the importance of algorithm in problem solving

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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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What Is An Algorithm and Why Are They Important

A common term people use in computer science and coding is 'algorithm.' What is it and why is it important for coding? In partnership with Juni Learning , we share their article here to define this important concept.

What Is An Algorithm?

An algorithm is a set of step-by-step procedures, or a set of rules to follow, for completing a specific task or solving a particular problem. Algorithms are all around us. The recipe for baking a cake, the method we use to solve a long division problem, and the process of doing laundry are all examples of an algorithm. Here’s what baking a cake might look like, written out as a list of instructions, just like an algorithm:

Preheat the oven

Gather the ingredients

Measure out the ingredients

Mix together the ingredients to make the batter

Grease a pan

Pour the batter into the pan

Put the pan in the oven

Set a timer

When the timer goes off, take the pan out of the oven

Algorithmic programming is all about writing a set of rules that instruct the computer how to perform a task. A computer program is essentially an algorithm that tells the computer what specific steps to execute, in what specific order, in order to carry out a specific task. Algorithms are written using particular syntax, depending on the programming language being used.

Types of Algorithms

Algorithms are classified based on the concepts that they use to accomplish a task. While there are many types of algorithms, the most fundamental types of computer science algorithms are:

Divide and conquer algorithms – divide the problem into smaller subproblems of the same type; solve those smaller problems, and combine those solutions to solve the original problem.

Brute force algorithms – try all possible solutions until a satisfactory solution is found.

Randomized algorithms – use a random number at least once during the computation to find a solution to the problem.

Greedy algorithms – find an optimal solution at the local level with the intent of finding an optimal solution for the whole problem.

Recursive algorithms – solve the lowest and simplest version of a problem to then solve increasingly larger versions of the problem until the solution to the original problem is found.

Backtracking algorithms – divide the problem into subproblems, each which can be attempted to be solved; however, if the desired solution is not reached, move backwards in the problem until a path is found that moves it forward.

Dynamic programming algorithms – break a complex problem into a collection of simpler subproblems, then solve each of those subproblems only once, storing their solution for future use instead of re-computing their solutions.

Example of an Algorithm

Solving a Rubik’s Cube

There are a number of different algorithms, from simple to very complicated, that exist for solving a Rubik’s cube. Below is just one simple algorithm. First, let’s specify a notation to use (similar to picking a programming language).

Each of the six faces of a Rubik’s cube can be represented by the first letter of their name:

Each face can be turned in three different ways/directions. Using U as an example, these are represented as:

U - clockwise quarter-turn of the upper face

U' - counter-clockwise quarter-turn of the upper face

U2 - half turn in either direction of the upper face

Now, let’s go through the steps in the algorithm to solve a Rubik’s Cube. Feel free to grab one of your own and follow along!

Step 1: The Cross

First, flip some edges so that there is a white cross on the upper face.

Apply the following turns: F, R’, D’, R, F2, R’, U, R, U’, R’, R2, L2, U2, R2, L2.

The cross is now solved.

Step 2: The White Corners

The edges on the white face are now complete, but the corners remain.

Depending on where the white-orange-green corner is in the puzzle, apply one of the following series of turns:

Bottom: R’, D’, R, D (repeat until the corner moves to its correct place)

Top: R’, D’, R, D (this moves the corner to the bottom; then, follow the above instructions)

Step 3: Middle Layer Edges

Flip the cube so that the white is on the bottom.

Look for an edge that is on the top face and doesn’t have yellow on it.

Perform a U-turn so that the color on the front face of the edge matches with the center.

Depending on the direction that the edge could go, apply one of the following series of turns:

Left: U’, L’, U, L, U, F, U’, F’

Right: U, R, U’, R’, U’, F’, U, F)

Step 4: Yellow Cross

Apply the following turns, until a yellow cross on the face appears with the yellow center: F, R, U, R’, U’, F’.

If there is an “L” shape, where the two yellow pieces showing are adjacent to each other, apply the following turns: F, U, R, U’, R’, F’.

If there is a “Line” shape, which is horizontal, apply the following turns: F, R, U, R’, U’, F’.

Step 5: Sune and Antisune

Look at the face with the yellow center.

Depending on the below contingencies, apply one of the following series of turns:

If there is only one oriented corner: R, U, R’, U, R, U2, R’ (repeat until the desired position is attained)

There is one oriented corner and one right-facing corner: U2, R, U2, R’, U’, R, U’, R’

Step 6: Finishing the puzzle

Look for sets of “headlights” (two stickers of the same color in the same row, separated by a sticker of a different color).

Depending on how many there are, apply one of the following series of turns:

If there are a set of headlights on each side: R, U’, R, U, R, U, R, U’, R’, U’, R2

Otherwise: R’, F, R’, B2, R, F’, R’, B2, R2

Sorting Algorithms

A sorting algorithm is an algorithm that puts elements of a list in a certain order, usually in numerical or lexicographical order. Sorting is often an important first step in algorithms that solves more complex problems. There are a large number of sorting algorithms, each with their own benefits and costs. Below, we will focus on some of the more famous sorting algorithms.

Linear sort: Find the smallest element in the list to be sorted, add it to a new list, and remove it from the original list. Repeat this until the original list is empty.

Bubble sort: Compare the first two elements in the list, and if the first is greater than the second, swap them. Repeat this with every pair of adjacent elements in the list. Then, repeat this process until the list is fully sorted.

Insertion sort: Compare each element in the list to all the prior elements until a smaller element is found. Swap these two elements. Repeat this process until the list is fully sorted.

Where are Algorithms Used in Computer Science?

Algorithms are used in every part of computer science. They form the field's backbone. In computer science, an algorithm gives the computer a specific set of instructions, which allows the computer to do everything, be it running a calculator or running a rocket. Computer programs are, at their core, algorithms written in programming languages that the computer can understand. Computer algorithms play a big role in how social media works: which posts show up, which ads are seen, and so on. These decisions are all made by algorithms. Google’s programmers use algorithms to optimize searches, predict what users are going to type, and more. In problem-solving, a big part of computer programming is knowing how to formulate an algorithm.

Why are Algorithms Important to Understand?

Algorithmic thinking, or the ability to define clear steps to solve a problem, is crucial in many different fields. Even if we’re not conscious of it, we use algorithms and algorithmic thinking all the time. Algorithmic thinking allows students to break down problems and conceptualize solutions in terms of discrete steps. Being able to understand and implement an algorithm requires students to practice structured thinking and reasoning abilities.

This article originally appeared on junilearning.com

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Introduction

The first step towards an understanding of why the study and knowledge of algorithms are so important is to define exactly what we mean by an algorithm. According to the popular algorithms textbook Introduction to Algorithms (Second Edition by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein), “an algorithm is any well-defined computational procedure that takes some value, or set of values, as input and produces some value, or set of values as output.” In other words, algorithms are like road maps for accomplishing a given, well-defined task. So, a chunk of code that calculates the terms of the Fibonacci sequence is an implementation of a particular algorithm. Even a simple function for adding two numbers is an algorithm in a sense, albeit a simple one. Some algorithms, like those that compute the Fibonacci sequences, are intuitive and may be innately embedded into our logical thinking and problem solving skills. However, for most of us, complex algorithms are best studied so we can use them as building blocks for more efficient logical problem solving in the future. In fact, you may be surprised to learn just how many complex algorithms people use every day when they check their e-mail or listen to music on their computers. This article will introduce some basic ideas related to the analysis of algorithms, and then put these into practice with a few examples illustrating why it is important to know about algorithms.

Runtime Analysis

One of the most important aspects of an algorithm is how fast it is. It is often easy to come up with an algorithm to solve a problem, but if the algorithm is too slow, it’s back to the drawing board. Since the exact speed of an algorithm depends on where the algorithm is run, as well as the exact details of its implementation, computer scientists typically talk about the runtime relative to the size of the input. For example, if the input consists of N integers, an algorithm might have a runtime proportional to N 2 , represented as O(N 2 ). This means that if you were to run an implementation of the algorithm on your computer with an input of size N, it would take C*N 2 seconds, where C is some constant that doesn’t change with the size of the input. However, the execution time of many complex algorithms can vary due to factors other than the size of the input. For example, a sorting algorithm may run much faster when given a set of integers that are already sorted than it would when given the same set of integers in a random order. As a result, you often hear people talk about the worst-case runtime, or the average-case runtime. The worst-case runtime is how long it would take for the algorithm to run if it were given the most insidious of all possible inputs. The average-case runtime is the average of how long it would take the algorithm to run if it were given all possible inputs. Of the two, the worst-case is often easier to reason about, and therefore is more frequently used as a benchmark for a given algorithm. The process of determining the worst-case and average-case runtimes for a given algorithm can be tricky, since it is usually impossible to run an algorithm on all possible inputs. There are many good online resources that can help you in estimating these values. Approximate completion time for algorithms, N = 100

Sorting provides a good example of an algorithm that is very frequently used by computer scientists. The simplest way to sort a group of items is to start by removing the smallest item from the group, and put it first. Then remove the next smallest, and put it next and so on. Unfortunately, this algorithm is O(N 2 ), meaning that the amount of time it takes is proportional to the number of items squared. If you had to sort a billion things, this algorithm would take around 1018 operations. To put this in perspective, a desktop PC can do a little bit over 109 operations per second, and would take years to finish sorting a billion things this way. Luckily, there are a number of better algorithms (quicksort, heapsort and mergesort, for example) that have been devised over the years, many of which have a runtime of O(N * Log(N)). This brings the number of operations required to sort a billion items down to a reasonable number that even a cheap desktop could perform. Instead of a billion squared operations (1018) these algorithms require only about 10 billion operations (1010), a factor of 100 million faster.

