a single form of pseudocode, leaving textbook authors with a need to design their own “dialects.” Fortunately, these dialects are so close to each other that anyone familiar with a modern programming language should be able to understand them all.

This book’s dialect was selected to cause minimal difficulty for a reader. For the sake of simplicity, we omit declarations of variables and use indentation to show the scope of such statements as for , if , and while . As you saw in the previous section, we use an arrow “ ← ” for the assignment operation and two slashes “ // ” for comments.

In the earlier days of computing, the dominant vehicle for specifying algo-rithms was a flowchart , a method of expressing an algorithm by a collection of connected geometric shapes containing descriptions of the algorithm’s steps. This representation technique has proved to be inconvenient for all but very simple algorithms; nowadays, it can be found only in old algorithm books.

The state of the art of computing has not yet reached a point where an algorithm’s description—be it in a natural language or pseudocode—can be fed into an electronic computer directly. Instead, it needs to be converted into a computer program written in a particular computer language. We can look at such a program as yet another way of specifying the algorithm, although it is preferable to consider it as the algorithm’s implementation.

Proving an Algorithm’s Correctness

Once an algorithm has been specified, you have to prove its correctness . That is, you have to prove that the algorithm yields a required result for every legitimate input in a finite amount of time. For example, the correctness of Euclid’s algorithm for computing the greatest common divisor stems from the correctness of the equality gcd (m, n) = gcd (n, m mod n) (which, in turn, needs a proof; see Problem 7 in Exercises 1.1), the simple observation that the second integer gets smaller on every iteration of the algorithm, and the fact that the algorithm stops when the second integer becomes 0.

For some algorithms, a proof of correctness is quite easy; for others, it can be quite complex. A common technique for proving correctness is to use mathemati-cal induction because an algorithm’s iterations provide a natural sequence of steps needed for such proofs. It might be worth mentioning that although tracing the algorithm’s performance for a few specific inputs can be a very worthwhile activ-ity, it cannot prove the algorithm’s correctness conclusively. But in order to show that an algorithm is incorrect, you need just one instance of its input for which the algorithm fails.

The notion of correctness for approximation algorithms is less straightforward than it is for exact algorithms. For an approximation algorithm, we usually would like to be able to show that the error produced by the algorithm does not exceed a predefined limit. You can find examples of such investigations in Chapter 12.

Analyzing an Algorithm

We usually want our algorithms to possess several qualities. After correctness, by far the most important is efficiency . In fact, there are two kinds of algorithm efficiency: time efficiency , indicating how fast the algorithm runs, and space ef-ficiency , indicating how much extra memory it uses. A general framework and specific techniques for analyzing an algorithm’s efficiency appear in Chapter 2.

Another desirable characteristic of an algorithm is simplicity . Unlike effi-ciency, which can be precisely defined and investigated with mathematical rigor, simplicity, like beauty, is to a considerable degree in the eye of the beholder. For example, most people would agree that Euclid’s algorithm is simpler than the middle-school procedure for computing gcd (m, n) , but it is not clear whether Eu-clid’s algorithm is simpler than the consecutive integer checking algorithm. Still, simplicity is an important algorithm characteristic to strive for. Why? Because sim-pler algorithms are easier to understand and easier to program; consequently, the resulting programs usually contain fewer bugs. There is also the undeniable aes-thetic appeal of simplicity. Sometimes simpler algorithms are also more efficient than more complicated alternatives. Unfortunately, it is not always true, in which case a judicious compromise needs to be made.

Yet another desirable characteristic of an algorithm is generality . There are, in fact, two issues here: generality of the problem the algorithm solves and the set of inputs it accepts. On the first issue, note that it is sometimes easier to design an algorithm for a problem posed in more general terms. Consider, for example, the problem of determining whether two integers are relatively prime, i.e., whether their only common divisor is equal to 1. It is easier to design an algorithm for a more general problem of computing the greatest common divisor of two integers and, to solve the former problem, check whether the gcd is 1 or not. There are situations, however, where designing a more general algorithm is unnecessary or difficult or even impossible. For example, it is unnecessary to sort a list of n numbers to find its median, which is its n/ 2 th smallest element. To give another example, the standard formula for roots of a quadratic equation cannot be generalized to handle polynomials of arbitrary degrees.

As to the set of inputs, your main concern should be designing an algorithm that can handle a set of inputs that is natural for the problem at hand. For example, excluding integers equal to 1 as possible inputs for a greatest common divisor algorithm would be quite unnatural. On the other hand, although the standard formula for the roots of a quadratic equation holds for complex coefficients, we would normally not implement it on this level of generality unless this capability is explicitly required.

If you are not satisfied with the algorithm’s efficiency, simplicity, or generality, you must return to the drawing board and redesign the algorithm. In fact, even if your evaluation is positive, it is still worth searching for other algorithmic solutions. Recall the three different algorithms in the previous section for computing the greatest common divisor: generally, you should not expect to get the best algorithm on the first try. At the very least, you should try to fine-tune the algorithm you already have. For example, we made several improvements in our implementation of the sieve of Eratosthenes compared with its initial outline in Section 1.1. (Can you identify them?) You will do well if you keep in mind the following observation of Antoine de Saint-Exupery,´ the French writer, pilot, and aircraft designer: “A designer knows he has arrived at perfection not when there is no longer anything to add, but when there is no longer anything to take away.” 1

Coding an Algorithm

  Most algorithms are destined to be ultimately implemented as computer pro-grams. Programming an algorithm presents both a peril and an opportunity. The peril lies in the possibility of making the transition from an algorithm to a pro-gram either incorrectly or very inefficiently. Some influential computer scientists strongly believe that unless the correctness of a computer program is proven with full mathematical rigor, the program cannot be considered correct. They have developed special techniques for doing such proofs (see [Gri81]), but the power of these techniques of formal verification is limited so far to very small programs.

As a practical matter, the validity of programs is still established by testing. Testing of computer programs is an art rather than a science, but that does not mean that there is nothing in it to learn. Look up books devoted to testing and debugging; even more important, test and debug your program thoroughly whenever you implement an algorithm.

Also note that throughout the book, we assume that inputs to algorithms belong to the specified sets and hence require no verification. When implementing algorithms as programs to be used in actual applications, you should provide such verifications.

Of course, implementing an algorithm correctly is necessary but not sufficient: you would not like to diminish your algorithm’s power by an inefficient implemen-tation. Modern compilers do provide a certain safety net in this regard, especially when they are used in their code optimization mode. Still, you need to be aware of such standard tricks as computing a loop’s invariant (an expression that does not change its value) outside the loop, collecting common subexpressions, replac-ing expensive operations by cheap ones, and so on. (See [Ker99] and [Ben00] for a good discussion of code tuning and other issues related to algorithm program-ming.) Typically, such improvements can speed up a program only by a constant factor, whereas a better algorithm can make a difference in running time by orders of magnitude. But once an algorithm is selected, a 10–50% speedup may be worth an effort.

A working program provides an additional opportunity in allowing an em-pirical analysis of the underlying algorithm. Such an analysis is based on timing the program on several inputs and then analyzing the results obtained. We dis-cuss the advantages and disadvantages of this approach to analyzing algorithms in Section 2.6.

In conclusion, let us emphasize again the main lesson of the process depicted in Figure 1.2:

As a rule, a good algorithm is a result of repeated effort and rework.

Even if you have been fortunate enough to get an algorithmic idea that seems perfect, you should still try to see whether it can be improved.

Actually, this is good news since it makes the ultimate result so much more enjoyable. (Yes, I did think of naming this book The Joy of Algorithms .) On the other hand, how does one know when to stop? In the real world, more often than not a project’s schedule or the impatience of your boss will stop you. And so it should be: perfection is expensive and in fact not always called for. Designing an algorithm is an engineering-like activity that calls for compromises among competing goals under the constraints of available resources, with the designer’s time being one of the resources.

In the academic world, the question leads to an interesting but usually difficult investigation of an algorithm’s optimality . Actually, this question is not about the efficiency of an algorithm but about the complexity of the problem it solves: What is the minimum amount of effort any algorithm will need to exert to solve the problem? For some problems, the answer to this question is known. For example, any algorithm that sorts an array by comparing values of its elements needs about n log 2 n comparisons for some arrays of size n (see Section 11.2). But for many seemingly easy problems such as integer multiplication, computer scientists do not yet have a final answer.

