CASE 4: IF today's date is Friday AND the document is located at 'D:/My Documents' AND there is NO paper in the printer THEN (i) display 'out of paper' error message and (ii) exit.
Note that CASE 3 includes two possibilities: (i) the document is NOT located at 'D:/My Documents' AND there's paper in the printer OR (ii) the document is NOT located at 'D:/My Documents' AND there's NO paper in the printer.
The sequence of IF-THEN-ELSE tests might look like this:
TEST 1: IF today's date is NOT Friday THEN done ELSE TEST 2:
TEST 2: IF the document is NOT located at 'D:/My Documents' THEN display 'document not found' error message ELSE TEST 3:
TEST 3: IF there is NO paper in the printer THEN display 'out of paper' error message ELSE print the document.
These examples' logic grants precedence to the instance of "NO document at 'D:/My Documents' ". Also observe that in a well-crafted CASE statement or sequence of IF-THEN-ELSE statements the number of distinct actions-4 in these examples: do nothing, print the document, display 'document not found', display 'out of paper' -- equals the number of cases.
Given unlimited memory, a computational machine with the ability to execute either a set of CASE statements or a sequence of IF-THEN-ELSE statements is Turing complete. Therefore, anything that is computable can be computed by this machine. This form of algorithm is fundamental to computer programming in all its forms (see more at McCarthy formalism).
[edit] Implementation
Most algorithms are intended to be implemented as computer programs. However, algorithms are also implemented by other means, such as in a biological neural network (for example, the human brain implementing arithmetic or an insect looking for food), in an electrical circuit, or in a mechanical device.
[edit] Example
Further information: Algorithm examples
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.One of the simplest algorithms is to find the largest number in an (unsorted) list of numbers. The solution necessarily requires looking at every number in the list, but only once at each. From this follows a simple algorithm, which can be stated in a high-level description English prose, as:
High-level description:
1.Assume the first item is largest.
2.Look at each of the remaining items in the list and if it is larger than the largest item so far, make a note of it.
3.The last noted item is the largest in the list when the process is complete.
(Quasi-)formal description: Written in prose but much closer to the high-level language of a computer program, the following is the more formal coding of the algorithm in pseudocode or pidgin code:
Algorithm LargestNumber
Input: A non-empty list of numbers L.
Output: The largest number in the list L.
largest ← L0
for each item in the list L≥1, do
if the item > largest, then
largest ← the item
return largest
"←" is a loose shorthand for "changes to". For instance, "largest ← item" means that the value of largest changes to the value of item.
algorithm
Start from the beginning
