EXAMPLE OF AN ALGORITHM

Before going into the details of problem-solving with algorithms, just to have an idea of what an algorithm is, we consider a well-known algorithm for finding Greatest Common Divisor (G.C.D) of two natural numbers and also mention some related historical facts. First, the algorithm is expressed in English. Then, we express the algorithm in a notation resembling a programming language.

ELEMEMTARY ALGORITHMICS INTRODUCTION

We are constantly involved in solving problem. The problems may concern our survival in a competitive and hostile environment, may concern our curiosity to know more and more of various facets of nature or may be about any other issues of interest to us. Problem may be a state of mind of a living being, of not being satisfied with some situation. However, for our purpose, we may take the unsatisfactory/ unacceptable/ undesirable situation itself, as a problem.

EVOLUTION OF SOFTWARE ENGINEERING

Any application on computer runs through software. As computer technologies have changed tremendously in the last five decades, accordingly, the software development has undergone significant changes in the last few decades of 20th century. In the early years, the software size used to be small and those were developed either by a single programmer or by a small programming team.

SOFTWARE ENGINEERING AND ITS MODELS

The field of software engineering is related to the development of software. Large software needs systematic development unlike simple programs which can be developed in isolation and there may not be any systematic approach being followed. In the last few decades, the computer industry has undergone revolutionary changes in hardware. That is, processor technology, memory technology, and integration of devices have changed very rapidly.

Arrange the following growth rates in increasing order

Question: Arrange the following growth rates in increasing order : 0 (4n), 0(n4), 0(1), 0(n3 logn), where '0' denotes 'big O'.

Solurion:

Let Lx denote floor function of x and Fx denote ceiling function of x. Find values of :

Question:  Let Lx denote floor function of x and Fx  denote ceiling function of x. Find values of :

  


Solution:

The Four - Colour Problem & The Fermat's Last Theorem

Question: State and describe any one of the following two problems :
(i)The Four - Colour Problem
(ii)The Fermat's Last Theorem


Solution:

Explain the relation/difference between a problem and its instance through an example of each.

Question : Explain the relation/difference between a problem and its instance through an example of each.

Solution: