The execution of an algorithm requires various resources of the computer system to complete the task. The performance of algorithms depends on the use of these resources. The important resources which contribute to the efficiency of the algorithms are the memory space and the time required for successful execution of algorithm. The efficiency of an algorithm is measured in terms of the time and the space required for its execution therefore analysis of algorithms is divided into two categories

1. Lecture Note-1: Algorithm and Its Properties 18 Jan 2016
By Rajesh K Shukla, HOD, Department of CSE, SIRTE Bhopal
Downloaded from www.RajeshkShukla.com
Definition of algorithms
An algorithm is a tool for solving any computational problem. It may be defined as a sequence of finite,
precise and unambiguous instructions which are applied either to perform a computation or to solve a
computational problem. These instructions are applied on some raw data called the input, and the
solution of the problem produced is called the output. It is shown in the diagram given below
It was named after 9th century (780-850) Persian mathematician Abu Ja ’far Muhammad ibn-i Musa al-
Khwarizmi and these were originally used in mathematical calculations but they are now widely used in
computer programs.
Properties of algorithms
Algorithms generally share a set of properties
 Input
An algorithm must be supplied with zero or some finite input values externally from a specified set
in order to solve the computational problem and generate some output. The input data is
transformed during the computation in order to produce the output
 Output
The algorithm produces some finite set of outputs after applying some operations on the given set
of input values. The output values are the solution. The output can be anything from data returned
to the calling algorithm, displaying the message, printing the calculation etc. It is possible to have
no output.
 Finiteness
The algorithm must be terminated after executing the finite number of steps so an algorithm must
be a well-defined, ordered set of instructions.
 Definiteness
Each step of an algorithm must be clear and unambiguous so that the actions can be carried out
without any ambiguity. For Example same symbol should not be used to mean multiplication as
well as division in two different places in the algorithm.
 Effectiveness
The algorithm must perform each step correctly and in a finite amount of time therefore time tends
to be more important in calculating the effectiveness of an algorithm. The space and other resources
taken up by algorithm also plays vital role in effectiveness of an algorithm. Effectiveness is precisely
measured after translating the algorithm into a computer program.
 Correctness.
An algorithm must produce the correct output values for all legal input instances of the problem
 Generality
The algorithm should be applicable to all problems of a similar form
 Multiple view
Same algorithm may be represented in different ways
 Multiple Availability
Several algorithms for solving the same problem may exist - with different properties