What is An Algorithm? Definition, Types, Characteristics

Use of The Algorithms

Algorithms are essential to many disciplines because they offer organized, practical answers to challenging issues. Here are a few significant applications of algorithms in various fields:

1. Data Analysis and Machine Learning

Algorithms are used in data analysis and machine learning to find patterns in big datasets and forecast outcomes. Thanks to machine learning methods like support vector machines, decision trees, and neural networks, computers can learn from data and improve over time. These techniques are essential for recommendation systems, natural language processing, and picture recognition.

2. Cryptography & Security

Cryptography algorithms safeguard data using encryption and decryption techniques, guaranteeing safe data storage and communication. Algorithms such as SHA-256, AES, and RSA are commonly employed in data integrity maintenance, user authentication, and sensitive information security. These algorithms comprise the foundation of cybersecurity measures used in secure communications, data encryption, and online transactions.

3. Information Retrieval and Search Engines

Search engines can efficiently index and retrieve pertinent information thanks to search algorithms such as PageRank and Hummingbird. By prioritizing web pages according to their significance and relevancy, these algorithms assist users in locating the most relevant information available online. Effective search algorithms are necessary to manage the enormous volume of online information.

4. Optimization problems

Optimization methods are utilized to select the optimal answer from various options. In various industries, including banking, engineering, logistics, and artificial intelligence, sophisticated issues are resolved using methods like gradient descent, linear programming, and genetic algorithms. These algorithms increase productivity, reduce expenses, and optimize resources for operations and decision-making.

5. Genomics and medical diagnostics

Due to their ability to analyze medical images, forecast disease outbreaks, and recognize genetic changes, algorithms are indispensable in medical diagnostics. Personalized medicine has been transformed by machine learning algorithms, in particular, which enable the creation of customized treatment regimens based on each patient's unique genetic profile. Additionally, algorithms help to speed up the sequencing and interpretation of genomic data, improving biotechnology and genomics research.

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Characteristics of An Algorithm

Now that we have understood what is an algorithm, let's explore the important factors that impact an algorithm's effectiveness:

1. Finiteness

An algorithm must always have a finite number of steps before it ends. When the operation is finished, it must have a defined endpoint or output and not enter an endless loop.

2. Definiteness

An algorithm needs to have exact definitions for each step. Clear and straightforward directions ensure that every step is understood and can be taken easily.

3. Input

An algorithm requires one or more inputs. The values supplied to the algorithm before its processing are known as inputs. These inputs come from a predetermined range of acceptable values.

4. Output

An algorithm must produce one or more outputs. The output is the algorithm's outcome after every step has been completed. The relationship between the input and the result should be clear.

5. Effectiveness

An algorithm's stages must be sufficiently straightforward to be carried out in a finite time utilizing fundamental operations. With the resources at hand, every operation in the algorithm should be doable and practicable.

6. Generality

Rather than being limited to a single particular case, an algorithm should be able to solve a group of issues. It should offer a generic fix that manages a variety of inputs inside a predetermined range or domain.

7. Achievable

A simple, practical, and basic algorithm is good when working within the limits of available resources. It should not rely on futuristic technologies or resources beyond what is currently accessible.

8. Cross-language Compatible

The algorithm must have small and simple instructions that can be implemented in any programming language. The results should be consistent and meet expectations regardless of the language used.

9. Precise and Straightforward

Every step in the algorithm should be well-defined and straightforward. To guarantee accuracy and consistency, there has to be only one interpretation for each instruction.

10. Specified Inputs and Outputs

The algorithm must clearly define the required inputs, whether optional or mandatory. It should specify the expected outputs and produce at least one, keeping them well-defined.

Properties of Algorithm

• Input Flexibility: Depending on the design, the algorithm may accept zero or more inputs.
• Output Generation: The algorithm should produce at least one output upon completion.
• Deterministic Behavior: The algorithm must produce the same output for identical inputs every time it is run.
• Finite Termination: The algorithm must always terminate after a finite number of steps.
• Effective Steps: Each step in the algorithm must be meaningful and perform a specific task. This task must contribute to achieving the desired outcome.

