Informally
•An algorithm is thus a sequence of computational steps that transform the input into the output.
•Solving a given problem:
§Data structure: Organization of data to solve the problem at hand.
§Algorithm: Outline, the essence of a computational procedure, step-by-step instructions.
§Program: Implementation of an algorithm in some programming language.
§Program: Implementation of an algorithm in some programming language.
Kinds of Problem to be solved
•Sorting and Searching are the basic and most common computational problem.
•Clever algorithms are employed for the Internet
§to manage large volume of data transfer.
§Finding good routes on which the data will travel.
§Search engine to quickly find requested pages.
§Etc…
•Numerical algorithms and number theory are employed in electronic commerce to keep and secure information such as credit card numbers, passwords, and bank statements.
•Allocating scarce resources in the most beneficial way.
§An oil company may wish to know where to place its wells in order to maximize its expected profit.
§A candidate may want to determine where to spend money buying campaign advertising in order to maximize the chances of winning at election.
§An airline may wish to assign crews to flight in the least expensive way possible, making sure that each flight is covered and that government policy regarding crew policies are met.
§Etc…
Definition of an Algorithm
•An algorithm is a sequence of unambiguous instructions for solving a problem, i.e., for obtaining a required output for any legitimate input in a finite amount of time.
•Properties:
§Precision
§Determinism
§Finiteness
•Efficiency
§Correctness
§Generality
§Finiteness
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