An algorithm is a step-by-step procedure that defines a set of instructions that must be carried out in a specific order to produce the desired result. Algorithms are generally developed independently of underlying languages, which means that an algorithm can be implemented in more than one programming language. Unambiguity, fineness, effectiveness, and language independence are some of the characteristics of an algorithm. The scalability and performance of an algorithm are the primary factors that contribute to its importance.
What is an Algorithm?
- An algorithm is a set of commands that must be followed for a computer to perform calculations or other problem-solving operations.
- According to its formal definition, an algorithm is a finite set of instructions carried out in a specific order to perform a particular task.
- It is not the entire program or code; it is simple logic to a problem represented as an informal description in the form of a flowchart or pseudocode.
- Problem: A problem can be defined as a real-world problem or real-world instance problem for which you need to develop a program or set of instructions. An algorithm is a set of instructions.
- Algorithm: An algorithm is defined as a step-by-step process that will be designed for a problem.
- Input: After designing an algorithm, the algorithm is given the necessary and desired inputs.
- Processing unit: The input will be passed to the processing unit, producing the desired output.
- Output: The outcome or result of the program is referred to as the output.
After defining what an algorithm is, you will now look at algorithm characteristics.
Characteristics of an Algorithm
An algorithm has the following characteristics:
- Input: An algorithm requires some input values. An algorithm can be given a value other than 0 as input.
- Output: At the end of an algorithm, you will have one or more outcomes.
- Unambiguity: A perfect algorithm is defined as unambiguous, which means that its instructions should be clear and straightforward.
- Finiteness: An algorithm must be finite. Finiteness in this context means that the algorithm should have a limited number of instructions, i.e., the instructions should be countable.
- Effectiveness: Because each instruction in an algorithm affects the overall process, it should be adequate.
- Language independence: An algorithm must be language-independent, which means that its instructions can be implemented in any language and produce the same results.
Moving on in this What is an Algorithm tutorial, you will look at why you need an algorithm.
Why Do You Need an Algorithm?
You require algorithms for the following reasons:
It aids in your understanding of scalability. When you have a sizable real-world problem, you must break it down into small steps to analyze it quickly.
The real world is challenging to break down into smaller steps. If a problem can be easily divided into smaller steps, it indicates that the problem is feasible.
After understanding what is an algorithm, why you need an algorithm, you will look at how to write one using an example.
How to Write an Algorithm?
- There are no well-defined standards for writing algorithms. It is, however, a problem that is resource-dependent. Algorithms are never written with a specific programming language in mind.
- As you all know, basic code constructs such as loops like do, for, while, all programming languages share flow control such as if-else, and so on. An algorithm can be written using these common constructs.
- Algorithms are typically written in a step-by-step fashion, but this is not always the case. Algorithm writing is a process that occurs after the problem domain has been well-defined. That is, you must be aware of the problem domain for which you are developing a solution.
Now, use an example to learn how to write algorithms.
Problem: Create an algorithm that multiplies two numbers and displays the output.
Step 1 − Start
Step 2 − declare three integers x, y & z
Step 3 − define values of x & y
Step 4 − multiply values of x & y
Step 5 − store result of step 4 to z
Step 6 − print z
Step 7 − Stop
Algorithms instruct programmers on how to write code. In addition, the algorithm can be written as:
Step 1 − Start mul
Step 2 − get values of x & y
Step 3 − z ← x * y
Step 4 − display z
Step 5 − Stop
In algorithm design and analysis, the second method is typically used to describe an algorithm. It allows the analyst to analyze the algorithm while ignoring all unwanted definitions easily. They can see which operations are being used and how the process is progressing. It is optional to write step numbers. To solve a given problem, you create an algorithm. A problem can be solved in a variety of ways.
As a result, many solution algorithms for a given problem can be derived. The following step is to evaluate the proposed solution algorithms and implement the most appropriate solution.
As you progress through this "what is an Algorithm" tutorial, you will learn about some of the components of an algorithm.
Factors of an Algorithm
The following are the factors to consider when designing an algorithm:
- Modularity: This feature was perfectly designed for the algorithm if you are given a problem and break it down into small-small modules or small-small steps, which is a basic definition of an algorithm.
- Correctness: An algorithm's correctness is defined as when the given inputs produce the desired output, indicating that the algorithm was designed correctly. An algorithm's analysis has been completed correctly.
- Maintainability: It means that the algorithm should be designed in a straightforward, structured way so that when you redefine the algorithm, no significant changes are made to the algorithm.
- Functionality: It takes into account various logical steps to solve a real-world problem.
- Robustness: Robustness refers to an algorithm's ability to define your problem clearly.
- User-friendly: If the algorithm is difficult to understand, the designer will not explain it to the programmer.
- Simplicity: If an algorithm is simple, it is simple to understand.