Types of Algorithms

1. Brute Force Algorithm: A straightforward approach that exhaustively tries all possible solutions. It is suitable for small problem instances but may become impractical for larger ones due to its high time complexity.

2. Recursive Algorithm: A method that breaks a problem into smaller, similar subproblems and repeatedly applies itself to solve them until reaching a base case, making it effective for tasks with recursive structures.

3. Encryption Algorithm: Utilized to transform data into a secure, unreadable form using cryptographic techniques, ensuring confidentiality and privacy in digital communications and transactions.

4. Backtracking Algorithm: A trial-and-error technique used to explore potential solutions by undoing choices when they lead to an incorrect outcome, commonly employed in puzzles and optimization problems.

5. Searching Algorithm: Designed to find a specific target within a dataset, enabling efficient retrieval of information from sorted or unsorted collections.

6. Sorting Algorithm: Aimed at arranging elements in a specific order, like numerical or alphabetical, to enhance data organization and retrieval.

7. Hashing Algorithm: Converts data into a fixed-size hash value, enabling rapid data access and retrieval in hash tables, commonly used in databases and password storage.

8. Divide and Conquer Algorithm: Breaks a complex problem into smaller subproblems, solves them independently, and then combines their solutions to address the original problem effectively.

9. Greedy Algorithm: Makes locally optimal choices at each step to find a global optimum. It is helpful for optimization problems but may not always lead to the best solution.

10. Dynamic Programming Algorithm: Stores and reuses intermediate results to avoid redundant computations, enhancing the efficiency of solving complex problems.

11. Randomized Algorithm: Utilizes randomness in its steps to achieve a solution, often used in situations where an approximate or probabilistic answer suffices.

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How to Write An Algorithm?

There are no well-defined standards for writing algorithms. However, this is a resource-dependent problem, and algorithms are never written with a specific programming language in mind.

While there are no strict standards for writing algorithms, most programming languages typically use common code constructs (e.g., loops like for, while, and flow control like if-else).

Some Essential Pre-Steps Before Writing an Algorithm: The algorithm is written to solve the problem effectively using these parameters.

• A clear problem definition is needed to know what needs to be solved.
• Consider constraints that may impact the solution.
• A clear understanding of the input required to solve the problem.
• Definition of the expected output.
• Ensure that the solution fits within the given constraints.

Algorithm Writing Through an Example 

Now, we will use an example to figure out how to write algorithms.

Problem: Create an algorithm that multiplies two numbers and displays the output.

1. Pre-Steps:

Before designing the algorithm, we need to understand the problem and the basic requirements:

• Step 1: Understand the Problem
• Clearly define the problem. In this case, we are tasked with multiplying two numbers and displaying the result.
• Step 2: Identify the Inputs and Outputs
• Inputs: Two numbers (x and y).
• Output: The result of the multiplication (z).
• Step 3: Identify Constraints
• Ensure the x and y values are within the allowable range for multiplication (e.g., integer values).

2. Design the Algorithm:

Now that the prerequisites are understood, we move on to designing the algorithm:

• Step 1: Define the Variables
• Declare the variables needed for the algorithm: x, y, and z.
• Step 2: Specify the Operations
• Define the process of multiplying the two numbers and storing the result.

3. Implement the Algorithm:

After designing the algorithm, we implement the steps to solve the problem.

• Step 3.1: Get Input
• Accept the values for x and y (either from user input or predefined values).
• Step 3.2: Multiply the Numbers
• Multiply x and y and store the result in z.
• Step 3.3: Output the Result
• Print or display the value of z.

4. Output:

Display the result.

Show the value of z, the product of x and y

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How to Analyze An Algorithm?

Before answering how to analyze an algorithm, one must know why to do so. The simplest reason is to find an algorithm's properties to assess its relevance for different applications or compare it to other algorithms. Furthermore, analyzing an algorithm can improve our understanding and offer well-informed suggestions for enhancements. Algorithms typically become shorter, clearer, and more impressive throughout the analysis process.

