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Algorithm is a set of instructions which tell us how to solve a problem. It's the blueprint for solving any type of computational problems.

An algorithm can be defined as a logical method or set of instructions written in any programming language i.e., a set of instructions to solve any concrete problem in less time with accuracy and better approach is always preferred against the other one, algorithms are also known as computer programs or application software, algorithms can be used for solving problems that require special attention or need optimum approach to reach certain level.

The complexity or the time taken by an algorithm to run may vary according to its nature and it can range from simple to complex one as well as from small size computing problems.

Here are various types of problem that needs to be solved algorithmically which we can help with.

- Recursive algorithms (breadth first search, depth first search)
- dynamic programming algorithms (Knapsack Problem, Optimal Substructure problem)
- data structure problems like sorting (merge sort, quick sort), searching etc. ,
- Graph related problems like graph coloring (4-coloring), shortest path, maximum flow, minimum spanning trees, all pairs shortest paths, maximum matching. ,
- geometric problems like hidden surface removal (Marching cubes), visibility problems, collision detection,
- character recognition such as OCR (optical character recognition) and handwritten digit recognition,
- computational geometry problems like convex hull, triangulation or polygon triangulation etc.,
- numerical methods for large scale computation problems in science and engineering fields such as optimization of nonlinear systems of equations, differential equations (linear equations and system of linear equations, polar coordinates system), ordinary differential equations, partial differential equations, discrete dynamical systems.

An algorithm is a step by step procedure which take input data using an input device such as keyboard or mouse to produce output data on the display screen or any output device connected to a computer.

The algorithms must be deterministic in nature and produce only one output from any given input(s). If we use these set of instructions or steps again and again with same inputs each time we get the same results every time. The procedure follows step by step rules which can be written in any programming language like C++, Objective-C, Java, Visual Basic etc., or can be recorded as part of application program on any computers such as Linux system or Macintosh systems, embedded (real time)based microprocessor control based system may execute these series of procedures.

Experts represent the problem by means of flow charts, diagrams and matrices understand the nature of the problem and ask questions to uncover hidden issues, analyze the data-information gathered, design a solution or algorithm to solve the problem then put this procedure in computer language using any text editor.

If we want to develop a good understanding of algorithms then we must know how exactly computer do their work.

Computer as an information processing device can be modeled as:

+ Input Device such as keyboard, mouse etc., connected to computer system containing two main hardware units CPU (central processing unit), memory which stores all the programs and data for computation at present time and also some history of operations done by it. This central processing unit is like brain of computer system where actual computations are executed (programs). Therefore good programming practices should be adopted to develop an algorithm in order to improve the efficiency and performance of our algorithms.

+ Output device such as display screen, printer etc., which output any data from computer system for human beings see and analyze them or use it further for some other purposes.

While developing an algorithm we must keep in mind that whatever input data we provide at input unit (regardless of its nature) is converted into binary form by doing some computations on inputs before these are stored in memory means while entering actual values into memory, a conversion is done from human understandable value like 2300 or 1234 into computer internal binary number (object representation) along with storing this number, also at the time of retrieving this particular number again then after retrieving it will again be converted back to human understandable value. Therefore computer system actually works in binary number only and not in real world values which we see here.

Mathematically an algorithm is a sequence of precise well-defined steps or instructions (sets of rules, procedures) to achieve some predefined objective or goals within a finite time using defined input data to produce exact output results when these procedures are applied repeatedly with same input data each time the same results will come out after execution of algorithms each time .

As discussed previously every program has following two parts: Program specification & design and Program implementation .

- The Specification and design part for any programming language i.e., C++, Java includes at least three sections namely problem analysis, solution design & algorithm development.
- Problem analysis section deals with gathering important information or data about the problem what kind of operations we have to perform on given input data in order to achieve required results. If a user has already solved this type of problems before then he can reuse the existing algorithms for solving current problem if it is not possible then he performs his own analysis and prepares a plan for designing an algorithm or program. In this part we represent all these activities through flow charts diagrams etc., means here will be no codes written till now (we may know that how exactly our programs will work). We determine which operations need to be performed for achieving required objective and also their sequence of execution over given input data.
- Solution design section deals with designing an algorithm to solve the concrete problem by considering the characteristics of given input data like size, range etc. Then we determine which operations need to be performed for achieving required objective using these inputs and also their sequence of execution over given input data.
- In implementation section when our main aim is to develop a program in some programming language then here we will use that specific language as discussed previously that every algorithm must have a certain instruction or set of instructions written in any programming language i.e., C++, java or any other high level programming languages, because directly writing actual codes (instructions) makes more sense than describing solution design in natural language means without coding them into dedicated programming languages such as C++, Java etc. we will not be able to write these algorithms in any particular programming language.

While designing algorithm or writing codes for it we need to use specific data table (looks like a matrix), every element of this table representing some input/output conditions and also what operations are performed on given inputs under that condition, specifically while entering actual values into memory means at the time of retrieving a stored value again then after retrieving it will again be converted back to human understandable value same operations need to be applied. After having both input and output data of all required conditions further using certain set of instructions (set of rules) appropriate operations can be performed on them leading desired results.

