Digital Analysis and Algorithms

UNIT – I
Analysis of Algorithm: INTRODUCTION – ANALYZING CONTROL STRUCTURES-AVERAGE CASE ANALYSIS-SOLVING RECURRENCES.

ALGORITHM

Informal Definition: An Algorithm is any well-defined computational procedure that takes some value or set of values as Input and produces a set of values or some value as output. Thus algorithm is a sequence of computational steps that transforms the i/p into the o/p.

Formal Definition: An Algorithm is a finite set of instructions that, if followed, accomplishes a particular task. In addition, all algorithms should satisfy the following criteria.

1. INPUT  Zero or more quantities are externally supplied.
2. OUTPUT  At least one quantity is produced.
3. DEFINITENESS  Each instruction is clear and unambiguous.
4. FINITENESS  If we trace out the instructions of an algorithm, then for all cases, the algorithm terminates after a finite number of steps.
5. EFFECTIVENESS  Every instruction must very basic so that it can be carried out, in principle, by a person using only pencil & paper.

Issues or study of Algorithm:

• How to device or design an algorithm  creating and algorithm.
• How to express an algorithm  definiteness.
• How to analysis an algorithm  time and space complexity.
• How to validate an algorithm  fitness.
• Testing the algorithm  checking for error. Algorithm Specification:

Algorithm can be described in three ways.

1. Natural language like English: When this way is choused care should be taken, we should ensure that each & every statement is definite.

2. Graphic representation called flowchart: This method will work well when the algorithm is small& simple.

3. Pseudo-code Method: In this method, we should typically describe algorithms