We analyze the running time of an algorithm while it is being analyzed and check its relevance. Following steps:

• The complete algorithm implementation
• Calculating the amount of time needed for each key task
• Determining unknown numbers to characterize the frequency of execution
• Creating a realistic program input model
• Analyzing unknown quantities on the assumption that the input is modeled
• Multiplying time by operation frequency and totaling all products yields the overall running time

Examples of Algorithm

There are many day-to-day and industrial examples of algorithms. It can range from simply deciding what to wear to some mathematical problem-solving. Some examples are as follows:

1. Searching for an Item in a List (Linear Search Algorithm)

Problem: Find if a specific item exists in a list.
Steps:

1. Start
2. Take the list and the item to search for as inputs
3. Compare each item in the list with the target item
4. If a match is found, return its position
5. If the end of the list is reached without finding the item, return "Not Found."
6. Stop

2. Sorting Numbers (Bubble Sort Algorithm)

Problem: Sort a list of numbers in ascending order.
Steps:

1. Start
2. Take the list of numbers as input
3. Compare adjacent numbers in the list
4. Swap them if they are in the wrong order
5. Repeat steps 3–4 until no swaps are needed
6. Return the sorted list
7. Stop

3. Calculating the Factorial of a Number

Problem: Compute the factorial of a number n (n! = n×(n−1)×(n−2)…×1).
Steps:

1. Start.
2. Input n
3. Initialize a variable result = 1
4. For i = 1 to n, multiply the result by i
5. Output result
6. Stop

4. Finding the Greatest Common Divisor (GCD)

Problem: Find the GCD of two numbers using the Euclidean Algorithm.
Steps:

1. Start.
2. Input two numbers, a and b
3. While b≠0:

• Replace a with b
• Replace b with a%b (remainder of a divided by b)

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Factors of An Algorithm

When exploring what is an algorithm, it's essential to understand the factors that define its efficiency and effectiveness. Mastering these factors helps optimize solutions for real-world applications.

• Finiteness

An algorithm must always have a finite number of steps before it ends. When the operation is finished, it must have a defined endpoint or output and not enter an endless loop.

• Definiteness

An algorithm needs exact definitions for each step. Clear and straightforward directions ensure that every step is understood and can be completed easily.

• Input

An algorithm requires one or more inputs. The values supplied to the algorithm before its processing are known as inputs. These inputs come from a predetermined range of acceptable values.

• Output

An algorithm must produce one or more outputs. The output is the algorithm's outcome after every step has been completed. The relationship between the input and the result should be clear.

• Effectiveness

An algorithm's stages must be sufficiently straightforward to be carried out in a finite time using fundamental operations. With the resources available, every operation in the algorithm should be doable and practicable.

• Generality

Rather than being limited to a single particular case, an algorithm should be able to solve a group of issues. It should offer a generic fix that manages a variety of inputs inside a predetermined range or domain.

• Feasibility

It shows that an algorithm is practical and can be implemented with available resources. An algorithm should be structured so that you make no significant changes when you redefine the algorithm.

• Time Complexity

Time complexity measures the amount of time an algorithm takes to complete as a function of the size of its input. It helps us analyze the algorithm's efficiency and predicts how the runtime will grow as the input size increases.

• Space Complexity

This one measures the amount of memory (space) an algorithm uses as a function of the size of its input. Space complexity consists of the memory required for input, output, and auxiliary (temporary) variables.

• Independent

The algorithm is language-independent and relies only on logical constructs. If an algorithm is simple, it is simple to understand.

• Parallel Computing

This feature divides tasks into smaller sub-tasks for parallel execution on multiple processors. This greatly improves performance and reduces execution time. This one is especially suitable for independent algorithms without sequential processing.

• Performance

It measures how well the algorithm works, including its correctness. An algorithm's correctness is reached when the inputs produce the desired output, indicating that it was designed correctly. It also means the algorithm's analysis has been completed correctly, achieving up-to-the-mark performance.

• Processing Steps

This refers to the sequence of steps in the algorithm. Also called modularity, it was perfectly designed for the algorithm if you are given a problem and break it down into small modules or small steps. This is an important step that helps to maintain clarity throughout the process.

• Unambiguous

Each step in the algorithm is clear and has one meaning. This determines an algorithm's robustness, i.e., its ability to define the problem clearly.

