Whatever activity we carry out with an electronic device, whatever operation we request from an app or a service, everything is governed by algorithms. A **algorithm** it is a “recipe” that, step by step, establishes how to solve simple and complex problems. The importance of algorithms is reflected in a wide spectrum of **application fields**. In medicine, algorithms help diagnose diseases and discover new drugs. In the financial sector, they optimize trading and portfolio management. In robotics, they allow robots to learn and improve. In e-commerce, they provide personalized suggestions and optimize logistics.

Algorithms are the beating heart of**informatica** modern: they are the basis of the functioning of all applications, operating systems, artificial intelligence, social networks, search engines and much more. Although we often think of algorithms as instructions or procedures **implemented in the software** to solve problems, optimize processes or make decisions, they also play a significant role in the world of hardware.

## Where does the name algorithm come from?

The term “*algorithm*” comes from the name of the Persian mathematician Muhammad ibn Musa **al-Khwarizmi**, lived in the eighth and ninth centuries. His name has been Latinized as “*Algorithms*” and subsequently transformed into the term “*algorithm*“.

Al-Khwarizmi played a significant role in the development of algebra and computational methods. His writings contained methods for **solve equations** and algebraic problems, making a notable contribution to the development of mathematics and problem solving.

Il **algorithm concept** it has been formalized and expanded over time, especially with the contributions of other mathematicians and logic experts throughout history. One of the turning points in the formal definition of algorithms was the work of **David Hilbert** and other mathematicians in the 20th century. The introduction of the “**Turing machine**” by the British computer scientist Alan Turing, in the 1930s, made it possible to devise an abstract model of calculation and demonstrated the power and limits of mathematical calculators.

## What is an algorithm in computer science

In computer science, an algorithm represents a series of well-defined and precise steps performed to solve a problem or perform a specific operation. Algorithms are the basis of **programming** and IT problem solving.

An algorithm is made up of a **sequence of instructions** to be performed in the pre-established order in order to achieve the desired result. Algorithms can be represented in different forms, using diagrams, pseudocode or actual programming code.

### The essential characteristics of an algorithm

**Clarity and precision**: Algorithms must be defined clearly, precisely and unambiguously, so that anyone who uses them can achieve the same result.**Finite and deterministic**: Algorithms must terminate after a finite number of steps and provide a defined result for each input. They must be predictable and leave no room for random interpretations.**Solves specific problems**: Algorithms are developed in order to solve specific problems, which may concern mathematical calculations, organization and manipulation of data, management of search or sorting algorithms and so on.**Efficiency**: A good algorithm tries to solve a problem in the shortest possible time and with the least use of available resources, such as memory or processor.

Once defined, the algorithms can be implemented in several **programming languages** to solve practical problems, such as developing software, managing databases, creating artificial intelligence models. Just to give some examples.

## Examples of algorithms using different programming languages

As we highlighted previously, an algorithm results in a **sequence of steps** useful for solving any kind of problem. Often an algorithm can acquire gods **incoming data** (input) to then produce, following a series of processing, output data.

### Algoritmo Bubble Sort

One of the classic examples of an algorithm is the **Bubble Sort**. It is a **sorting algorithm** which repeatedly loops through the input list, comparing adjacent elements and swapping them if they are in the wrong order. Continue carrying out the operation as long as the entire **list** it is not **tidy**. The Bubble Sort algorithm can obviously be implemented with any programming language. In **Python** you can make it like this:

`def bubble_sort(arr):`

n = len(arr)

for i in range(n):

for j in range(0, n-i-1):

if arr[j] > arr[j+1]:

arr[j], arr[j+1] = arr[j+1], arr[j]

`# Utilizzo`

array = [64, 34, 25, 12, 22, 11, 90]

bubble_sort(array)

print("Array ordinato:", array)

In the example, the function `bubble_sort()`

it is precisely the Bubble Sort algorithm. The code below the comment `# Utilizzo`

all it does is pass to this function a list of numbers, in the form of an array, to be sorted.

### Binary search algorithm

The **binary search** is another search algorithm that deals with identifying the value of interest within an ordered list by repeatedly dividing the search in half. Below is an example of **C++ code**:

#include <iostream> using namespace std; int binary_search(int arr[], int left, int right, int target) { while (left <= right) { int mid = left + (right - left) / 2; if (arr[mid] == target) return mid; if (arr[mid] < target) left = mid + 1; else right = mid - 1; } return -1; } // Utilizzo int main() { int arr[] = {11, 12, 22, 25, 34, 64, 90}; int target = 34; int n = sizeof(arr) / sizeof(arr[0]); int result = binary_search(arr, 0, n - 1, target); (result == -1) ? cout << "Elemento non trovato." : cout << "Elemento trovato alla posizione: " << result; return 0; }

### Algorithm for calculating the factorial

The one for the **calculation of the factorial** is an algorithm that returns the product of all positive integers up to a certain number. In the example below we carry out this type of processing using **codice JavaScript**:

`function factorial(n) {`

if (n === 0 || n === 1)

return 1;

else

return n * factorial(n - 1);

}

`// Utilizzo`

const number = 5;

const result = factorial(number);

console.log(`Il fattoriale di ${number} è: ${result}`);

The example calculates the factorial of 5: obviously the value of the constant `number`

it is freely customizable. The factorial of 5 is calculated as `5! = 5 x 4 x 3 x 2 x 1 = 120`

. The result is printed in the browser console (`console.log`

).

## Important aspects to consider when developing algorithms

Algorithms are the basis of many technological innovations. From artificial neural networks to**machine learning**the functioning of search engines, cryptography, algorithms drive technological progress.

The analysis of **complexity of the algorithms** is critical. The developer is asked to check how much time or resources an algorithm requires as the size of the problem grows. In this way it is possible to establish which algorithms are most efficient for solving a given problem.

Some variations of the various algorithms can solve the same problem more efficiently and using a smaller volume of resources. For this reason the**algorithm optimization** it is an essential activity that aims to improve efficiency and performance. In short, algorithms are not static but are subject to constant revisions and developments.

The skills when it comes to **abstraction** and the ability to analyze and logically decompose a problem are essential to the design and development of effective algorithms.

With the growing demand for AI-based applications and the demand for decision-making systems, the need arises to also consider the**ethical aspect** of algorithms, weighing issues such as transparency, impartiality and fairness.

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