CS404 Design and Analysis of Algorithms

1. CS404 Design and Analysis of Algorithms BBy DDr. M V S Peri Sastry BB.E, PhD(BITS-Pilani)

2. Introduction Algorithms: Definition: An algorithm is an unambiguous, ordered sequence of steps that are carried out to get a solution to a problem. An algorithm is a technique to solve a problem systematically. It takes a set of input values and produces the desired output. A correct algorithm always outputs correct answer and halts. Several algorithms may exist to solve a given problem.

3. Algorithms Algorithm Input Output Any algorithm should consist of the following: Input: The range of inputs for which an algorithm works perfectly. ( An algorithm without inputs may also exist sometimes) Output: An algorithm should always produce correct results and it should halt. (It should NOT hang) Algorithm:should have finite sequence of Instructions.

4. Problem Soving on Computer Computer Output PROBLEM Algorithm INPUT Algorithms Should be written in simple English statements(pseudo code with mathematical expressions as needed.) In computer science, the relationship to external problems and Algorithms can be seen as below:

5. Steps in Problem Solving Understand the problem Decide on computational means Exact vs approximate solution Data structures Algorithm design technique Design an algorithm Prove correctness Analyze the algorithm Code the algorithm

6. The Process of Designing an Algorithm • Formulating the problem • with enough mathematical precision • we can ask a concrete question • start to solve it. • Design the algorithm • list the “precise” steps. (an expert can translate the algorithm into a computer program.) • Analyze the algorithm • prove that it is correct • establish the efficiency • the running time or sometimes space

7. Properties Or Characteristics of Algorithms Definiteness (Simple, Precise and Un-ambiguous) Range of Inputs (should be specific) Maintain Order (of execution of instructions) Finite and correct (must solve problem in certain steps ) Termination (must halt and terminate gracefully) Speed (Time complexity) as desired for input Space (RAM occupancy) as desired for input Representable as Flowchart, Pseudo code, Code

8. Effii c ient Euclid’s algorithm for GCD(Greatest Common Divisor) Algorithm GCD (m, n) in plain English // Input: Two non-negative and non-zero integer values m and n Step1: if n = 0 return m and stop Step2: Divide m by n and assign the reminder to r Step3: Assign the value of n to m, and value of r to n Step4: Go to Step1

9. Efficient Euclid’s algorithm for GCD(Greatest Common Divisor) in pseudo code Algorithm GCD (m, n) // Input: Two non-negative and non-zero integer values m and n Step1: [ display result] if n = 0 return m and stop Step2: [Compute GCD recursively] Return GCD (n, m mod n);

10. Efficient Euclid’s algorithm for GCD(Greatest Common Divisor) in some computer language code • Algorithm GCD (m, n) • // Input: Two non-negative and non-zero integer values m and n • While (n!= 0) r = m mod n m = n n = r end while return m // End of function

11. The Process of Analysing an Algorithm • Correctness • Time Complexity as Input size increases • Space Complexity ie; Memory requirement as Input size increases • Establishing the efficiency • the running time and / or • sometimes space (RAM space)

12. Example of another Algorithm

13. Application of Algorithms(Kinds Domains & Examples) Sorting, Searching, Shuffling Etc; String processing Graph problems Combinatorial problems Geometric problems Numerical problems

14. Application of Algorithms(Kinds Domains & Examples) continued Human Genome Project (100,000 Genes, 3 billion base pairs of human DNA ; data storage, search, analysis etc;) Internet (routing, search, analysis etc;) E commerce Public key cryptography and digital signatures management Manufacturing (Scheduling) Flight scheduling etc; Travelling Salesman’s problem etc;

15. Thank YouQuestions and Discussion