ALGs

Algs is a shorthand term for algorithms—precise, finite procedures that take input values, perform a sequence of well-defined steps, and produce an output. An alg must terminate after a finite number of steps; each step is unambiguous and executable, and the procedure is independent of any particular programming language. In practice, algs are implemented as programs but can be described in natural language, pseudocode, or flowcharts.

Historically, algs emerged in ancient mathematics with Euclid's algorithm for gcd. The 20th century formalization—via Turing machines, the Church-Turing thesis, and formal language theory—established precise notions of computability and efficiency. Since then, a wide range of algorithmic techniques has been developed, including exact methods, heuristics, and randomized approaches.

Algs are commonly classified by purpose and method: exact versus approximate, deterministic versus probabilistic, online versus offline. Design paradigms include brute force, divide and conquer, dynamic programming, greedy methods, and graph algorithms, among others. Performance is analyzed in terms of time and space, typically described using asymptotic notation such as O(n). Practical analysis also considers average versus worst-case behavior, memory hierarchy, and implementation details.

Applications span nearly every field of computing and data processing: searching, sorting, pathfinding, cryptography, compression, machine learning, and optimization problems. Good alg design emphasizes correctness, efficiency, scalability, and robustness, often accompanied by testing and formal verification.

See also complexity theory, data structures, and algorithm design techniques.