Shortest Path

Algorithms for finding the shortest path from one point to another have been researched for years. Applications abound, but lets keep things simple by saying we want to find the shortest path from point A to point B in a city with just a few streets and intersections. There are quite a few different algorithms that have been developed to solve such problems, all with different benefits and drawbacks. Before we delve into them though, lets consider how long a naive algorithm – one that tries every conceivable option – would take to run. If the algorithm considered every possible path from A to B (that didn’t go in circles), it would not finish in our lifetimes, even if A and B were both in a small town. The runtime of this algorithm is exponential in the size of the input, meaning that it is O(CN) for some C. Even for small values of C, CN becomes astronomical when N gets even moderately large. One of the fastest algorithms for solving this problem has a runtime of O(E V Log(V)), where E is the number of road segments, and V is the number of intersections. To put this in perspective, the algorithm would take about 2 seconds to find the shortest path in a city with 10,000 intersections, and 20,000 road segments (there are usually about 2 road segments per intersection). The algorithm, known as Djikstra’s Algorithm, is fairly complex, and requires the use of a data structure known as a priority queue. In some applications, however, even this runtime is too slow (consider finding the shortest path from New York City to San Francisco – there are millions of intersections in the US), and programmers try to do better by using what are known as heuristics. A heuristic is an approximation of something that is relevant to the problem, and is often computed by an algorithm of its own. In the shortest path problem, for example, it is useful to know approximately how far a point is from the destination. Knowing this allows for the development of faster algorithms (such as A*, an algorithm that can sometimes run significantly faster than Djikstra’s algorithm) and so programmers come up with heuristics to approximate this value. Doing so does not always improve the runtime of the algorithm in the worst case, but it does make the algorithm faster in most real-world applications.

Approximate algorithms

Sometimes, however, even the most advanced algorithm, with the most advanced heuristics, on the fastest computers is too slow. In this case, sacrifices must be made that relate to the correctness of the result. Rather than trying to get the shortest path, a programmer might be satisfied to find a path that is at most 10% longer than the shortest path. In fact, there are quite a few important problems for which the best-known algorithm that produces an optimal answer is insufficiently slow for most purposes. The most famous group of these problems is called NP, which stands for non-deterministic polynomial (don’t worry about what that means). When a problem is said to be NP-complete or NP-hard, it mean no one knows a good way to solve them optimally. Furthermore, if someone did figure out an efficient algorithm for one NP-complete problem, that algorithm would be applicable to all NP-complete problems. A good example of an NP-hard problem is the famous traveling salesman problem. A salesman wants to visit N cities, and he knows how long it takes to get from each city to each other city. The question is “how fast can he visit all of the cities?” Since the fastest known algorithm for solving this problem is too slow – and many believe this will always be true – programmers look for sufficiently fast algorithms that give good, but not optimal solutions.

Random Algorithms

Yet another approach to some problems is to randomize an algorithm is some way. While doing so does not improve the algorithm in the worst case, it often makes very good algorithms in the average case. Quicksort is a good example of an algorithm where randomization is often used. In the worst case, quicksort sorts a group of items in O(N 2 ), where N is the number of items. If randomization is incorporated into the algorithm, however, the chances of the worst case actually occurring become diminishingly small, and on average, quicksort has a runtime of O(N Log(N)). Other algorithms guarantee a runtime of O(N Log(N)), even in the worst case, but they are slower in the average case. Even though both algorithms have a runtime proportional to N Log(N), quicksort has a smaller constant factor – that is it requires C N Log(N) operations, while other algorithms require more like 2 C N Log(N) operations. Another algorithm that uses random numbers finds the median of a group of numbers with an average runtime of O(N). This is a significant improvement over sorting the numbers and taking the middle one, which takes O(N*Log(N)). Furthermore, while deterministic (non-random) algorithms exist for finding the median with a runtime of O(N), the random algorithm is attractively simple, and often faster than the deterministic algorithms. The basic idea of the median algorithm is to pick one of the numbers in the group at random, and count how many of the numbers in the group are less than it. Lets say there are N numbers, and K of them are less than or equal to the number we picked at random. If K is less than half of N, then we know that the median is the (N/2-K) th number that is greater than the random number we picked, so we discard the K numbers less than or equal to the random number. Now, we want to find the (N/2-K) th smallest number, instead of the median. The algorithm is the same though, and we simply pick another number at random, and repeat the above steps.

Compression

Another class of algorithm deals with situations such as data compression. This type of algorithm does not have an expected output (like a sorting algorithm), but instead tries to optimize some other criteria. In the case of data compression, the algorithm (LZW, for instance) tries to make the data use as few bytes as possible, in such a way that it can be decompressed to its original form. In some cases, this type of algorithm will use the same techniques as other algorithms, resulting in output that is good, but potentially sub-optimal. JPG and MP3 compression, for example, both compress data in a way that makes the final result somewhat lower quality than the original, but they create much smaller files. MP3 compression does not retain every feature of the original song file, but it attempts to maintain enough of the details to capture most of the quality, while at the same time ensuring the significantly reduced file size that we all know and love. The JPG image file format follows the same principle, but the details are significantly different since the goal is image rather than audio compression.

The Importance of Knowing Algorithms

As a computer scientist, it is important to understand all of these types of algorithms so that one can use them properly. If you are working on an important piece of software, you will likely need to be able to estimate how fast it is going to run. Such an estimate will be less accurate without an understanding of runtime analysis. Furthermore, you need to understand the details of the algorithms involved so that you’ll be able to predict if there are special cases in which the software won’t work quickly, or if it will produce unacceptable results. Of course, there are often times when you’ll run across a problem that has not been previously studied. In these cases, you have to come up with a new algorithm, or apply an old algorithm in a new way. The more you know about algorithms in this case, the better your chances are of finding a good way to solve the problem. In many cases, a new problem can be reduced to an old problem without too much effort, but you will need to have a fundamental understanding of the old problem in order to do this. As an example of this, lets consider what a switch does on the Internet. A switch has N cables plugged into it, and receives packets of data coming in from the cables. The switch has to first analyze the packets, and then send them back out on the correct cables. A switch, like a computer, is run by a clock with discrete steps – the packets are send out at discrete intervals, rather than continuously. In a fast switch, we want to send out as many packets as possible during each interval so they don’t stack up and get dropped. The goal of the algorithm we want to develop is to send out as many packets as possible during each interval, and also to send them out so that the ones that arrived earlier get sent out earlier. In this case it turns out that an algorithm for a problem that is known as “stable matching” is directly applicable to our problem, though at first glance this relationship seems unlikely. Only through pre-existing algorithmic knowledge and understanding can such a relationship be discovered.

More Real-world Examples

Other examples of real-world problems with solutions requiring advanced algorithms abound. Almost everything that you do with a computer relies in some way on an algorithm that someone has worked very hard to figure out. Even the simplest application on a modern computer would not be possible without algorithms being utilized behind the scenes to manage memory and load data from the hard drive. There are dozens of applications of complicated algorithms, but I’m going to discuss two problems that require the same skills as some past TopCoder problems. The first is known as the maximum flow problem, and the second is related to dynamic programming, a technique that often solves seemingly impossible problems in blazing speed.

Maximum Flow

The maximum flow problem has to do with determining the best way to get some sort of stuff from one place to another, through a network of some sort. In more concrete terms, the problem first arose in relation to the rail networks of the Soviet Union, during the 1950′s. The US wanted to know how quickly the Soviet Union could get supplies through its rail network to its satellite states in Eastern Europe. In addition, the US wanted to know which rails it could destroy most easily to cut off the satellite states from the rest of the Soviet Union. It turned out that these two problems were closely related, and that solving the max flow problem also solves the min cut problem of figuring out the cheapest way to cut off the Soviet Union from its satellites. The first efficient algorithm for finding the maximum flow was conceived by two Computer Scientists, named Ford and Fulkerson. The algorithm was subsequently named the Ford-Fulkerson algorithm, and is one of the more famous algorithms in computer science. In the last 50 years, a number of improvements have been made to the Ford-Fulkerson algorithm to make it faster, some of which are dauntingly complex. Since the problem was first posed, many additional applications have been discovered. The algorithm has obvious relevance to the Internet, where getting as much data as possible from one point to another is important. It also comes up in many business settings, and is an important part of operations research. For example, if you have N employees and N jobs that need to be done, but not every employee can do every job, the max flow algorithm will tell you how to assign your N employees to jobs in such a way that every job gets done, provided that’s possible. Graduation, from SRM 200, is a good example of a TopCoder problem that lends itself to a solution using max flow.

Sequence comparison

Many coders go their entire careers without ever having to implement an algorithm that uses dynamic programming. However, dynamic programming pops up in a number of important algorithms. One algorithm that most programmers have probably used, even though they may not have known it, finds differences between two sequences. More specifically, it calculates the minimum number of insertions, deletions, and edits required to transform sequence A into sequence B. For example, lets consider two sequences of letters, “AABAA” and “AAAB”. To transform the first sequence into the second, the simplest thing to do is delete the B in the middle, and change the final A into a B. This algorithm has many applications, including some DNA problems and plagiarism detection. However, the form in which many programmers use it is when comparing two versions of the same source code file. If the elements of the sequence are lines in the file, then this algorithm can tell a programmer which lines of code were removed, which ones were inserted, and which ones were modified to get from one version to the next. Without dynamic programming, we would have to consider a – you guessed it – exponential number of transformations to get from one sequence to the other. As it is, however, dynamic programming makes for an algorithm with a runtime of only O(N*M), where N and M are the numbers of elements in the two sequences.

The different algorithms that people study are as varied as the problems that they solve. However, chances are good that the problem you are trying to solve is similar to another problem in some respects. By developing a good understanding of a large range of algorithms, you will be able to choose the right one for a problem and apply it properly. Furthermore, solving problems like those found in TopCoder’s competitions will help you to hone your skills in this respect. Many of the problems, though they may not seem realistic, require the same set of algorithmic knowledge that comes up every day in the real world.

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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.

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How quickly do algorithms improve?

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Algorithms are sort of like a parent to a computer. They tell the computer how to make sense of information so they can, in turn, make something useful out of it.