Another important issue of algorithmic problem solving is the question of whether or not every problem can be solved by an algorithm. We are not talking here about problems that do not have a solution, such as finding real roots of a quadratic equation with a negative discriminant. For such cases, an output indicating that the problem does not have a solution is all we can and should expect from an algorithm. Nor are we talking about ambiguously stated problems. Even some unambiguous problems that must have a simple yes or no answer are “undecidable,” i.e., unsolvable by any algorithm. An important example of such a problem appears in Section 11.3. Fortunately, a vast majority of problems in practical computing can be solved by an algorithm.

Before leaving this section, let us be sure that you do not have the misconception—possibly caused by the somewhat mechanical nature of the diagram of Figure 1.2—that designing an algorithm is a dull activity. There is nothing further from the truth: inventing (or discovering?) algorithms is a very creative and rewarding process. This book is designed to convince you that this is the case.

Exercises 1.2

             Old World puzzle A peasant finds himself on a riverbank with a wolf, a goat, and a head of cabbage. He needs to transport all three to the other side of the river in his boat. However, the boat has room for only the peasant himself and one other item (either the wolf, the goat, or the cabbage). In his absence, the wolf would eat the goat, and the goat would eat the cabbage. Solve this problem for the peasant or prove it has no solution. (Note: The peasant is a vegetarian but does not like cabbage and hence can eat neither the goat nor the cabbage to help him solve the problem. And it goes without saying that the wolf is a protected species.)

            New World puzzle There are four people who want to cross a rickety bridge; they all begin on the same side. You have 17 minutes to get them all across to the other side. It is night, and they have one flashlight. A maximum of two people can cross the bridge at one time. Any party that crosses, either one or two people, must have the flashlight with them. The flashlight must be walked back and forth; it cannot be thrown, for example. Person 1 takes 1 minute to cross the bridge, person 2 takes 2 minutes, person 3 takes 5 minutes, and person 4 takes 10 minutes. A pair must walk together at the rate of the slower person’s pace. (Note: According to a rumor on the Internet, interviewers at a well-known software company located near Seattle have given this problem to interviewees.)

            Which of the following formulas can be considered an algorithm for comput-ing the area of a triangle whose side lengths are given positive numbers a , b , and c ?

            Write pseudocode for an algorithm for finding real roots of equation ax 2 + bx + c = 0 for arbitrary real coefficients a, b, and c. (You may assume the availability of the square root function sqrt (x). )

            Describe the standard algorithm for finding the binary representation of a positive decimal integer

                     in English.

                     in pseudocode.

            Describe the algorithm used by your favorite ATM machine in dispensing cash. (You may give your description in either English or pseudocode, which-ever you find more convenient.)

            a.  Can the problem of computing the number π be solved exactly?

                     How many instances does this problem have?

Look up an algorithm for this problem on the Internet.

                                                                    Give an example of a problem other than computing the greatest common divisor for which you know more than one algorithm. Which of them is simpler? Which is more efficient?

                                                                    Consider the following algorithm for finding the distance between the two closest elements in an array of numbers.

ALGORITHM                       MinDistance (A [0 ..n − 1] )

//Input: Array A [0 ..n − 1] of numbers

//Output: Minimum distance between two of its elements dmin ← ∞

for i ← 0 to n − 1 do

for j ← 0 to n − 1 do

if i  = j and |A[i] − A[j ]| < dmin dmin ← |A[i] − A[j ]|

return dmin

Make as many improvements as you can in this algorithmic solution to the problem. If you need to, you may change the algorithm altogether; if not, improve the implementation given.

One of the most influential books on problem solving, titled How To Solve It [Pol57], was written by the Hungarian-American mathematician George Polya´ (1887–1985). Polya´ summarized his ideas in a four-point summary. Find this summary on the Internet or, better yet, in his book, and compare it with the plan outlined in Section 1.2. What do they have in common? How are they different?

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• What Is an Algorithm? | Definition & Examples

What Is an Algorithm? | Definition & Examples

Published on August 9, 2023 by Kassiani Nikolopoulou . Revised on August 29, 2023.

An algorithm is a set of steps for accomplishing a task or solving a problem. Typically, algorithms are executed by computers, but we also rely on algorithms in our daily lives. Each time we follow a particular step-by-step process, like making coffee in the morning or tying our shoelaces, we are in fact following an algorithm.

In the context of computer science , an algorithm is a mathematical process for solving a problem using a finite number of steps. Algorithms are a key component of any computer program and are the driving force behind various systems and applications, such as navigation systems, search engines, and music streaming services.

