What is the algorithm?

In this article, we want to provide a brief and informative overview of the algorithm.

In computer programming terms, an algorithm is a set of well-defined instructions to solve a particular problem. It takes a set of input(s) and produces the desired output. For example, An algorithm to add two numbers:

What is the definition of algorithm?

The word Algorithm means A set of finite rules or instructions to be followed in calculations or other problem-solving operations Or A procedure for solving a mathematical problem in a finite number of steps that frequently involves recursive operations.

Therefore Algorithm refers to a sequence of finite steps to solve a particular problem.

Use of the Algorithms:

Algorithms play a crucial role in various fields and have many applications. Some of the key areas where algorithms are used include:

Computer Science: Algorithms form the basis of computer programming and are used to solve problems ranging from simple sorting and searching to complex tasks such as artificial intelligence and machine learning.
Mathematics: Algorithms are used to solve mathematical problems, such as finding the optimal solution to a system of linear equations or finding the shortest path in a graph.
Operations Research: Algorithms are used to optimize and make decisions in fields such as transportation, logistics, and resource allocation.
Artificial Intelligence: Algorithms are the foundation of artificial intelligence and machine learning, and are used to develop intelligent systems that can perform tasks such as image recognition, natural language processing, and decision-making.

These are just a few examples of the many applications of algorithms. The use of algorithms is continually expanding as new technologies and fields emerge, making it a vital component of modern society.

Algorithms can be simple and complex depending on what you want to achieve.

It can be understood by taking the example of cooking a new recipe. To cook a new recipe, one reads the instructions and steps and executes them one by one, in the given sequence. The result thus obtained is the new dish is cooked perfectly. Every time you use your phone, computer, laptop, or calculator you are using Algorithms. Similarly, algorithms help to do a task in programming to get the expected output.

The Algorithm designed are language-independent, i.e. they are just plain instructions that can be implemented in any language, and yet the output will be the same, as expected.

What is the need for algorithms?

Algorithms are necessary for solving complex problems efficiently and effectively.
They help to automate processes and make them more reliable, faster, and easier to perform.
Algorithms also enable computers to perform tasks that would be difficult or impossible for humans to do manually.
They are used in various fields such as mathematics, computer science, engineering, finance, and many others to optimize processes, analyze data, make predictions, and provide solutions to problems.

What are the Characteristics of an Algorithm?

As one would not follow any written instructions to cook the recipe, but only the standard one. Similarly, not all written instructions for programming are an algorithm. For some instructions to be an algorithm, it must have the following characteristics:

Clear and Unambiguous: The algorithm should be unambiguous. Each of its steps should be clear in all aspects and must lead to only one meaning.
Well-Defined Inputs: If an algorithm says to take inputs, it should be well-defined inputs. It may or may not take input.
Well-Defined Outputs: The algorithm must clearly define what output will be yielded and it should be well-defined as well. It should produce at least 1 output.
Finite-ness: The algorithm must be finite, i.e. it should terminate after a finite time.
Feasible: The algorithm must be simple, generic, and practical, such that it can be executed with the available resources. It must not contain some future technology or anything.
Language Independent: The Algorithm designed must be language-independent, i.e. it must be just plain instructions that can be implemented in any language, and yet the output will be the same, as expected.
Input: An algorithm has zero or more inputs. Each that contains a fundamental operator must accept zero or more inputs.
Output: An algorithm produces at least one output. Every instruction that contains a fundamental operator must accept zero or more inputs.
Definiteness: All instructions in an algorithm must be unambiguous, precise, and easy to interpret. By referring to any of the instructions in an algorithm one can clearly understand what is to be done. Every fundamental operator in instruction must be defined without any ambiguity.
Finiteness: An algorithm must terminate after a finite number of steps in all test cases. Every instruction which contains a fundamental operator must be terminated within a finite amount of time. Infinite loops or recursive functions without base conditions do not possess finiteness.
Effectiveness: An algorithm must be developed by using very basic, simple, and feasible operations so that one can trace it out by using just paper and pencil.

Properties of Algorithm:

It should terminate after a finite time.
It should produce at least one output.
It should take zero or more input.
It should be deterministic means giving the same output for the same input case.
Every step in the algorithm must be effective i.e. every step should do some work.

Types of Algorithms:

There are several types of algorithms available. Some important algorithms are:

Searching Algorithm: Searching algorithms are the ones that are used for searching elements or groups of elements from a particular data structure. They can be of different types based on their approach or the data structure in which the element should be found.
Sorting Algorithm: Sorting is arranging a group of data in a particular manner according to the requirement. The algorithms which help in performing this function are called sorting algorithms. Generally sorting algorithms are used to sort groups of data in an increasing or decreasing manner.
Hashing Algorithm: Hashing algorithms work similarly to the searching algorithm. But they contain an index with a key ID. In hashing, a key is assigned to specific data.
Randomized Algorithm: In the randomized algorithm, we use a random number so it gives immediate benefit. The random number helps in deciding the expected outcome.
To learn more about the types of algorithms refer to the article about “Types of Algorithms“.

Advantages of Algorithms:

It is easy to understand.
An algorithm is a step-wise representation of a solution to a given problem.
In an Algorithm the problem is broken down into smaller pieces or steps hence, it is easier for the programmer to convert it into an actual program.