The more efficient the algorithm, the less work the computer has to do. For all of the technological progress in computing hardware, and the much debated lifespan of Moore’s Law, computer performance is only one side of the picture.

Behind the scenes a second trend is happening: Algorithms are being improved, so in turn less computing power is needed. While algorithmic efficiency may have less of a spotlight, you’d definitely notice if your trusty search engine suddenly became one-tenth as fast, or if moving through big datasets felt like wading through sludge.

This led scientists from MIT’s Computer Science and Artificial Intelligence Laboratory (CSAIL) to ask: How quickly do algorithms improve?  

Existing data on this question were largely anecdotal, consisting of case studies of particular algorithms that were assumed to be representative of the broader scope. Faced with this dearth of evidence, the team set off to crunch data from 57 textbooks and more than 1,110 research papers, to trace the history of when algorithms got better. Some of the research papers directly reported how good new algorithms were, and others needed to be reconstructed by the authors using “pseudocode,” shorthand versions of the algorithm that describe the basic details.

In total, the team looked at 113 “algorithm families,” sets of algorithms solving the same problem that had been highlighted as most important by computer science textbooks. For each of the 113, the team reconstructed its history, tracking each time a new algorithm was proposed for the problem and making special note of those that were more efficient. Ranging in performance and separated by decades, starting from the 1940s to now, the team found an average of eight algorithms per family, of which a couple improved its efficiency. To share this assembled database of knowledge, the team also created Algorithm-Wiki.org.

The scientists charted how quickly these families had improved, focusing on the most-analyzed feature of the algorithms — how fast they could guarantee to solve the problem (in computer speak: “worst-case time complexity”). What emerged was enormous variability, but also important insights on how transformative algorithmic improvement has been for computer science.

For large computing problems, 43 percent of algorithm families had year-on-year improvements that were equal to or larger than the much-touted gains from Moore’s Law. In 14 percent of problems, the improvement to performance from algorithms vastly outpaced those that have come from improved hardware. The gains from algorithm improvement were particularly large for big-data problems, so the importance of those advancements has grown in recent decades.

The single biggest change that the authors observed came when an algorithm family transitioned from exponential to polynomial complexity. The amount of effort it takes to solve an exponential problem is like a person trying to guess a combination on a lock. If you only have a single 10-digit dial, the task is easy. With four dials like a bicycle lock, it’s hard enough that no one steals your bike, but still conceivable that you could try every combination. With 50, it’s almost impossible — it would take too many steps. Problems that have exponential complexity are like that for computers: As they get bigger they quickly outpace the ability of the computer to handle them. Finding a polynomial algorithm often solves that, making it possible to tackle problems in a way that no amount of hardware improvement can.

As rumblings of Moore’s Law coming to an end rapidly permeate global conversations, the researchers say that computing users will increasingly need to turn to areas like algorithms for performance improvements. The team says the findings confirm that historically, the gains from algorithms have been enormous, so the potential is there. But if gains come from algorithms instead of hardware, they’ll look different. Hardware improvement from Moore’s Law happens smoothly over time, and for algorithms the gains come in steps that are usually large but infrequent. 

“This is the first paper to show how fast algorithms are improving across a broad range of examples,” says Neil Thompson, an MIT research scientist at CSAIL and the Sloan School of Management and senior author on the new paper . “Through our analysis, we were able to say how many more tasks could be done using the same amount of computing power after an algorithm improved. As problems increase to billions or trillions of data points, algorithmic improvement becomes substantially more important than hardware improvement. In an era where the environmental footprint of computing is increasingly worrisome, this is a way to improve businesses and other organizations without the downside.”

Thompson wrote the paper alongside MIT visiting student Yash Sherry. The paper is published in the Proceedings of the IEEE . The work was funded by the Tides foundation and the MIT Initiative on the Digital Economy.

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1: Algorithmic Problem Solving

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Unit Objectives

Upon completion of this unit the learner should be able to:

• describe an algorithm
• explain the relationship between data and algorithm
• outline the characteristics of algorithms
• apply pseudo codes and flowcharts to represent algorithms

Unit Introduction

This unit introduces learners to data structures and algorithm course. The unit is on the different data structures and their algorithms that can help implement the different data structures in the computer. The application of the different data structures is presented by using examples of algorithms and which are not confined to a particular computer programming language.

• Data: the structural representation of logical relationships between elements of data
• Algorithm: finite sequence of steps for accomplishing some computational task
• Pseudo code: an informal high-level description of the operating principle of a computer program or other algorithm
• Flow chart: diagrammatic representation illustrates a solution model to a given problem.

Learning Activities

• 1.1: Activity 1 - Introduction to Algorithms and Problem Solving In this learning activity section, the learner will be introduced to algorithms and how to write algorithms to solve tasks faced by learners or everyday problems. Examples of the algorithm are also provided with a specific application to everyday problems that the learner is familiar with. The learners will particularly learn what is an algorithm, the process of developing a solution for a given task, and finally examples of application of the algorithms are given.
• 1.2: Activity 2 - The characteristics of an algorithm This section introduces the learners to the characteristics of algorithms. These characteristics make the learner become aware of what to ensure is basic, present and mandatory for any algorithm to qualify to be one. It also exposes the learner to what to expect from an algorithm to achieve or indicate. Key expectations are: the fact that an algorithm must be exact, terminate, effective, general among others.
• 1.3: Activity 3 - Using pseudo-codes and flowcharts to represent algorithms The student will learn how to design an algorithm using either a pseudo code or flowchart. Pseudo code is a mixture of English like statements, some mathematical notations and selected keywords from a programming language. It is one of the tools used to design and develop the solution to a task or problem. Pseudo codes have different ways of representing the same thing and emphasis is on the clarity and not style.
• 1.4: Unit Summary In this unit, you have seen what an algorithm is. Based on this knowledge, you should now be able to characterize an algorithm by stating its properties. We have explored the different ways of representing an algorithm such as using human language, pseudo codes and flow chart. You should now be able to present solutions to problems in form of an algorithm.

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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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The Essential Role of Algorithms in Programming: A Practical Perspective

Is learning algorithms a waste of time? This question often surfaces among aspiring and practicing programmers. The common belief is that algorithms and data structures are crucial only for building advanced systems or for clearing interviews at top tech firms like FAANG. But what about the everyday coding scenarios? Is algorithmic knowledge relevant there?

Basic Algorithms and Problem-Solving in Programming

Every experienced programmer can attest that a solid understanding of basic algorithms and problem-solving skills is fundamental, regardless of the complexity of the task at hand. Even for tasks that appear simple, such as developing a feature for a website or app, algorithmic thinking can be crucial.

Real-World Examples of Algorithm Use in Development

1. front-end development: carousel functionality.

Consider the carousel on AlgoCademy.com’s landing page, displaying testimonials. The carousel shifts one testimonial to the left upon clicking the right arrow. This seemingly straightforward functionality relies on a basic algorithm to group and display the testimonials effectively. Without a basic understanding of algorithms, implementing such a feature, especially when pre-existing solutions are inadequate, becomes a daunting task.

2. Custom Search Feature

Another example is the development of a custom search feature. Many JavaScript libraries can provide basic search functionalities, but they often fall short when dealing with misspelled words. Developing a search algorithm that accounts for misspelling requires a deeper understanding of how search algorithms work and how they can be adapted to specific requirements.

3. Interactive Coding Tutorial

The core feature of AlgoCademy, an interactive coding tutorial, is another testament to the importance of algorithms in programming. The development of this feature involved months of perfecting the underlying algorithm. Understanding and manipulating data structures like trees becomes essential when creating such interactive and dynamic features.

The Necessity of Algorithms in Backend Development

In backend development, technologies often rely on complex algorithms. For instance, database indexing, a critical aspect of database management, requires understanding how indexing algorithms enhance performance and scalability.

Algorithms in Innovative Technologies

Consider the algorithms behind the technologies we use daily:

• Google Search : Utilizes inverted document indexing for instant search results, meet-in-the-middle algorithms for autocorrect, and graphs for analyzing website quality.
• Google Maps : Employs shortest path algorithms and quad or kd trees for proximity searches.
• Keyboard Autocorrect and Swipe Typing : Relies on Ternary Search Trees.
• Facebook : Uses graph algorithms to store and analyze connections.
• Amazon, Spotify, YouTube : All use sophisticated recommendation algorithms.

These examples highlight that algorithms are not just academic exercises; they are integral to the technologies that shape our world.

Can You Get By Without Algorithms?

Technically, yes. It’s possible to work in programming without a deep understanding of algorithms. However, this limitation will likely confine you to routine tasks, depriving you of opportunities to work on exciting projects or in teams where learning and growth are continuous.

The Essence of Programming

It’s crucial to remember that every program is, by definition, an algorithm. Whether it’s a simple function or a complex system, you’re creating a set of instructions to solve a problem or perform a task. This is the essence of algorithmic thinking.

Conclusion: The Value of Algorithms in Your Programming Career

In conclusion, while you might not need advanced algorithmic knowledge for every programming task, a solid grasp of basic algorithms and problem-solving skills is indispensable. These skills not only enable you to tackle a wide range of problems more effectively but also open doors to exciting projects and career growth opportunities. As a programmer, embracing algorithms is not just about solving complex problems; it’s about enriching your toolkit, enhancing your creativity, and preparing you for the challenges of the ever-evolving tech landscape.

Open and Interactive Learning Resources for Algorithmic Problem Solving

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• First Online: 11 August 2020
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• João F. Ferreira 25 &
• Alexandra Mendes 26 , 27  

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12233))

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Algorithmic problem solving is a way of approaching and solving problems by using the advances that have been made in the principles of correct-by-construction algorithm design. The approach has been taught at first-year undergraduate level since September 2003 and, since then, a substantial amount of learning materials have been developed. However, the existing materials are distributed in a conventional and static way (e.g. as a textbook and as several documents in PDF format available online), not leveraging the capabilities provided by modern collaborative and open-source platforms.

In this paper, we propose the creation of an online, open-source repository of interactive learning materials on algorithmic problem solving. We show how the existing framework Mathigon can be used to support such a repository. By being open and hosted on a platform such as GitHub, the repository enables collaboration and anyone can create and submit new material. Furthermore, by making the material interactive, we hope to encourage engagement with and a better understanding of the materials.

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Mathigon’s website: https://mathigon.org (accessed 18 July 2019).

Wikipedia link: https://en.wikipedia.org/wiki/River_crossing_puzzle (accessed 18 July 2019).

The restatement of the problem and the subsequent two paragraphs are extracted from [ 1 ].

The implementation of the puzzle that we used was created by Victor Ribeiro ( https://github.com/victorqribeiro/bridge ).

See the repository textbooks (folder content/river-crossing ) in https://github.com/algprobsolving .

MyScript webpage: https://www.myscript.com .

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Acknowledgments

This work is partially financed by National Funds through the Portuguese funding agency, FCT - Fundação para a Ciência e a Tecnologia through the project: UID/EEA/50014/2019.

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Ferreira, J.F., Mendes, A. (2020). Open and Interactive Learning Resources for Algorithmic Problem Solving. In: Sekerinski, E., et al. Formal Methods. FM 2019 International Workshops. FM 2019. Lecture Notes in Computer Science(), vol 12233. Springer, Cham. https://doi.org/10.1007/978-3-030-54997-8_13

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The Importance of Algorithms in Computer Programming

What is an algorithm? Why are algorithms important in computer programming? To answer these questions, let’s start by looking at these two analogies.

You are planning to build a big house but at the same time, you are not sure whether the resources that you have are enough. What will you do? You will define a work plan that will ensure you spend the little resources available at your disposal to finish the building. Secondly, you are planning to travel several miles away but there is very little time available. It is quite obvious that you will get the shortest or fastest route that will get you to your destination.

Importance of Algorithms

When it comes to computer programming , algorithms work in a similar manner. In layman’s language, an algorithm can be defined as a step-by-step procedure for accomplishing a task. In the world of programming, an algorithm is a well-structured computational procedure that takes some values as input and some values as output.

Algorithms give us the most ideal option for accomplishing a task. Here is some importance of algorithms in computer programming.

1. To improve the efficiency of a computer program

In programming, there are different ways of solving a problem. However, the efficiency of the methods available varies. Some methods are well suited to give more accurate answers than others. Algorithms are used to find the best possible way of solving a problem. In doing so they improve the efficiency of a program.

When it comes to programming, efficiency can be used to mean different things. One of them is the accuracy of the software. With the best algorithm, a computer program will be able to produce very accurate results.

Another way of looking at the efficiency of the software is speed. An algorithm can be used to improve the speed at which a program executes a problem. A single algorithm has the potential of reducing the time that a program takes to solve a problem.

2. Proper utilization of resources

A typical computer has different resources. One of them is computer memory . During the execution phase, a computer program will require some amount of memory. Some programs use more memory space than others. The usage of computer memory depends on the algorithm that has been used.

The right choice of algorithm will ensure that a program consumes the least amount of memory. Apart from memory, the algorithm can determine the amount of processing power that is needed by a program.

3. Algorithms

Given that we have mentioned the impact of an algorithm on resources, it will be imperative to look at the cost. This is because each resource comes with a price tag. You can decide to use an algorithm that will use the least resources. The leaner the resources, the less the cost.

Types of Algorithms

To give you a better picture, here are the most common type of algorithms:

• Searching algorithms
• Pathfinding algorithm
• Sorting algorithms
• Compression algorithms
• Tree and graph-based algorithms
• Pattern matching algorithm among many others

Different algorithms play different roles in programming. You only need to define your problem and then select the right algorithm to use.

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What Is Problem Solving? How Software Engineers Approach Complex Challenges

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

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

What Is Problem Solving?

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

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

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

The Importance of Problem-Solving Skills for Software Engineers

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

Driving Development Forward

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

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

Innovation and Optimization

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

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

Increasing Efficiency and Productivity

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

Improving Software Quality

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

Problem-Solving Techniques in Software Engineering

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

Decomposition

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

Abstraction

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

Algorithmic Thinking

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

Parallel Thinking

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

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

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

Testing and Validation

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

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Evaluating Problem-Solving Skills

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

Recognizing Problem-Solving Skills in Candidates

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

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

Assessing Problem-Solving Skills

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

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

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

Key Takeaways

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

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

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

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

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What Is an Algorithm in Psychology?

Definition, Examples, and Uses

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

 James Lacy, MLS, is a fact-checker and researcher.

How Does an Algorithm Work?

Examples of algorithms.

• Reasons to Use Algorithms
• Potential Pitfalls

Algorithms vs. Heuristics

When solving a problem , choosing the right approach is often the key to arriving at the best solution. In psychology, one of these problem-solving approaches is known as an algorithm. While often thought of purely as a mathematical term, the same type of process can be followed in psychology to find the correct answer when solving a problem or making a decision.

An algorithm is a defined set of step-by-step procedures that provides the correct answer to a particular problem. By following the instructions correctly, you are guaranteed to arrive at the right answer.

At a Glance

Algorithms involve following specific steps in order to reach a solution to a problem. They can be a great tool when you need an accurate solution but tend to be more time-consuming than other methods.

This article discusses how algorithms are used as an approach to problem-solving. It also covers how psychologists compare this approach to other problem-solving methods.

An algorithm is often expressed in the form of a graph, where a square represents each step. Arrows then branch off from each step to point to possible directions that you may take to solve the problem.

In some cases, you must follow a particular set of steps to solve the problem. In other instances, you might be able to follow different paths that will all lead to the same solution.

Algorithms are essential step-by-step approaches to solving a problem. Rather than guessing or using trial-and-error, this approach is more likely to guarantee a specific solution. 

Using an algorithm can help you solve day-to-day problems you face, but it can also help mental health professionals find ways to help people cope with mental health problems.

For example, a therapist might use an algorithm to treat a person experiencing something like anxiety. Because the therapist knows that a particular approach is likely to be effective, they would recommend a series of specific, focused steps as part of their intervention.

There are many different examples of how algorithms can be used in daily life. Some common ones include:

• A recipe for cooking a particular dish
• The method a search engine uses to find information on the internet
• Instructions for how to assemble a bicycle
• Instructions for how to solve a Rubik's cube
• A process to determine what type of treatment is most appropriate for certain types of mental health conditions

Doctors and mental health professionals often use algorithms to diagnose mental disorders . For example, they may use a step-by-step approach when they evaluate people.

This might involve asking the individual about their symptoms and their medical history. The doctor may also conduct lab tests, physical exams, or psychological assessments.

Using this information, they then utilize the "Diagnostic and Statistical Manual of Mental Disorders" (DSM-5-TR) to make a diagnosis.

Reasons to Use Algorithms in Psychology

The upside of using an algorithm to solve a problem or make a decision is that yields the best possible answer every time. There are situations where using an algorithm can be the best approach:

When Accuracy Is Crucial

Algorithms can be particularly useful in situations when accuracy is critical. They are also a good choice when similar problems need to be frequently solved.

Computer programs can often be designed to speed up this process. Data then needs to be placed in the system so that the algorithm can be executed for the correct solution.

Artificial intelligence may also be a tool for making clinical assessments in healthcare situations.

When Each Decision Needs to Follow the Same Process

Such step-by-step approaches can be useful in situations where each decision must be made following the same process. Because the process follows a prescribed procedure, you can be sure that you will reach the correct answer each time.

Potential Pitfalls When Using Algorithms

The downside of using an algorithm to solve the problem is that this process tends to be very time-consuming.

So if you face a situation where a decision must be made very quickly, you might be better off using a different problem-solving strategy.

For example, an emergency room doctor making a decision about how to treat a patient could use an algorithm approach. However, this would be very time-consuming and treatment needs to be implemented quickly.

In this instance, the doctor would instead rely on their expertise and past experiences to very quickly choose what they feel is the right treatment approach.

Algorithms can sometimes be very complex and may only apply to specific situations. This can limit their use and make them less generalizable when working with larger populations.

Algorithms can be a great problem-solving choice when the answer needs to be 100% accurate or when each decision needs to follow the same process. A different approach might be needed if speed is the primary concern.

In psychology, algorithms are frequently contrasted with heuristics . Both can be useful when problem-solving, but it is important to understand the differences between them.

What Is a Heuristic?

A heuristic is a mental shortcut that allows people to quickly make judgments and solve problems.

These mental shortcuts are typically informed by our past experiences and allow us to act quickly. However, heuristics are really more of a rule-of-thumb; they don't always guarantee a correct solution.

So how do you determine when to use a heuristic and when to use an algorithm? When problem-solving, deciding which method to use depends on the need for either accuracy or speed.

When to Use an Algorithm

If complete accuracy is required, it is best to use an algorithm. By using an algorithm, accuracy is increased and potential mistakes are minimized.

If you are working in a situation where you absolutely need the correct or best possible answer, your best bet is to use an algorithm. When you are solving problems for your math homework, you don't want to risk your grade on a guess.

By following an algorithm, you can ensure that you will arrive at the correct answer to each problem.

When to Use a Heuristic

On the other hand, if time is an issue, then it may be best to use a heuristic. Mistakes may occur, but this approach allows for speedy decisions when time is of the essence.

Heuristics are more commonly used in everyday situations, such as figuring out the best route to get from point A to point B. While you could use an algorithm to map out every possible route and determine which one would be the fastest, that would be a very time-consuming process. Instead, your best option would be to use a route that you know has worked well in the past.

Psychologists who study problem-solving have described two main processes people utilize to reach conclusions: algorithms and heuristics. Knowing which approach to use is important because these two methods can vary in terms of speed and accuracy.

While each situation is unique, you may want to use an algorithm when being accurate is the primary concern. But if time is of the essence, then an algorithm is likely not the best choice.

