ELEMEMTARY ALGORITHMICS SUMMARY

1. In this unit the following concepts have been formally or informally defined and discussed:

Problem, Solution of a Problem, Algorithm, Program, Process (all section 1.1) . Instance of a problem (Section 1.2)

PROBLEMS, AVAILABLE TOOLS & ALGORITHMS

In order to explain an important point in respect of the available tools, of which one must take care while designing an algorithm for a given problem, we consider some alternative algorithms for finding the product m*n of two natural numbers m and n.

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.

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:

Using Insertion Sort or Bubble Sort

Question :Using Insertion Sort or Bubble Sort 
(state before starting the solution, which algorithm for sorting, you are using),
sort the following sequence of integers in decreasing order :
85 36 34 109 49 36

Solution: 

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:

State any four characteristics of an algorithm, with an appropriate examples.

Question :State any four characteristics of an algorithm, with an appropriate examples.

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: