An algorithm consists of an ordered list of operations that have the purpose of finding the solution to a problem in mathematics, computing and related disciplines.
For the mathematical and computer sciences , an algorithm is a list that, given an initial state and an input, proposes successive steps to arrive at a final state obtaining a solution. However, the algorithm is not exclusive to the hard sciences or mathematics . Also in everyday life these types of operations are used almost without noticing it: for example, in instructions or user manuals that include examples of technical problem solving.
The use of algorithms is not exclusively typical of complex operations or those linked to the field of scientific research . When developing a computer program, to cite an example, we are often developing or implementing a method to solve some problem. In short, it is a problem-solution relationship that takes place through computing. A typical algorithm is finite, accurate, has both input and output, and is effective in solving a problem.
Its most frequent use is in mathematics and computer science and there are famous algorithms for use in history. Among them, the Euclid algorithm , which has the purpose of calculating the greatest common divisor of two positive integers . Or, for example, the Gaussian algorithm for solving linear systems of equations. The Floyd-Warshall one , for example, looks at ways of finding the minimum path in weighted graphs for computing. Another well-known algorithmic system is that of Turing , a computational method created by Alan Turing through which he demonstrated that there were problems that a machine - such as a computer- could not solve. Thus, this machine formalizes the concept of algorithm and to this day it continues to be used frequently.