Disadvantages of Algorithms:

Writing an algorithm takes a long time so it is time-consuming.
Understanding complex logic through algorithms can be very difficult.
Branching and Looping statements are difficult to show in Algorithms.

How to Design an Algorithm?

To write an algorithm, the following things are needed as a pre-requisite:

The problem that is to be solved by this algorithm i.e. clear problem definition.
The constraints of the problem must be considered while solving the problem.
The input to be taken to solve the problem.
The output is to be expected when the problem is solved.
The solution to this problem is within the given constraints.

Then the algorithm is written with the help of the above parameters such that it solves the problem.

Example: Consider the example to add three numbers and print the sum.

Step 1: Fulfilling the pre-requisites

As discussed above, to write an algorithm, its prerequisites must be fulfilled.

The problem that is to be solved by this algorithm: Add 3 numbers and print their sum.
The constraints of the problem that must be considered while solving the problem: The numbers must contain only digits and no other characters.
The input to be taken to solve the problem: The three numbers to be added.
The output to be expected when the problem is solved: The sum of the three numbers taken as the input i.e. a single integer value.
The solution to this problem, in the given constraints: The solution consists of adding the 3 numbers. It can be done with the help of the + operator, or bit-wise, or any other method.

Step 2: Designing the algorithm

Now let’s design the algorithm with the help of the above pre-requisites:

Algorithm to add 3 numbers and print their sum:

START
Declare 3 integer variables num1, num2, and num3.
Take the three numbers, to be added, as inputs in variables num1, num2, and num3 respectively.
Declare an integer variable sum to store the resultant sum of the 3 numbers.
Add the 3 numbers and store the result in the variable sum.
Print the value of the variable sum
END

Step 3: Testing the algorithm by implementing it.

# Python3 program to add three numbers
# with the help of above designed
# algorithm


if __name__ == "__main__":

	# Variables to take the input of
	# the 3 numbers
	num1 = num2 = num3 = 0

	# Variable to store the resultant sum
	sum = 0

	# Take the 3 numbers as input
	num1 = int(input("Enter the 1st number: "))

	num2 = int(input("Enter the 2nd number: "))

	num3 = int(input("Enter the 3rd number: "))

	# Calculate the sum using + operator
	# and store it in variable sum
	sum = num1 + num2 + num3

	# Print the sum
	print("\nSum of the 3 numbers is:", sum)

Output

Enter the 1st number: 1
Enter the 2nd number: 5
Enter the 3rd number: 4

Sum of the 3 numbers is: 10

One problem, many solutions: The solution to an algorithm can be or cannot be more than one. It means that while implementing the algorithm, there can be more than one method to implement it. For example, in the above problem of adding 3 numbers, the sum can be calculated in many ways:

+ operator
Bit-wise operators
. . etc.

Algorithm Examples

Add two numbers entered by the user

Step 1: Start
Step 2: Declare variables num1, num2 and sum. 
Step 3: Read values num1 and num2. 
Step 4: Add num1 and num2 and assign the result to sum.
        sum←num1+num2 
Step 5: Display sum 
Step 6: Stop

This algorithm starts by declaring three variables: num1, num2, and sum. It then reads input values for num1 and num2. The algorithm adds num1 and num2 together and assigns the result to the sum variable. Finally, it displays the value of the sum variable and stops the program. Overall, this algorithm performs the addition of two numbers and outputs the sum.

Find the largest number among three numbers

Step 1: Start
Step 2: Declare variables a,b and c.
Step 3: Read variables a,b and c.
Step 4: If a > b
           If a > c
              Display a is the largest number.
           Else
              Display c is the largest number.
        Else
           If b > c
              Display b is the largest number.
           Else
              Display c is the greatest number.  
Step 5: Stop

This algorithm starts by declaring three variables: a, b, and c. It then reads the values of a, b, and c. The algorithm performs a series of comparisons to determine the largest number among a, b, and c. If a is greater than b, it further checks if a is greater than c. If so, it displays that a is the largest number. If a is not greater than c, it displays that c is the largest number. On the other hand, if a is not greater than b, it checks if b is greater than c. If so, it displays that b is the largest number. If b is not greater than c, it displays that c is the greatest number. Finally, the algorithm stops. Overall, this algorithm determines and displays the largest number among three variables: a, b, and c.

Find the factorial of a number

Step 1: Start
Step 2: Declare variables n, factorial and i.
Step 3: Initialize variables
          factorial ← 1
          i ← 1
Step 4: Read value of n
Step 5: Repeat the steps until i = n
     5.1: factorial ← factorial*i
     5.2: i ← i+1
Step 6: Display factorial
Step 7: Stop

This algorithm begins by declaring three variables: n, factorial, and i. It then initializes the variables factorial and i to 1. Next, it reads the value of n. The algorithm enters a loop that repeats until i is equal to n. Within the loop, it multiplies the factorial variable by i and increments i by 1. After the loop, it displays the value of the factorial variable. Finally, the algorithm stops. Overall, this algorithm calculates the factorial of a given number n and displays the result.

Conclusion

In conclusion, an algorithm is a fundamental set of instructions used for problem-solving and task completion across various fields and industries. They play a critical role in developing software, automating processes, and decision-making. Algorithms can be represented visually through flowcharts or pseudocode, and while they offer many advantages, such as accuracy and efficiency, they remain prone to errors and limitations. Despite this, algorithms continue to be an essential tool for problem-solving and decision-making, fueling the advancement of science and technology.

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