Lang JM, Ford JD, Fitzgerald MM. An algorithm for determining use of trauma-focused cognitive-behavioral therapy . Psychotherapy (Chic) . 2010;47(4):554-69. doi:10.1037/a0021184

Stein DJ, Shoptaw SJ, Vigo DV, et al. Psychiatric diagnosis and treatment in the 21st century: paradigm shifts versus incremental integration .  World Psychiatry . 2022;21(3):393-414. doi:10.1002/wps.20998

Bobadilla-Suarez S, Love BC. Fast or frugal, but not both: decision heuristics under time pressure . J Exp Psychol Learn Mem Cogn . 2018;44(1):24-33. doi:10.1037/xlm0000419

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By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

• Guide to Teaching Algorithms in Computer Programming for K-12 Students

by Lcom Team | Apr 9, 2024 | Blogs

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Purpose of Algorithms in Computer Programming  

The purpose of an algorithm in computer programming is to solve problems by providing a clear set of instructions that a computer can execute. Whether it’s calculating the fastest route from one location to another, sorting a list of names or searching for specific information within a database, algorithms are the tools that enable these tasks to be performed efficiently and accurately.

Importance of Algorithms

By converting complex problems into manageable steps, algorithms enable computers to perform operations from the simplest calculations to the most complex data analysis and artificial intelligence functions. Furthermore, the principles of algorithmic thinking—such as decomposition, pattern recognition, and abstraction—equip individuals with a powerful framework for tackling problems not just in computing, but in everyday life as well.

As technology continues to advance, the role of algorithms in enabling innovation, improving productivity, and enhancing our understanding of the world around us only grows more critical, making them an indispensable element of modern society.

Below are some of the top reasons algorithms are important:

1. Efficiency and Performance

The efficiency of an algorithm often determines the speed and resource consumption in the solving of a problem. An efficient algorithm can significantly reduce the time and memory required to perform a task. In the computer programming world, this is critical for applications that process large amounts of data or require real-time responsiveness.

2. Problem-Solving Skills

Understanding algorithms helps develop problem-solving skills. It encourages thinking about how to break down problems into manageable parts and then devising a systematic approach to solving them.  

3. Foundation for Advanced Learning

Knowledge of algorithms is fundamental to more advanced topics in computer science, such as data structures, artificial intelligence, and machine learning. A solid grasp of basic algorithms paves the way for understanding these complex subjects.

Teaching Algorithms to K-12 Students

Introducing algorithms to K-12 students can seem daunting, but it can be done effectively with the right strategies and tools. Here are some approaches to help teach this concept:

Start with Everyday Examples

Begin by sharing real-life examples of algorithms that students are already familiar with. For example, a recipe is an algorithm for cooking a dish and the steps to solve a math problem can be viewed as an algorithm. This approach helps demystify algorithms and shows students that they already use algorithmic thinking without realizing it.

Use Visual and Interactive Tools  

Leverage visual and interactive programming environments like Scratch, Blockly, or Tynker. These tools allow students to create programs using blocks that represent different parts of an algorithm. They provide a hands-on learning experience without the initial complexity of syntax, making it easier for students to grasp the concepts.  

Encourage Algorithmic Thinking

Focus on developing algorithmic thinking rather than just coding skills. Present students with puzzles and challenges that require them to think about the steps needed to reach a solution. Encourage them to articulate their thought process, either through flowcharts, pseudocode, or simple explanations. This practice helps them understand the importance of planning and structuring their solutions before diving into coding.

Implement Project-Based Learning

Project-based learning can be highly effective in teaching algorithms. Allow students to work on projects that interest them, guiding them to apply algorithmic thinking to plan and execute their projects. This approach not only reinforces their understanding of algorithms but also enhances engagement and motivation.

Introduce Complexity Gradually  

Start with simple algorithms and gradually introduce more complexity as students become more comfortable with the concept. For example, begin with linear search algorithms before moving on to binary search, or start with basic sorting algorithms like bubble sort before introducing quicksort or mergesort. This gradual progression helps build confidence and deepens understanding.

Collaborate and Share

Encourage students to work in pairs or small groups to solve problems. Collaboration fosters a deeper understanding as students explain their thinking to peers and learn from each other’s approaches. Additionally, create opportunities for students to share their projects and solutions with the class, further reinforcing their learning through teaching.

Contextualize Learning

Show students how algorithms impact the world around them. Discuss examples of how algorithms are used in various fields , such as medicine, finance, and entertainment. This not only illustrates the relevance of what they’re learning but also inspires them to consider how they might apply these concepts in their future careers.

Understanding Algorithms: Activities for Students

Creating and understanding algorithms is a fundamental skill in computer programming. Teaching this concept to K-12 students can be both enjoyable and informative, preparing them for more advanced computational thinking and problem-solving skills. Here are ideas for activities designed to engage students of various ages in the principles of algorithms.

1. Recipe Creation and Execution

Ages: Elementary to Middle School

Objective: Teach students the importance of clear, step-by-step instructions.

Activity: Have students write a “recipe” for a simple task, such as making a sandwich or drawing a basic picture. Then, in pairs, they exchange recipes and follow the instructions exactly as written. This activity highlights the need for precision in algorithms.  

2. The Human Robot

Ages: Elementary  

Objective: Introduce the concept of algorithms as instructions for computers.  

Activity: Designate one student as the “robot” and the others as programmers. The programmers must give the robot a set of instructions to perform a simple task, like moving a book from one desk to another. The robot follows the instructions literally, illustrating the importance of specificity and order in algorithms.

3. Treasure Hunt

Ages: Middle School

Objective: Demonstrate how algorithms use conditions and loops.

Activity: Create a treasure hunt where students must follow a series of clues to find a prize. Each clue requires performing a task or solving a puzzle that involves conditional logic (if this, then that) or repetition (do something several times). This can be done in the classroom or outdoors.

4. Algorithm Art  

Ages: Middle to High School

Objective: Show how algorithms can create complex and beautiful patterns.

Activity: Challenge students to create art using simple algorithms. This can be done with paper and pencils or with online tools like TurtleArt. Students can use loops and conditionals to draw patterns, learning about the mathematical principles behind algorithms.  

5. Sorting Race

Objective: Teach about sorting algorithms and their efficiency.

Activity: Divide students into groups and give each group a set of numbered cards. Each group must come up with their own method to sort the cards in ascending order as quickly as possible. After the race, discuss the different methods (algorithms) used and introduce formal sorting algorithms like bubble sort or quick sort.

6. Sequencing

Ages: Early Elementary

Objective: Teach basic algorithm concept and sequencing

Activity: Divide students into groups and give each group a set of cards with illustrations depicting different steps for an activity (such as making a sandwich). Ask them to put the cards in order from beginning to end. Discuss what other activities they do in everyday life might be considered an algorithm, then as a class, brainstorm the steps to complete an activity.

7. Escape Room Challenge

Ages: High School

Objective: Apply algorithmic thinking to problem-solving in a complex scenario.

Activity: Design a classroom escape room where students must solve puzzles that require algorithmic thinking to “escape.” Each puzzle can cover a different aspect of algorithms, such as decoding messages (understanding encryption algorithms), finding the shortest path out of a maze (pathfinding algorithms), or solving a logical puzzle.

These activities are designed to make the concept of algorithms accessible and engaging for students from kindergarten to 12th grade. By starting with simple, tangible tasks and gradually introducing more complexity, students can develop a solid understanding of algorithms and their applications in computer programming and everyday problem-solving.

Final Thoughts

Learning.com Team

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Founded in 1999, Learning.com provides educators with solutions to prepare their students with critical digital skills. Our web-based curriculum for grades K-12 engages students as they learn keyboarding, online safety, applied productivity tools, computational thinking, coding and more.

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What Is An Algorithm? Its Uses And Importance In Coding.

Today, the entire world is digitalised. Every typical device that makes our lives so easy and fast has an intellect and a feeling of communication. These technological advancements are aided by software, a collection of programmes designed to solve a specific problem. And every programme is based on an Algorithm, which is a logic/solution. Our experts, through this post, will clarify what is an algorithm and what is an algorithm used for. So, keep reading!!

Introduction

People often ask us, “what is an algorithm?” To answer them, an algorithm is a step-by-step technique that specifies a series of instructions that must be followed in a precise order to achieve the intended outcome. Algorithms are usually designed independently of the underlying programming languages, which implies that they may be implemented in several languages. An algorithm's properties include ambiguity, fineness, efficacy, and language independence. An algorithm's scalability and performance are the major elements that influence its relevance.

Table Of Contents

1. What is an algorithm?

2. Characteristics of an algorithm

3. Types of algorithms

4. Factors of an algorithm

5. Analysis of an algorithm

6. What is an algorithm used for?

7. Why do kids have to understand the importance of programming?

8. Applications of an algorithm

9. Conclusion

10. Frequently asked questions

JetLearn is an education platform that offers online coding and robotics classes for kids aged 5-16. It facilitates problem-solving, logical reasoning, and creative thinking. Projects include the creation of apps and games.

What Is An Algorithm?

An algorithm is a collection of instructions that a computer must follow in order to execute computations or other problem-solving tasks. An algorithm is a finite set of instructions carried out in a certain order to execute a job according to its formal specification.

It is not the whole programme or code; rather, it is basic reasoning for a problem expressed in the form of a flowchart or pseudocode.

Problem: A issue is a real-world problem or a real-world example problem for which you must create a programme or set of instructions. A set of instructions is referred to as an algorithm.

Algorithm: An algorithm is a step-by-step technique that is created to solve a problem.

Input: The algorithm is given the required and desirable inputs after being designed.

Processing Unit: The data will be sent to the processing unit, which will provide the desired result.

Output: The output of a programme is the outcome or result of the programme.

Characteristics Of An Algorithm

Every algorithm should have certain qualities, and here is a list of some of them, which we will go through one by one.

1. Input specified: The information that will be altered throughout the computation to produce the result is referred to as the input. An algorithm should have at least 0 described inputs all around it. Input precision needs a thorough understanding of the type of data, how much of it should be, and how it should be organised.

