Procedure:

1. A manner of proceeding; a way of performing or effecting something. 2. A series of steps taken to accomplish an end.
[The American Heritage Dictionary of The English Language, Third Edition Electronic Version, Houghton Mifflin, 1992]

Algorithm (for a problem):

A procedure for solving the problem that is unambiguous and effective (finite and correct).

Example: To determine if a number (decimal, integer) is divisible by 3, add its digits. If the result is divisible by 3, so is the original number.

• It takes twice as long to put stamps on 20 envelopes as it does to put stamps on 10 envelopes: O(n).
• It takes four times as long to write a table of the distances between each of 20 cities as it does to write a table of the distances between each of 10 cities: O(n²).
• Sorting takes O(n log n).

Böhm-Jacopini Theorem [Corrado Böhm and Giuseppe Jacopini (CACM, 1966)]: Any procedure can be written with the following control structures:

1. Sequence: Do one action, and then another, and then another, etc.
2. Selection: Do one action or another, based on some condition.
3. Loop: Repeatedly do an action as long as some condition holds.