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Table of contents

What is an algorithm, how do algorithms work, examples of algorithms, other interesting articles, frequently asked questions about algorithms.

An algorithm is a sequence of instructions that a computer must perform to solve a well-defined problem. It essentially defines what the computer needs to do and how to do it. Algorithms can instruct a computer how to perform a calculation, process data, or make a decision.

The best way to understand an algorithm is to think of it as a recipe that guides you through a series of well-defined actions to achieve a specific goal. Just like a recipe produces a replicable result, algorithms ensure consistent and reliable outcomes for a wide range of tasks in the digital realm.

And just like there are numerous ways to make, for example, chocolate chip cookies by following different steps or using slightly different ingredients, different algorithms can be designed to solve the same problem, with each taking a distinct approach but achieving the same result.

Algorithms are virtually everywhere around us. Examples include the following:

• Search engines rely on algorithms to find and present relevant results as quickly as possible
• Social media platforms use algorithms to prioritize the content that we see in our feeds, taking into account factors like our past behavior, the popularity of posts, and relevance.
• With the help of algorithms, navigation apps determine the most efficient route for us to reach our destination.
• It must be correct . In other words, it should take a given problem and provide the right answer or result, even if it stops working due to an error.
• It must consist of clear, practical steps that can be completed in a limited time, whether by a person or the machine that must execute the algorithm. For example, the instructions in a cookie recipe might be considered sufficiently concrete for a human cook, but they would not be specific enough for programming an automated cookie-making machine.
• There should be no confusion about which step comes next , even if choices must be made (e.g., when using “if” statements).
• It must have a set number of steps (not an infinite number) that can be managed using loops (statements describing repeated actions or iterations).
• It must eventually reach an endpoint and not get stuck in a never-ending loop.

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Algorithms use a set of initial data or input , process it through a series of logical steps or rules, and produce the output (i.e., the outcome, decision, or result).

If you want to make chocolate chip cookies, for instance, the input would be the ingredients and quantities, the process would be the recipe you choose to follow, and the output would be the cookies.

Algorithms are eventually expressed in a programming language that a computer can process. However, when an algorithm is being created, it will be people, not a computer, who will need to understand it. For this reason, as a first step, algorithms are written as plain instructions.

• Input: the input data is a single-digit number (e.g., 5).
• Transformation/processing: the algorithm takes the input (number 5) and performs the specific operation (i.e., multiplies the number by itself).
• Output: the result of the calculation is the square of the input number, which, in this case, would be 25 (since 5 * 5 = 25).

We could express this as an algorithm in the following way:

Algorithm: Calculate the square of a number

• Input the number (N) whose square you want to find.
• Multiply the number (N) by itself.
• Store the result of the multiplication in a variable (result).
• Output the value of the variable (result), which represents the square of the input number.

It is important to keep in mind that an algorithm is not the same as a program or code. It is the logic or plan for solving a problem represented as a simple step-by-step description. Code is the implementation of the algorithm in a specific programming language (like C++ or Python), while a program is an implementation of code that instructs a computer on how to execute an algorithm and perform a task.

Instead of telling a computer exactly what to do, some algorithms allow computers to learn on their own and improve their performance on a specific task. These machine learning algorithms use data to identify patterns and make predictions or conduct data mining to uncover hidden insights in data that can inform business decisions.

Broadly speaking, there are three different types of algorithms:

• Linear sequence algorithms follow a specific set or steps, one after the other. Just like following a recipe, each step depends on the success of the previous one.
• For example, in the context of a cookie recipe, you would include the step “if the dough is too sticky, you might need to refrigerate it.”
• For example, a looping algorithm could be used to handle the process of making multiple cookies from a single batch of dough. The algorithm would repeat a specific set of instructions to form and bake cookies until all the dough has been used.

Algorithms are fundamental tools for problem-solving in both the digital world and many real-life scenarios. Each time we try to solve a problem by breaking it down into smaller, manageable steps, we are in fact using algorithmic thinking.

• Identify which clothes are clean.
• Consider the weather forecast for the day.
• Consider the occasion for which you are getting dressed (e.g., work or school etc.).
• Consider personal preferences (e.g., style or which items match).

In mathematics, algorithms are standard methods for performing calculations or solving equations because they are efficient, reliable, and applicable to various situations.