2. Output specified: The information obtained as a result of the computation is the output. At least one overall described output is required for an algorithm, and the ideal output should be coordinated. Exactness in output also demands knowing what kind of information, how much, and what format the output should be. ​​

3. Clear and Unambiguous: Algorithms must decide each step, and each step must be distinct in all behaviours and lead to a single meaning. As a result, the algorithm should be simple and straightforward. Each step's specifics must also be discussed (counting how to deal with errors). Everything in it should be measurable, not subjective.

4. Feasible: The algorithm must be effective, which means that all of the steps required to get the desired result must be achievable with the available resources. It should not include any unnecessary or excessive developments that might render an algorithm ineffective.

5. Independent: Step-by-step instructions should be included in an algorithm, and they should be independent of any programming code. It should be done with the expectation that there may be a sudden increase in demand for any programming languages.

6. Finiteness: At some point, the algorithm will have to stop working. If you stop, you could obtain the typical output. Algorithms must terminate when a certain number of steps have been completed. An algorithm should not be limitless and should always come to a halt after a set number of steps. There is no use in developing an infinite algorithm since it will be useless to humans.

Types Of Algorithms

Divide and conquer algorithms.

This is a simple implementation of the algorithm. It allows you to build an algorithm in a step-by-step manner. It breaks down the algorithm in order to tackle the problem in a variety of ways. It enables you to break down the problem into multiple techniques and generate valid output from valid input. This precise output is passed on to a different function.

Brute force algorithms

This method is designed using the generic logic framework. It's also known as an exhaustive search algorithm since it looks at all possible solutions before deciding on one. There are two types of algorithms like this:

1. Optimizing: If the best answer is discovered, the process of finding all viable solutions to a problem and then picking the best one will come to an end.

2. Sacrificing: It will end as soon as the best answer is discovered.

Randomised Algorithms

You have predetermined input and output, just as with a normal algorithm. Deterministic algorithms have a specified set of inputs and outputs, as well as a set of steps to follow. Non-deterministic algorithms are less efficient than deterministic algorithms.

Branch And Bound Algorithms

The branch and bound approach can only be used to tackle integer programming issues. All conceivable solution sets are divided into smaller subsets using this strategy. The optimum solution is then found by evaluating these subgroups further.

Greedy Algorithms

This is an algorithm paradigm in which each iteration makes the best decision feasible to find the optimal result. It's easy to set up and use, and it takes less time to complete. However, there are just a few instances where this is the best option.

Backtracking Algorithms

It's an algorithmic process that iteratively discards solutions that don't meet the problem's requirements.

Dynamic Programming Algorithms

It enhances the algorithm's performance by storing intermediate outcomes. To identify the best answer to the problem, it goes through five steps:

• To discover the optimum solution it splits the issue into subproblems.
• After breaking down the problem into subproblems, it finds the optimal solution to these subproblems.
• The process of memorising the results of subproblems is known as memorisation.
• To avoid recomputing the solution for the same subproblems, reuse it.
• Finally, it calculates the output of the complicated programme.

Factors Of An Algorithm

When creating an algorithm, keep the following aspects in mind:

• Modularity: If you are given a problem and break it down into small-small modules or small-small stages, which is a basic description of an algorithm, this feature was made for it.
• Correctness: The correctness of an algorithm is defined as when the provided inputs yield the expected result, suggesting that the algorithm was successfully developed. The analysis of an algorithm has been finished appropriately.
• Maintainability: It indicates that the algorithm should be built in a simple, organised manner so that no substantial modifications are made to the method when it is redefined.
• Functionality: It considers a number of logical stages in order to solve a real-world situation.
• Robustness: The capacity of an algorithm to properly explain your problem is referred to as robustness.
• User-friendly: The designer will not communicate the method to the programmer if it is difficult to comprehend.
• Simplicity: When an algorithm is basic, it is easy to comprehend.
• Extensibility: If another algorithm designer or programmer wants to utilise your algorithm, it should be expandable.

Analysis Of An Algorithm

Before and after it is generated, the algorithm may be analysed on two levels. The following are the two algorithm analyses:

Priori Analysis: Priori analysis, in this context, refers to the theoretical analysis of an algorithm conducted before its implementation. Before implementing the method, numerous parameters might be considered, such as processor speed, which has no bearing on the implementation.

Posterior Analysis: A practical analysis of an algorithm is referred to as posterior analysis in this context. The algorithm may be written in any computer language to experiment. This study reveals how much time and space are required for running.

What Is An Algorithm Used For?

Algorithms are employed across the field of computer science. They are the backbone of the field. In computer science, an algorithm is a collection of instructions that allows a computer to perform any task, such as operating a calculator or launching a rocket.

At their foundation, computer programmes are algorithms defined in programming languages that the machine understands. The way computer algorithms heavily influence social media works: which postings appear, which adverts are visible, and so on. Algorithms make all of these judgments.

Google engineers use algorithms to improve searches, forecast what users will enter, etc. Knowing how to create an algorithm is an important component of computer programming when it comes to problem-solving.

There are two crucial aspects of the algorithm:

Theoretical significance: You must break down a real-world challenge into smaller modules when provided one. To deconstruct the issue, you must first grasp all of its theoretical components.

Practical Significance: As you are all aware, the theory is useless until it is put into practice. As a consequence, the theoretical and practical relevance of algorithms may be evaluated.

Why Do Kids Have To Understand The Importance Of Programming

Many disciplines need algorithmic thinking or the ability to outline unambiguous procedures to solve a problem. We employ algorithms and algorithmic thinking all the time, even if we aren't aware of it. Students can use algorithmic thinking to break down issues and construct solutions in distinct phases. Students must use organised thinking and reasoning abilities in order to grasp and apply an algorithm.

Applications Of The Algorithm

Here are a few examples of how the algorithms may be used in practice:

• First, we'll look at the internet, which is critical to our everyday lives and without which we couldn't picture our lives. The internet is the result of brilliant and innovative algorithms. Only these algorithms allow a large number of websites on the internet to operate and fake such a large amount of data.
• Every day electronic commerce activities, such as credit or debit card numbers, passwords, OTPs, and many more, are heavily reliant on our data. Public-key cryptocurrencies and digital signatures based on mathematical methods are among the core technologies employed.
• Even though a programme does not require algorithm content at the application level, it is heavily reliant on algorithms because it relies on hardware, GUI, networking, or object direction, all of which require the usage of algorithms.
• There are also additional critical use cases where the algorithm has been employed, such as when we view a video on YouTube, we will receive related-type advice in the form of recommended videos for us the next time we visit.

Even if we one day have an exceedingly fast processor and an infinite memory, we still need to analyse and build algorithms to check if the solution finishes and does so correctly. Whether it's commercial applications, scientific computing, engineering, operational research, or artificial intelligence, defining challenges, devising efficient algorithms to address them, and dealing with data structures will always be necessary.

Frequently Asked Questions

In layman's words, what is an algorithm.

An algorithm is a collection of instructions for completing a task or solving a problem. A recipe, which consists of particular directions for cooking a dish or meal, is a frequent example of an algorithm.

What is an algorithm used for?

Algorithms are instructions for performing a job or solving a problem. Recipes, like arithmetic formulae, are algorithms. Algorithmic code is a type of computer code. Algorithms are used to manage the internet and conduct online searches.

What exactly do you mean when you say "algorithm"?

In the broadest definition, an algorithm is a collection of instructions that tells a computer how to turn a set of facts about the world into usable information. The usable information is knowledge for humans, instructions for computers, or input for yet another algorithm, and the facts are data.

In computer science, what is an algorithm?

A process for addressing a well-defined computer issue is known as an algorithm. All parts of computer science, including artificial intelligence, databases, graphics, networking, operating systems, and security, rely on the invention and study of algorithms.

What are some algorithms examples?

An algorithm can be found in a recipe for making a cake, a method for solving a long division problem, the process of doing laundry, and the functioning of a search engine, to name a few. Visit https://www.jetlearn.com/

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Why Data Structures and Algorithms Are Important to Learn?

Array, Linked List, Stack, Queues, Searching, Sorting, Tree, Graph…   Do you have questions that why should I study all the above-complicated stuff if it has absolutely no use in real life?? Why do companies ask questions related to data structures and algorithms if it’s not useful in a daily job?? 

A lot of beginners and experienced programmers avoid learning Data Structures and Algorithms because it’s complicated and they think that there is no use of all the above stuff in real life. So before we discuss the topic we are going to throw a simple problem at you and you need to find the solution for that. 

If you need to search your roll number in 20000 pages of PDF document (roll numbers are arranged in increasing order) how would you do that? 

• If you will try to search it randomly or in a sequential manner it will take too much time. You might get frustrated after some time.
• Go to page no. 10000
• If your roll no. is not there, but all other roll no. in that page are lesser than your than
• Go to page no. 15000
• Still if your roll no. is not there. but this time all other roll no. is greater than your.
• Go to page no. 12500

Continue the same process and within 30-40 seconds you will find your roll number. Congratulations… you just have used the Binary Search algorithm unintentionally..  

This was just a simple example and you might have understood a little bit that why you need to learn data structure and algorithms and its importance in real life. There are plenty of examples you can find in your daily life. So if you think that this skill is only important to crack the interviews of product-based companies then you are totally wrong. 

From the above example, we can straightforward give two reasons to Learn Data Structure and Algorithms … 

• If you want to crack the interviews and get into the product based companies
• If you love to solve real-world complex problems.

To Crack the Interviews of the Top Product Based Companies

Do you know that under the hood all your SQL and Linux commands are algorithms and data structures? You might not realize this, but that’s how the software works. 

