What is an Algorithm

Algorithm (Algorithm) is an accurate and complete description of a solution to a problem, a clear set of instructions for solving a problem, an algorithm represents a systematic approach to describing a strategic mechanism for solving a problem. That is to say, the ability to obtain the required output in a limited time for a certain specification of input. If an algorithm is flawed or unsuitable for a given problem, executing it will not solve the problem. Different algorithms may accomplish the same task in different amounts of time, space, or efficiency. The strength of an algorithm can be measured in terms of space complexity versus time complexity.

An instruction in an algorithm describes a computation that when run can start from an initial state and (possibly empty) initial inputs, go through a finite and well-defined set of states, and ultimately produce an output and stop at a final state. The transfer from one state to another is not necessarily deterministic. Some algorithms, including randomized algorithms, contain some random inputs.

The concept of formalized algorithms originated in part from attempts to solve the determination problem posed by Hilbert, and took shape in subsequent attempts to define efficient computability or efficient methods. These attempts included the recursive functions proposed by Kurt G?del, Jacques Herbrand, and Stephen Cole Kleeney in 1930, 1934, and 1935, respectively, the λ-algorithm proposed by Alonzo Church in 1936, Emil Leon Post's Formulation 1 in 1936, and Alan Turing's 1937 Turing machine in 1937. Even at the present time, it is still often the case that intuitive ideas are difficult to define as formal algorithms.