Algorithm
![Flow chart of an algorithm (Euclid's algorithm) for calculating the greatest common divisor (g.c.d.) of two numbers a and b in locations named A and B. The algorithm proceeds by successive subtractions in two loops: IF the test B ≥ A yields](/Images/godic/202412/18/Euclid_flowchart.svg3059.png")
![Logical NAND algorithm implemented electronically in 7400 chip](/Images/godic/202412/18/TTL_npn_nand.svg3059.png")
![Flowchart examples of the canonical Böhm-Jacopini structures: the SEQUENCE (rectangles descending the page), the WHILE-DO and the IF-THEN-ELSE. The three structures are made of the primitive conditional GOTO (IF test=true THEN GOTO step xxx) (a diamond), the unconditional GOTO (rectangle), various assignment operators (rectangle), and HALT (rectangle). Nesting of these structures inside assignment-blocks result in complex diagrams (cf Tausworthe 1977:100,114).](/Images/godic/202412/18/Euclid's_algorithm_structured_blocks_13059.png")
![An animation of the quicksort algorithm sorting an array of randomized values. The red bars mark the pivot element; at the start of the animation, the element farthest to the right hand side is chosen as the pivot.](/Images/godic/202412/18/Sorting_quicksort_anim3059.gif")
In mathematics and computer science, an algorithm (/ˈælɡərɪðəm/ AL-gə-ri-dhəm) is a self-contained step-by-step set of operations to be performed. Algorithms perform calculation, data processing, and/or automated reasoning tasks.
The words 'algorithm' and 'algorism' come from the name al-Khwārizmī. Al-Khwārizmī (Persian:خوارزمی, c. 780-850) was a Persian mathematician, astronomer, geographer, and scholar.