A sample algorithmic problem

An algorithmic problem is specified by describing the complete set of instances it must work on and of its output after running on one of these instances. This distinction, between a problem and an instance of a problem, is fundamental. The algorithmic problem known as sorting is defined as follows: [Skiena:2008:ADM:1410219]

• Problem: Sorting
• Input: A sequence of n keys, a_1, a_2, ..., a_n.
• Output: The reordering of the input sequence such that a'_1 <= a'_2 <= ... <= a'_{n-1} <= a'_n

An instance of sorting might be an array of strings, such as { Haskell, Emacs } or a sequence of numbers such as { 154, 245, 1337 }.