# Introduction to Algorithms

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.

Data Science: Algorithms are used to analyze, process, and extract insights from large amounts of data in fields such as marketing, finance, and healthcare.

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?

1. Algorithms are necessary for solving complex problems efficiently and effectively.
2. They help to automate processes and make them more reliable, faster, and easier to perform.
3. Algorithms also enable computers to perform tasks that would be difficult or impossible for humans to do manually.
4. 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.

### Characteristics of an Algorithm

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:

1. 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.

2. Well-defined inputs: If an algorithm says to take inputs, it should be well-defined inputs. It may or may not take input.

3. 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.

4. Finite-ness: The algorithm must be finite, i.e. it should terminate after a finite time.

5. 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.

6. 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.

7. Input: An algorithm has zero or more inputs. Each that contains a fundamental operator must accept zero or more inputs.

8. Output: An algorithm produces at least one output. Every instruction that contains a fundamental operator must accept zero or more inputs.

9. 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.

10. 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.

11. 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

1. It should terminate after a finite time.
2. It should produce at least one output.
3. It should take zero or more input.
4. It should be deterministic means giving the same output for the same input case.
5. 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:

#### 1. Brute Force Algorithm

It is the simplest approach to a problem. A brute force algorithm is the first approach that comes to finding when we see a problem.

#### 2. Recursive Algorithm

A recursive algorithm is based on recursion. In this case, a problem is broken into several sub-parts and called the same function again and again.

#### 3. Backtracking Algorithm

The backtracking algorithm builds the solution by searching among all possible solutions. Using this algorithm, we keep on building the solution following criteria. Whenever a solution fails we trace back to the failure point build on the next solution and continue this process till we find the solution or all possible solutions are looked after.

#### 4. 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.

#### 5. 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.

#### 6. 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.

#### 7. Divide and Conquer Algorithm

This algorithm breaks a problem into sub-problems, solves a single sub-problem, and merges the solutions to get the final solution. It consists of the following three steps:

• Divide
• Solve
• Combine

#### 8. Greedy Algorithm

In this type of algorithm, the solution is built part by part. The solution for the next part is built based on the immediate benefit of the next part. The one solution that gives the most benefit will be chosen as the solution for the next part.

#### 9. Dynamic Programming Algorithm

This algorithm uses the concept of using the already found solution to avoid repetitive calculation of the same part of the problem. It divides the problem into smaller overlapping subproblems and solves them.

#### 10. 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(imp).

### How to Design an Algorithm?

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

1. The problem that is to be solved by this algorithm i.e. clear problem definition.
2. The constraints of the problem must be considered while solving the problem.
3. The input to be taken to solve the problem.
4. The output is to be expected when the problem is solved.
5. 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.