Suppose you want to add the numbers 345 and 278. You would follow a set of steps (i.e., the standard algorithm for addition):

• Write down the numbers so the digits align.
• Start from the rightmost digits (the ones place) and add them together: 5 + 8 = 13. Write down the 3 and carry over the 1 to the next column.
• Move to the next column (the tens place) and add the digits along with the carried-over value: 4 + 7 + 1 = 12. Write down the 2 and carry over the 1 to the next column.
• Move to the leftmost column (the hundreds place) and add the digits along with the carried-over value: 3 + 2 + 1 = 6. Write down the 6.

The final result is 623

Navigation systems are another example of the use of algorithms. Such systems use algorithms to help you find the easiest and fastest route to your destination while avoiding traffic jams and roadblocks.

If you want to know more about ChatGPT, AI tools , fallacies , and research bias , make sure to check out some of our other articles with explanations and examples.

• ChatGPT vs human editor
• ChatGPT citations
• Is ChatGPT trustworthy?
• Using ChatGPT for your studies
• Sunk cost fallacy
• Straw man fallacy
• Slippery slope fallacy
• Red herring fallacy
• Ecological fallacy
• Logical fallacy

Research bias

• Implicit bias
• Framing bias
• Cognitive bias
• Optimism bias
• Hawthorne effect
• Unconscious bias

In computer science, an algorithm is a list of unambiguous instructions that specify successive steps to solve a problem or perform a task. Algorithms help computers execute tasks like playing games or sorting a list of numbers. In other words, computers use algorithms to understand what to do and give you the result you need.

Algorithms and artificial intelligence (AI) are not the same, however they are closely related.

• Artificial intelligence is a broad term describing computer systems performing tasks usually associated with human intelligence like decision-making, pattern recognition, or learning from experience.
• Algorithms are the instructions that AI uses to carry out these tasks, therefore we could say that algorithms are the building blocks of AI—even though AI involves more advanced capabilities beyond just following instructions.

Algorithms and computer programs are sometimes used interchangeably, but they refer to two distinct but interrelated concepts.

• An algorithm is a step-by-step instruction for solving a problem that is precise yet general.
• Computer programs are specific implementations of an algorithm in a specific programming language. In other words, the algorithm is the high-level description of an idea, while the program is the actual implementation of that idea.

Algorithms are valuable to us because they:

• Form the basis of much of the technology we use in our daily lives, from mobile apps to search engines.
• Power innovations in various industries that augment our abilities (e.g., AI assistants or medical diagnosis).
• Help analyze large volumes of data, discover patterns and make informed decisions in a fast and efficient way, at a scale humans are simply not able to do.
• Automate processes. By streamlining tasks, algorithms increase efficiency, reduce errors, and save valuable time.

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What is Problem Solving Algorithm?, Steps, Representation

• Post author: Disha Singh
• Post published: 6 June 2021
• Post category: Computer Science
• Post comments: 0 Comments

Table of Contents

• 1 What is Problem Solving Algorithm?
• 2 Definition of Problem Solving Algorithm
• 3.1 Analysing the Problem
• 3.2 Developing an Algorithm
• 3.4 Testing and Debugging
• 4.1 Flowchart
• 4.2 Pseudo code

What is Problem Solving Algorithm?

Computers are used for solving various day-to-day problems and thus problem solving is an essential skill that a computer science student should know. It is pertinent to mention that computers themselves cannot solve a problem. Precise step-by-step instructions should be given by us to solve the problem.

Thus, the success of a computer in solving a problem depends on how correctly and precisely we define the problem, design a solution (algorithm) and implement the solution (program) using a programming language.

Thus, problem solving is the process of identifying a problem, developing an algorithm for the identified problem and finally implementing the algorithm to develop a computer program.

Definition of Problem Solving Algorithm

These are some simple definition of problem solving algorithm which given below:

Steps for Problem Solving

When problems are straightforward and easy, we can easily find the solution. But a complex problem requires a methodical approach to find the right solution. In other words, we have to apply problem solving techniques.

Problem solving begins with the precise identification of the problem and ends with a complete working solution in terms of a program or software. Key steps required for solving a problem using a computer.

For Example: Suppose while driving, a vehicle starts making a strange noise. We might not know how to solve the problem right away. First, we need to identify from where the noise is coming? In case the problem cannot be solved by us, then we need to take the vehicle to a mechanic.