- Extensibility: Your algorithm should be extensible if another algorithm designer or programmer wants to use it.
You will now see why an algorithm is so essential after understanding some of its components.
Importance of an Algorithm
There are two factors in which the algorithm is fundamental:
When you are given a real-world problem, you must break it down into smaller modules. To deconstruct the problem, you must first understand all of its theoretical aspects.
As you all know, theory cannot be completed without practical application. As a result, the significance of algorithms can be considered both theoretically and practically.
As you progress through this "what is an algorthim" tutorial, you will see algorithmic approaches.
Approaches of an Algorithm
Following consideration of both the theoretical and practical importance of designing an algorithm, the following approaches were used:
Brute Force Algorithm
This algorithm uses the general logic structure to design an algorithm. It is also called an exhaustive search algorithm because it exhausts all possibilities to provide the required solution. There are two kinds of such algorithms:
- Optimizing: Finding all possible solutions to a problem and then selecting the best one, will terminate if the best solution is known.
- Sacrificing: It will stop as soon as the best solution is found.
Divide and Conquer
This is a straightforward algorithm implementation. It enables you to create an algorithm in a step-by-step fashion. It deconstructs the algorithm to solve the problem in various ways. It allows you to divide the problem into different methods, generating valid output for valid input. This accurate output is forwarded to another function.
This is an algorithm paradigm that makes the best choice possible on each iteration in the hopes of choosing the best solution. It is simple to set up and has a shorter execution time. However, there are very few cases where it is the best solution.
It improves the efficiency of the algorithm by storing intermediate results. It goes through five steps to find the best solution to the problem:
- It divides the problem into subproblems to find the best solution.
- After breaking down the problem into subproblems, it finds the best solution from these subproblems.
- Memorization is the process of storing the results of subproblems.
- Reuse the result to prevent it from being recomputed for the same subproblems.
- Finally, it computes the complex program's output.
Branch and Bound Algorithm
Only integer programming problems can be solved using the branch and bound algorithm. This method divides all feasible solution sets into smaller subsets. These subsets are then evaluated further to find the best solution.
As with a standard algorithm, you have predefined input and output. Deterministic algorithms have a defined set of information and required results and follow some described steps. They are more efficient than non-deterministic algorithms.
It is an algorithmic procedure that recursively and discards the solution if it does not satisfy the constraints of the problem.
Following your understanding of what is an algorith, and its approaches, you will now look at algorithm analysis.
Analysis of an Algorithm
The algorithm can be examined at two levels: before and after it is created. The two algorithm analyses are as follows:
In this context, priori analysis refers to the theoretical analysis of an algorithm performed before implementing the algorithm. Before implementing the algorithm, various factors such as processor speed, which does not affect the implementation, can be considered.
In this context, posterior analysis refers to a practical analysis of an algorithm. The algorithm is implemented in any programming language to perform the experimental research. This analysis determines how much running time and space is required.
Moving on in this "what is an algorithm" tutorial, you will now look at the complexity of an algorithm.
The Complexity of an Algorithm
The algorithm's performance can be measured in two ways:
The amount of 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. The asymptotic notation for describing time complexity, in this case, is big O notation. The time complexity is calculated primarily by counting the number of steps required to complete the execution. Let us look at an example of time complexity.
mul = 1;
// Suppose you have to calculate the multiplication of n numbers.
for i=1 to n
mul = mul *1;
// when the loop ends, then mul holds the multiplication of the n numbers
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. While 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.
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:
- To store program instructions.
- To store track of constant values.
- To store track of variable values.
- To store track of function calls, jumping statements, and so on.
Space Complexity = Auxiliary Space + Input Size
Finally after understanding what is an algorithm, its analysis and approches, you will look at different types of algorithms.
Types of Algorithms
There are two types of algorithms:
- Search Algori
- Sort Algorithm
Every day, you look for something in your daily life. Similarly, in the case of a computer, a large amount of data is stored in the computer, and whenever a user requests data, the computer searches for that data in the memory and returns it to the user. There are primarily two methods for searching data in an array:
The searching algorithm is of two types:
Linear search is a simple algorithm that begins searching for an element or a value at the beginning of an array and continues until the required element is not found. It compares the element to be searched with all the elements in an array; if a match is found, the element index is returned; otherwise, -1 is returned. This algorithm can be applied to an unsorted list.
A binary algorithm is the most basic algorithm, and it searches for elements very quickly. It is used to find an element in a sorted list. To implement the binary algorithm, the elements must be stored in sequential order or sorted. If the elements are stored randomly, binary search cannot be implemented.
Sorting algorithms rearrange elements in an array or a given data structure in ascending or descending order. The comparison operator decides the new order of the elements.
Now that you have completed the tutorial on "what is an algorithm," you will summarise what you have learned so far.
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