Data structures and algorithms play a major role in implementing software and in the hiring process as well. A lot of students and professionals have the question of why these companies’ interviews are focused on DSA instead of language/frameworks/tools specific questions? Let us explain why it happens… 

When you ask someone to make a decision for something the good one will be able to tell you “ I choose to do X because it’s better than A, B in these ways. I could have gone with C, but I felt this was a better choice because of this “. In our daily life, we always go with that person who can complete the task in a short amount of time with efficiency and using fewer resources. The same things happen with these companies. The problem faced by these companies is much harder and on a much larger scale. Software developers also have to make the right decisions when it comes to solving the problems of these companies. 

Knowledge of DS and Algo like Hashing , Tree , Graph , and various algorithms goes a long way in solving these problems efficiently and the interviewers are more interested in seeing how candidates use these tools to solve a problem. Just like a car mechanic needs the right tool to fix a car and make it run properly, a programmer needs the right tool (algorithm and data structure) to make the software run properly. So the interviewer wants to find a candidate who can apply the right set of tools to solve the given problem. . If you know the characteristics of one data structure in contrast to another you will be able to make the right decision in choosing the right data structure to solve a problem. 

Engineers working in Google, Microsoft, Facebook, Amazon-like such companies are different than others and paid higher as compared to other companies…but why? In these companies coding is just the implementation and roughly takes 20-30% of the time allotted to a project. Most of the time goes into designing things with the best and optimum algorithms to save on the company’s resources (servers, computation power, etc). This is the main reason why interviews in these companies are focused on algorithms as they want people who can think out of the box to design algorithms that can save the company thousands of dollars. Youtube, Facebook, Twitter, Instagram, GoogleMaps all these sites have the highest number of users in the world. To handle more users on these sites it requires more optimization to be done and that’s the reason product-based companies only hire candidates who can optimize their software as per user demand. 

Example: Suppose you are working in a Facebook company. You come up with an optimal solution of a problem (like sorting a list of users from India) with time complexity of O(nLogn) instead of O(n^2) and assume that n for the problem here for the company in real life scenario is 100 million (very fair assumption considering the number of users registered on Facebook exceeds 1 billion). nLogn would be 800 million, while n^2 would be 10^7 billion. In cost terms, you can see that the efficiency has been improved more than 10^7 times, which could be a huge saving in terms of server cost and time.  Now you might have got that companies want to hire a smart developer who can make the right decision and save company resources, time, and money. So before you give the solution to use a Hash table instead of List to solve a specific problem think about the big scale and all the case scenarios carefully. It can generate revenue for the company or the company can lose a huge amount of money.  

To Solve Some Real-World Complex Problems

Have you ever been scolded by your parents when you were unable to find your book or clothes in your messed-up room? Definitely yes…your parents are right when they give the advice to keep everything in the right place so the next time you can get your stuff easily. Here you need to arrange and keep everything (data) in such a structure that whenever you need to search for something you get that easily and as soon as possible. This example gives a clear idea that how important it is to arrange or structure the data in real life. 

Now take the example of a library. If you need to find a book on Set Theory from a library, you will go to the maths section first, then the Set Theory section. If these books are not organized in this manner and just distributed randomly then it will be frustrating to find a specific book. So data structures refer to the way we organize information on our computers. Computer scientists process and look for the best way we can organize the data we have, so it can be better processed based on the input provided. 

A lot of newbie programmers have this question that where we use all the stuff of data structure and algorithms in our daily life and how it’s useful in solving the real-world complex problem. We need to mention that whether you are interested in getting into the top tech giant companies or not DSA concepts still help a lot in your day-to-day life. Don’t you believe us…Let’s consider some examples… 

• Facebook (Yes… we are talking about your favourite application). Can you just imagine that your friends on Facebook, friends of friends, mutual friends they all can be represented easily by Graph? Relax….sit for a couple of moments and think again…you can apply a graph to represent friends’ connections on Facebook.
• If you need to keep a deck of cards and arrange it properly how would you do that? You will throw it randomly or you will arrange the cards one over another and from a proper deck. You can use Stack here to make a proper arrangement of cards one over another.
• If you need to search for a word in the dictionary, what would be your approach? Do you go page by page or do you open some page and if the word is not found you open a page prior to/later to one opened depending upon the order of words to the current page (Binary Search).

The first two were a good example of choosing the right data structure for a real-world problem and the third one is a good example of choosing the right algorithm to solve a specific problem in less amount time. 

All the above examples give you a clear understanding that how the organization of data is really important in our day-to-day life. Arranging data in a specific structure is really helpful in saving a lot of time and it becomes easier to manipulate or use them. The same goes for the algorithm…we all want to save our time, energy and resources. We all want to choose the best approach to solve the problems in our daily life. A lot of problems exist in the world that can take hours or days to be solved with the native solution, it also may take years ! can you imagine! watch this: Importance of Data Structure and Algorithms   We are surrounded by a lot of real-world complex problems for which no one has the solution. Observe the problems in-depth and you can help this world by giving the solution that no one has given before.  

Data structure and algorithms help in understanding the nature of the problem at a deeper level and thereby a better understanding of the world.

If you want to know more about Why Data Structures and Algorithms then you must watch this video of Mr. Sandeep Jain (CEO & Founder, GeeksforGeeks).

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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 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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Algorithm in Math – Definition with Examples

What is an algorithm, advantages of algorithms, properties of algorithms, solved examples, practice problems, frequently asked questions.

An algorithm is a step-by-step process to solve a particular problem.

Think of it as a mathematical “recipe” to get to the bottom of a problem. If you follow the steps, you’ll be able to get to the answer in no time!

Example of an algorithm:  A simple example of an algorithm you use every day is your morning routine. Say you get up at 6:30 a.m. to go to school. If you always get up, brush your teeth, drink water, go to the bathroom, and then have a bath, that can be the algorithm your body follows! Algorithms are all around us. It’s important to spot them to know how they function and later create our own.

There are a lot of procedures we apply in day-to-day life that we don’t realize are algorithms.

They include:

Tying your shoelaces

The daily timetable you follow in school

The rules to algebra formulae, like addition and subtraction

A technique you follow while playing sports

The rules to games you play with friends

Algorithms in Math

Definition of Math Algorithm An algorithm in math is a procedure, a description of a set of steps that can be used to solve a mathematical computation. For example, a step-by-step procedure used in long divisions is a common example of a mathematical algorithm.

Example of Math Algorithm:  The process of solving a mathematical problem such as, “What is 82 divided by 3?” could be achieved by doing the following algorithm:

How many times does 3 go into 8?

The answer is 2.

How many are left over now? 2

Put the 2 (tens) in front of the 3.

How many times does 3 go into 22?

The answer is 7, with a remainder of one.

And of course, the answer is 27 with a remainder of 1.

Standard Algorithm for Addition 

There are four simple steps for the standard algorithm for addition:

Step 1: Line up the numbers vertically by matching the place values.

Step 2: Add together the numbers that share the same place value, starting with the ones column.

Step 3: Write the sum below each column.

Step 4: If the sum of a column is greater than 9, carry over the tens digit to the next column.

Standard Algorithm for Subtraction 

Step 2: Subtract the numbers that share the same place value, starting with the ones column.

Step 3: Write the difference below each column.

Step 4: If the number on the top in a column is less than the number at the bottom, then regroup before subtracting.

Standard Algorithm for Multiplication

Follow the link  to check the standard algorithm of multiplication. 

Related Worksheets

Algorithms are essential because of the large variety of applications in which they are used. Understanding how algorithms work is also crucial for developing problem-solving skills and building logical reasoning. Listed below are a few advantages of an algorithm:

• The algorithm creation process allows you to look at something in a rational and calculative manner, which helps greatly when it comes to solving different kinds of problems.
• Algorithms aid in bridging the communication gap, where following the procedure will help you reach the solution needed without going over the process repeatedly. You can follow the rules set up beforehand to reach the solution quicker.
• Algorithms use a definite procedure, and by using and optimizing them, people can solve problems much quicker. 
• Algorithms are easy to debug because each step has its logical sequence.
• When we use algorithms, we can break down the problems into smaller steps or pieces, and therefore a programmer can easily convert them into an actual program.

Once you understand the foundation of algorithms, you will be able to create your own, saving yourself a lot of time. With SplashLearn’s fun activities and games, you can put your mathematical skills to the test and find algorithms in the questions you solve.

Algorithms should be used to solve three objectives:

• Correctly execute a task:  The job you want to do should be carried out with the intended results.
• Efficiently process the information given:  Your system’s time and resources should be appropriately used to understand and later resolve the problem.
• Be easily understood:  Algorithms are meant to make a job easier and, ideally, should be kept at a fundamental level of understanding.

Examples of algorithms in the real world

Many companies in the real world use algorithms to help their customers or grow their businesses and often try to improve those every day.

• YouTube : When you watch a few videos of a certain channel, you’ll notice that more and more videos by the same channel get recommended to you. It is due to YouTube’s recommendation algorithm, which collects information from your previous history to present videos of the same kind in your feed, so that you continue to watch videos on the platform.
• Social media : If you navigate to the ‘Explore’ page on Instagram, you’ll notice that many of the posts that show up are related to the ones you usually search for or like/comment on. The algorithm here identifies the posts you interact with and shows you more such posts because it believes that you enjoy such posts.
• Google : Google uses a very famous algorithm called PageRank to sort search results into an order that shows the most visited and authentic sites at the top. This algorithm considers dozens of parameters and provides the websites you would like to find fast.
• Lyft/Uber : Cab sharing companies like Lyft or Uber use positioning algorithms to help customers find vehicles close to them for an optimal experience. These global positioning algorithms also help drivers find the fastest routes to reach a certain destination. Algorithms also help such applications decide which customer they should pick or drop first.
• Facial recognition : Whenever companies require users to be verified, they can move past methods like user IDs and passwords to more secure authentications like facial recognition. Here, algorithms are used to identify a person and check if they have access to the things they want to get to.

Tips to Master Algorithms

You can master algorithms by learning how to spot them in your day-to-day life. After that, you can break down the algorithm into bite-sized steps. You might have to test it a few times to notice a pattern in the way something takes place, but once you find it, you’ll be able to spot it again and again.

Try to figure out why each step in a process takes place. Once you understand why something happens, you’ll be able to connect the dots easier and figure out the logical sequence of events. In addition, it comes in very handy for figuring out how to create algorithms for yourself. With the help of the fun activities and games on SplashLearn, you’ll be able to master the basics of algorithms in no time!

Example 1 : Write down the steps for making peanut butter and jelly sandwich.

Answer:  Steps for making a peanut butter and jelly sandwich: Step 1: Take 2 slices of bread. Step 2: Apply peanut butter on one side of a slice. Step 3: Apply jelly on one side of the other slice. Step 4: Press both the slices of bread together.

Example 2:  Write down the steps for the standard algorithm of subtraction.

Answer:  The standard algorithm for subtraction follows these 4 steps: Step 1: Line up the numbers vertically by matching the place values. Step 2: Subtract the numbers that share the same place value, starting with the ones column. Step 3: Write the difference below each column. Step 4: If the number on the top in a column is less than the number at the bottom, then regroup before subtracting.

Example 3:  Write an algorithm to know whether a number is odd or even.

Answer:  The algorithm to find whether a number is odd or even: Step 1: Divide the number by 2. Step 2: If the number is completely divisible by 2, it is even, else it is odd.

Example 4:  Write an algorithm to find the area of a rectangle.

Answer:  The algorithm to find the area of the rectangle: Step 1: Record the length of the shorter side as ‘b’. Step 2: Record the length of the longer side as ‘l’. Step 3: Area of a rectangle will be the product of ‘l’ and ‘b’.

Attend this Quiz & Test your knowledge.

Which sequence will give the correct picture of an owl?

Which sequence will give the correct algorithm for boiling water? 1. Heat the pot until water boils 2. Turn the stove on 3. Take an empty pot 4. Put the water-filled pot on the fire 5. Pour water in empty pot

What will be the first step of addition algorithm, which of the following correctly multiplies 45 ✕ 7 using the standard algorithm.

How are algorithms related to math?

An algorithm in mathematics is a procedure, a set of steps describing how a mathematical problem can be solved. For example, the step by step procedures of long division or decimal multiplication.

Where do we use algorithms in real life?

Algorithms are primarily used in computing. In our day-to-day lives, algorithms can be seen all around us, solving our daily problems. YouTube and Netflix recommendations, Google searches, GPS applications, among others, all are powered by algorithms.

What are the disadvantages of using algorithms?

Algorithms are hard to apply to bigger and more complex tasks. They are time-consuming. It is not always easy to show branching and looping in algorithms. It can be very challenging to understand complex logic applied in algorithms.

What are the important characteristics of algorithms?

The steps of algorithms should be precisely stated. The algorithm receives input and produces an output after executing a finite number of instructions.

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AI Prompt Engineering Isn’t the Future

• Oguz A. Acar

Asking the perfect question is less important than really understanding the problem you’re trying to solve.

Despite the buzz surrounding it, the prominence of prompt engineering may be fleeting. A more enduring and adaptable skill will keep enabling us to harness the potential of generative AI? It is called problem formulation — the ability to identify, analyze, and delineate problems.

Prompt engineering has taken the generative AI world by storm. The job, which entails optimizing textual input to effectively communicate with large language models, has been hailed by World Economic Forum as the number one “job of the future” while Open AI CEO Sam Altman characterized it as an “amazingly high-leveraged skill.” Social media brims with a new wave of influencers showcasing “magic prompts” and pledging amazing outcomes.

• Oguz A. Acar is a Chair in Marketing at King’s Business School, King’s College London.

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What Are Algorithms & Why Are They Important?

What is an algorithm.

An algorithm is a set of step-by-step procedures, or a set of rules to follow, for completing a specific task or solving a particular problem. Algorithms are all around us. The recipe for baking a cake, the method we use to solve a long division problem, and the process of doing laundry are all examples of an algorithm. Here’s what baking a cake might look like, written out as a list of instructions, just like an algorithm:

• Preheat the oven
• Gather the ingredients
• Measure out the ingredients
• Mix together the ingredients to make the batter
• Grease a pan
• Pour the batter into the pan
• Put the pan in the oven
• Set a timer
• When the timer goes off, take the pan out of the oven

Algorithmic programming is all about writing a set of rules that instruct the computer how to perform a task. A computer program is essentially an algorithm that tells the computer what specific steps to execute, in what specific order, in order to carry out a specific task. Algorithms are written using particular syntax, depending on the programming language being used.

Types of Algorithms

Algorithms are classified based on the concepts that they use to accomplish a task. While there are many types of algorithms, the most fundamental types of computer science algorithms are:

• Divide and conquer algorithms – divide the problem into smaller subproblems of the same type; solve those smaller problems, and combine those solutions to solve the original problem.
• Brute force algorithms – try all possible solutions until a satisfactory solution is found.
• Randomized algorithms – use a random number at least once during the computation to find a solution to the problem.
• Greedy algorithms – find an optimal solution at the local level with the intent of finding an optimal solution for the whole problem.
• Recursive algorithms – solve the lowest and simplest version of a problem to then solve increasingly larger versions of the problem until the solution to the original problem is found.
• Backtracking algorithms – divide the problem into subproblems, each which can be attempted to be solved; however, if the desired solution is not reached, move backwards in the problem until a path is found that moves it forward.
• Dynamic programming algorithms – break a complex problem into a collection of simpler subproblems, then solve each of those subproblems only once, storing their solution for future use instead of re-computing their solutions.

Example of an Algorithm – Solving a Rubik’s Cube

There are a number of different algorithms, from simple to very complicated, that exist for solving a Rubik’s cube. Below is just one simple algorithm. First, let’s specify a notation to use (similar to picking a programming language).

Each of the six faces of a Rubik’s cube can be represented by the first letter of their name:

Each face can be turned in three different ways/directions. Using U as an example, these are represented as:

• U – clockwise quarter-turn of the upper face
• U’ – counter-clockwise quarter-turn of the upper face
• U2 – half turn in either direction of the upper face

Now, let’s go through the steps in the algorithm to solve a Rubik’s Cube. Feel free to grab one of your own and follow along!

Step 1: The Cross

First, flip some edges so that there is a white cross on the upper face. Apply the following turns:

• F, R’, D’, R, F2, R’, U, R, U’, R’, R2, L2, U2, R2, L2.

The cross is now solved.

Step 2: The White Corners

The edges on the white face are now complete, but the corners remain. Depending on where the white-orange-green corner is in the puzzle, apply one of the following series of turns:

• Bottom: R’, D’, R, D (repeat until the corner moves to its correct place)
• Top: R’, D’, R, D (this moves the corner to the bottom; then, follow the above instructions)

Step 3: Middle Layer Edges

• Flip the cube so that the white is on the bottom.
• Look for an edge that is on the top face and doesn’t have yellow on it.
• Perform a U-turn so that the color on the front face of the edge matches with the center.
• Depending on the direction that the edge could go, apply one of the following series of turns: — Left: U’, L’, U, L, U, F, U’, F’ — Right: U, R, U’, R’, U’, F’, U, F)

Step 4: Yellow Cross

• Apply the following turns, until a yellow cross on the face appears with the yellow center: F, R, U, R’, U’, F’.
• If there is an “L” shape, where the two yellow pieces showing are adjacent to each other, apply the following turns: F, U, R, U’, R’, F’.
• If there is a “Line” shape, which is horizontal, apply the following turns: F, R, U, R’, U’, F’.

Step 5: Sune and Antisune

• Look at the face with the yellow center.
• Depending on the below contingencies, apply one of the following series of turns:
• If there is only one oriented corner: R, U, R’, U, R, U2, R’ (repeat until the desired position is attained)
• There is one oriented corner and one right-facing corner: U2, R, U2, R’, U’, R, U’, R’

Step 6: Finishing the puzzle

• Look for sets of “headlights” (two stickers of the same color in the same row, separated by a sticker of a different color).
• Depending on how many there are, apply one of the following series of turns:
• If there are a set of headlights on each side: R, U’, R, U, R, U, R, U’, R’, U’, R2
• Otherwise: R’, F, R’, B2, R, F’, R’, B2, R2

Sorting Algorithms

A sorting algorithm is an algorithm that puts elements of a list in a certain order, usually in numerical or lexicographical order. Sorting is often an important first step in algorithms that solves more complex problems. There are a large number of sorting algorithms, each with their own benefits and costs. Below, we will focus on some of the more famous sorting algorithms.

Linear sort

Find the smallest element in the list to be sorted, add it to a new list, and remove it from the original list. Repeat this until the original list is empty.

Bubble sort

Compare the first two elements in the list, and if the first is greater than the second, swap them. Repeat this with every pair of adjacent elements in the list. Then, repeat this process until the list is fully sorted.

Insertion sort

Compare each element in the list to all the prior elements until a smaller element is found. Swap these two elements. Repeat this process until the list is fully sorted.

Where Algorithms are Used in Computer Science?

Algorithms are used in every part of computer science. They form the field’s backbone. In computer science, an algorithm gives the computer a specific set of instructions, which allows the computer to do everything, be it running a calculator or running a rocket. Computer programs are, at their core, algorithms written in programming languages that the computer can understand. Computer algorithms play a big role in how social media works: which posts show up, which ads are seen, and so on. These decisions are all made by algorithms. Google’s programmers use algorithms to optimize searches, predict what users are going to type, and more. In problem-solving, a big part of computer programming is knowing how to formulate an algorithm.

Why are Algorithms Important to Understand?

Algorithmic thinking, or the ability to define clear steps to solve a problem, is crucial in many different fields. Even if we’re not conscious of it, we use algorithms and algorithmic thinking all the time. Algorithmic thinking allows students to break down problems and conceptualize solutions in terms of discrete steps. Being able to understand and implement an algorithm requires students to practice structured thinking and reasoning abilities.

This is a guest post by junilearning.com

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