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2.  A step by step process to solve any problem is called algorithm.  Algorithm is a process which take some values as input and provide us output. So it convert input into output. 2

3.  A computer algorithm is a detailed step-by- step method for solving a problem by using a computer.  An algorithm is a sequence of unambiguous instructions for solving a problem in a finite amount of time.  An Algorithm is well defined computational procedure that takes some value, or set of values, as input and produces some value, or set of values as output.  More generally, an Algorithm is any well defined computational procedure that takes collection of elements as input and produces a collection of elements as output. 3

4. 4  The word Algorithm comes from the name of the muslim author Abu Ja’far Mohammad ibn Musa al- Khowarizmi. He was born in the eighth century at Khwarizm.  Much of al-Khwarizmi’s work was written in a book titled al Kitab al-mukhatasar fi hisab al-jabr wa’l- muqabalah  It is from the titles of these writings and his name that the words algebra and algorithm are derived.  As a result of his work, al-Khwarizmi is regarded as the most outstanding mathematician of his time.

5.  Most basic and popular algorithms are ◦ Sorting algorithms ◦ Searching algorithms 5

6.  Mainly, it depends upon various factors, for example in case of sorting ◦ The number of items to be sorted ◦ The extent to which the items are already sorted ◦ Possible restrictions on the item values ◦ The kind of storage device to be used etc. 6

7. Problem  The statement of the problem specifies, in general terms, the desired input/output relationship. Algorithm  The algorithm describes a specific computational procedure for achieving input/output relationship. Example  One might need to sort a sequence of numbers into non-decreasing order. Algorithms  Various algorithms e.g. merge sort, quick sort, heap sorts etc. 7

8.  Analysis independent of the variations in ◦ Machine ◦ Operating system ◦ Programming languages ◦ Compiler etc.  Low-level details will not be considered  Our model will be an abstraction of a standard generic single-processor machine, called a random access machine or RAM 8

9.  A RAM is assumed to be an idealized machine ◦ Infinitely large random-access memory ◦ Instructions execute sequentially  Every instruction is in fact a basic operation on two values in the machines memory which takes unit time.  These might be characters or integers.  Example of basic operations include ◦ Assigning a value to a variable ◦ Arithmetic operation (+, -, ×, /) on integers ◦ Performing any comparison e.g. a < b ◦ Boolean operations ◦ Accessing an element of an array. 9

10.  Algorithms help us to understand scalability.  Performance often draws the line between what is feasible and what is impossible.  Algorithmic mathematics provides a languagefor talking about program behavior.  Performance is the currency of computing.  Speed is fun! 10

11.  Input:sequence 〈 a1, a2, …, an 〉 of numbers.  Output: 〈 a'1, a'2, …, a'n 〉 such that a'1≤a'2≤…≤a'n.  Example:  Input:8 2 4 9 3 6  Output:2 3 4 6 8 9 11

12. A good understanding of algorithms is essential for a good understanding of the most basic element of computer science: programming. Unlike a program, an algorithm is a mathematical entity, which is independent of a specific programming language, machine, or compiler. Thus, in some sense, algorithm 1. INTRODUCTION design is all about the mathematical theory behind the design of good programs. 12

13. 13  The fact is that many of the courses in computer science deal with efficient algorithms and data structure

14. 14  compilers  operating systems  databases  artificial intelegence  computer graphics  networks