In the above simple discussion, we only considered basic concepts involved while designing algorithms and writing codes for them without considering any complexities involved, in reality these things become more complex when we will add complexity to our programs.

As discussed previously that the main advantage of using algorithms is that it provides required solutions in less time with less memory space and also gives us confidence about the correctness of program design, if a problem can be solved by applying best possible algorithm then it becomes most desirable option so every programmer always tries to apply his knowledge about algorithms during programming process but this does not mean that all problems are like this because sometimes it is really difficult to find out an exact solution for given problem or it may require too many computing power which makes impossible to apply these types of techniques for solving such kind of problems.

In the real world we always deal with incomplete information about problem i.e., we never have full details about the input data or output values so here to solve this type of problems are also some algorithms that do not require complete information about inputs and outputs while solving a concrete problem like these algorithms are called partial knowledge based algorithm or heuristic approach programming.

For a successful completion of any program there is always an essential need to select up right set of algorithms because if wrong choice is made then final result may be satisfactory but it will produce unacceptable inaccurate results after running for long time period means even though code works well in short time frame but its accuracy can be questionable over longer run. To avoid this type is necessary to analyze such situations and then select the most suitable algorithm that offers accuracy with minimum computing time or memory consumption.

Previously, we have discussed algorithms for solving problems of finite character but if there are some infinite problems then they may not be solved by using any specific set of instructions because after executing a specific instruction further where to execute next is uncertain so here we have to apply different approach to handle such type of problem i.e., the concept of recursion is also used in place of iterative process, which requires repeating same operation over given input data till certain condition is satisfied.

In real world many business houses have their own developed procedures to manage their day-to-day activities but still they also use some kind of algorithms to store data into databases so that it becomes more convenient for them while retrieving required data easily without wasting much time. Same way programmers use algorithms while developing program code i.e., multi-player game playing domains are an example where immense amount of computing power is applied by programmers during coding using more-than-one processing engines to make a game challenging for users with more number of options.

Recently, this subject has emerged with the name of medical algorithms. Medical algorithms are computer implemented applications that use clinical guidelines and data to make decisions which can be used in diagnosis or follow up care of patients. This field is still an emerging technology and there are ongoing controversies about how far it will aid health care professionals in making appropriate decisions when treating patients. The controversy is mainly due to lack of experience using these computer programs, since the main purpose of these methods is not only to save money but also to provide better health care services by reducing human biases. Some say it may improve healthcare services while others say it may reduce the quality of medical services.

There are many other uses for algorithms in different fields, some are listed below:-

Algorithms (in communication assignment help) - can be used to create a secure and private channel between two communicating parties over a network even if the network is not safe from unauthorized access or eavesdropping. Cryptographic applications like Public Key Encryption are based on mathematical algorithms that work with digital data. In this type of encryption, one party (the sender) encrypts plaintext message using public key of receiver which can be decrypted by using its corresponding private key. This ensures security since only the intended recipient can decrypt the message sent by him/her. One more example could help us understand how algorithms are applied in communications field. Voice over Internet Protocol (VOIP) is used for sending voice data across the internet in packets rather than using traditional PSTN lines or cell networks; it may also be called as a form of digital telephony. The algorithms used to implement VOIP are implemented as software running on one or more servers, and they manage the user's voice traffic on the network by performing various set functions.

**Read more:** computer network and communications assignment help

Algorithms in Engineering assignment help: Currently many engineering professionals use Computer-aided design (CAD) software based on algorithms to create architectural blueprints, electrical circuit diagrams and any other type of engineering drawings. These programs allow the users to easily manipulate complex objects like doors, windows, etc., that can be represented using solid modeling techniques. There are various other applications of algorithms in engineering such as:

- For simulation and modeling of physical systems.

In finance assignment help, algorithms learn the market price for a good or service over time, based on the demands that cause them to have variable supply due to unplanned events like floods, drought etc., so with this demand-supply fluctuations if we know the algorithm used by regulatory authorities then predicting prices becomes very easy. There are many more uses of algorithms in stock trading where they can be used to predict stock movements and predict asset prices so that one can invest accordingly at right time which will help make huge amounts of money.

In short, any kind of activity that involves decision making process has room for implementation of algorithms while trying to make it more accurate, efficient and effective.

In this assignment we will discuss about few basic algorithms such as:

-Insertion Algorithm for Singly Linked List.

-LinkedListMaximum() method of Java ArrayList class

-Linear Algebraic Algorithm to solve system of linear equations Ax = b using Gaussian Elimination Method which is similar to LU factorization method and then use back substitution method to solve the system of linear equations. Check do my math homework services

-When we are given an array of integers, how do we find out whether there exists any missing element in the given array or not?

Algorithms are still in their infancy but they have already started making a huge impact on our lives by taking over most of the decision-making process using computer programs which may or may not also be based on **artificial intelligence **(AI). As we research further new uses for algorithms will emerge and these will surely change the way people live and interact with each other.

Algorithms can be defined as an effective method to reach a certain goal in finite number of steps. They are applicable to every field where making rational decisions is required like in medical science, engineering etc.

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