The mechanic will analyse the problem to identify the source of the noise, make a plan about the work to be done and finally repair the vehicle in order to remove the noise. From the example, it is explicit that, finding the solution to a problem might consist of multiple steps.

Following are Steps for Problem Solving :

Analysing the Problem

Developing an algorithm, testing and debugging.

It is important to clearly understand a problem before we begin to find the solution for it. If we are not clear as to what is to be solved, we may end up developing a program which may not solve our purpose.

Thus, we need to read and analyse the problem statement carefully in order to list the principal components of the problem and decide the core functionalities that our solution should have. By analysing a problem, we would be able to figure out what are the inputs that our program should accept and the outputs that it should produce.

It is essential to device a solution before writing a program code for a given problem. The solution is represented in natural language and is called an algorithm. We can imagine an algorithm like a very well-written recipe for a dish, with clearly defined steps that, if followed, one will end up preparing the dish.

We start with a tentative solution plan and keep on refining the algorithm until the algorithm is able to capture all the aspects of the desired solution. For a given problem, more than one algorithm is possible and we have to select the most suitable solution.

After finalising the algorithm, we need to convert the algorithm into the format which can be understood by the computer to generate the desired solution. Different high level programming languages can be used for writing a program. It is equally important to record the details of the coding procedures followed and document the solution. This is helpful when revisiting the programs at a later stage.

The program created should be tested on various parameters. The program should meet the requirements of the user. It must respond within the expected time. It should generate correct output for all possible inputs. In the presence of syntactical errors, no output will be obtained. In case the output generated is incorrect, then the program should be checked for logical errors, if any.

Software industry follows standardised testing methods like unit or component testing, integration testing, system testing, and acceptance testing while developing complex applications. This is to ensure that the software meets all the business and technical requirements and works as expected.

The errors or defects found in the testing phases are debugged or rectified and the program is again tested. This continues till all the errors are removed from the program. Once the software application has been developed, tested and delivered to the user, still problems in terms of functioning can come up and need to be resolved from time to time.

The maintenance of the solution, thus, involves fixing the problems faced by the user, answering the queries of the user and even serving the request for addition or modification of features.

Representation of Algorithms

Using their algorithmic thinking skills, the software designers or programmers analyse the problem and identify the logical steps that need to be followed to reach a solution. Once the steps are identified, the need is to write down these steps along with the required input and desired output.

There are two common methods of representing an algorithm —flowchart and pseudocode. Either of the methods can be used to represent an algorithm while keeping in mind the following:

• It showcases the logic of the problem solution, excluding any implementational details.
• It clearly reveals the flow of control during execution of the program.

A flowchart is a visual representation of an algorithm . A flowchart is a diagram made up of boxes, diamonds and other shapes, connected by arrows. Each shape represents a step of the solution process and the arrow represents the order or link among the steps.

A flow chart is a step by step diagrammatic representation of the logic paths to solve a given problem. Or A flowchart is visual or graphical representation of an algorithm .

The flowcharts are pictorial representation of the methods to b used to solve a given problem and help a great deal to analyze the problem and plan its solution in a systematic and orderly manner. A flowchart when translated in to a proper computer language, results in a complete program.

Advantages of Flowcharts:

• The flowchart shows the logic of a problem displayed in pictorial fashion which felicitates easier checking of an algorithm
• The Flowchart is good means of communication to other users. It is also a compact means of recording an algorithm solution to a problem.
• The flowchart allows the problem solver to break the problem into parts. These parts can be connected to make master chart.
• The flowchart is a permanent record of the solution which can be consulted at a later time.

Differences between Algorithm and Flowchart

Pseudo code.

The Pseudo code is neither an algorithm nor a program. It is an abstract form of a program. It consists of English like statements which perform the specific operations. It is defined for an algorithm. It does not use any graphical representation.

In pseudo code , the program is represented in terms of words and phrases, but the syntax of program is not strictly followed.

Advantages of Pseudocode

• Before writing codes in a high level language, a pseudocode of a program helps in representing the basic functionality of the intended program.
• By writing the code first in a human readable language, the programmer safeguards against leaving out any important step. Besides, for non-programmers, actual programs are difficult to read and understand.
• But pseudocode helps them to review the steps to confirm that the proposed implementation is going to achieve the desire output.

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