Algorithms
This word did appear on Webster’s new world dictionary in late 1957 with its older form as ‘algorism’ with its ancient meaning, the process of doing arithmetic using Arabic numerals.
Early linguists attempted to guess at its derivation by making combinations like algiros →Painful + arithmos →number.
Finally historians of the mathematics found out that this word algorism came from a name of a famous Persian author, and also referred as a father of Algebra called Muḥammad ibn Mūsā al-Khwārizmī.
Finally it is corrupted by passing through many regions and turned out as Algorithm.
By 1950, The word algorithm was most frequently associated with Euclid’s algorithm, a process for finding the greatest common divisor of two numbers that appears in Euclid’s Elements.
Euclid’s algorithm:
Given two positive integers ‘m’ and ’n’, find their greatest common divisor , that is, the largest positive integer that evenly divides both m and n.
- [find reminder] Divide m by n and let r be the reminder. we will have 0 ≤ r ≤ n.
2. [is it zero?] if r =0, the algorithm terminates and the answer is n.
3. [Reduce] Set m←n, n←r, and go back to step 1.
→ Defining a finite set of rules that gives a sequence of operations for solving a specific type of problem, an algorithm has 5 important features.
- Finiteness: An algorithm must always terminate after a finite number of steps.
- Definiteness: Each step of an algorithm must be precisely defined. The actions to be carried out must be rigorously and unambiguously specified for each case.
- Input: An algorithm has 0 or more inputs. These are quantities that are given to it initially before the algorithm begins or dynamically after as the algorithm runs.
- Output: An algorithm has 1 or more outputs. These are quantities that have a specified relation to the inputs.
- Effectiveness: it also expected to be effective. like in a finite number of steps by comparing time to take to produce outputs.
An algorithm that has all characteristics of an algorithm except that it possibly lack of finiteness is called a computational method.
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