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How to Represent An Algorithm?

We can express an algorithm in many ways, including

Natural Language

Natural language is a widely acceptable option for representing algorithms. Its popularity is because it can be understood by all, irrespective of their programming background. However, using natural language also has certain drawbacks, as it can sometimes be very vague due to a lack of predefined structure.

Flow Charts

Flow charts are popular among computer scientists and programmers. It is a more formal way to put forward an algorithm. It is a diagram with spheres or boxes connected by arrows.

Pseudocode

The majority of algorithms eventually turn into computer code. Before that, programmers frequently prefer to express algorithms in pseudocode, code that uses all the language's frameworks but doesn't execute anywhere.

Programming Languages

After you plan an algorithm using any of the above methods or a combination, you can transform it into running code. Programmers and coders know how to translate an algorithm idea into any general-purpose programming language.

Qualities of a Good Algorithm

• Efficiency: A good algorithm should perform its task quickly and use minimal resources.
• Correctness: It must produce accurate output for all valid inputs.
• Clarity: The algorithm should be easy to understand and comprehend, making it maintainable and modifiable.
• Scalability: It should handle larger data sets and problem sizes without significantly decreasing performance.
• Reliability: The algorithm should consistently deliver correct results under different conditions and environments.
• Optimality: Striving for the most efficient solution within the given problem constraints.
• Robustness: Capable of handling unexpected inputs or errors gracefully without crashing.
• Adaptability: Ideally, it can be applied to a range of related problems with minimal adjustments.
• Simplicity: Keeping the algorithm simple while meeting its requirements, avoiding unnecessary complexity.

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The Complexity of An Algorithm

The algorithm's performance can be measured in two ways:

Time Complexity

The time required to complete an algorithm's execution is called time complexity. The big O notation is used to represent an algorithm's time complexity. In this case, the asymptotic notation for describing time complexity is a big O notation. The time complexity is calculated primarily by counting the steps required to complete the execution. Let us look at an example of time complexity.

The time complexity of the loop statement in the preceding code is at least n, and as the value of n escalates, so does the time complexity. The code's complexity, i.e., returns mul, will be constant because its value is not dependent on the importance of n and will provide the result in a single step. The worst-time complexity is generally considered because it is the maximum time required for any given input size.

Space Complexity

The amount of space an algorithm requires to solve a problem and produce an output is called its space complexity. Space complexity, like time complexity, is expressed in big O notation.

The space is required for an algorithm for the following reasons:

1. To store program instructions.
2. To store track of constant values.
3. To store track of variable values.
4. To store track of function calls, jumping statements, and so on.

Space Complexity = Auxiliary Space + Input Size

Advantages and Disadvantages of Algorithms

Next Steps

In this "What is an algorithm" tutorial, you learned what an algorithm is, its characteristics, properties, and advantages and disadvantages. After that, you examine why you need algorithms, how to write them, and how important they are. After you learned about the approaches and factors of an algorithm, you learned about the complexity and types of algorithms.

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FAQs

1. Why is it called an algorithm?

The term algorithm comes from the Medieval Latin term algorism. It refers to the rules for performing arithmetic using the Hindu-Arabic numeral system. 

2. Who is the father of the algorithm?

Muhammad ibn Musa Al-Khwarizmi, a 9th-century Muslim scientist, is the father of algorithms. He invented algorithms and algebra, which are steps in solving problems.

3. Why write an algorithm?

We write algorithms to solve problems using precise instructions that a computer can follow. 

4. Why name algorithm?

Al-Khwarizmi's work introduced Hindu-Arabic numerals, the ten symbols we use today, to Western mathematicians. He also laid the foundation for the concept of algorithms. Originally, the word algorithm meant the "Arabic" system of numbers (including zero). The word algorithm was imported into English via French and Latin.

5. What is the theory of algorithms?

The theory of algorithms involves their structure and complexity. It comprises metric (quantitative) and descriptive (qualitative) theories. Descriptive theory focuses on the correspondence between the initial data and the algorithm's output. Metric theory concerns the algorithm's complexity and the calculations it defines.