algoritmov

An algorithm is a finite, well-defined sequence of instructions that, given input data, produces output and terminates after a finite number of steps. Algorithms are central to computer science and data processing. The term traces to al-Khwarizmi, a Persian mathematician, and the modern form comes from Latinized renditions of his name.

Core properties include finiteness, definiteness, and determinism: each step is precise and the process terminates. An algorithm should be correct for all valid inputs and handle edge cases. Efficiency is crucial, typically measured by time complexity and space consumption; Big-O notation classifies growth with input size.

Algorithms vary by approach and domain. Deterministic algorithms follow a fixed sequence of steps, while nondeterministic ones may involve randomness or parallel exploration. Common design techniques include brute-force search, divide-and-conquer, dynamic programming, greedy methods, backtracking, and randomized algorithms.

Representative examples include the Euclidean algorithm for greatest common divisor, binary search in sorted lists, and sorting algorithms such as quicksort and mergesort. In graph theory, Dijkstra’s algorithm and the Floyd–Warshall algorithm compute shortest paths, while numerical methods and cryptographic algorithms illustrate broader applications.

Algorithms have broad uses in science, engineering, business, and everyday technology. Some problems have no efficient algorithm or are undecidable; others remain computationally intractable for large inputs. Ongoing research continues to improve performance, reliability, and applicability across computing paradigms.