Analysis of Algorithm data structure.ppt
- 1. Algorithm What is an Algorithm? • An algorithm is a process or a set of rules required to perform calculations or some other problem-solving operations. • Contains the finite set of instructions which are being carried in a specific order to perform the specific task. • It is not the complete program or code; it is just a solution (logic) of a problem • Transforms input of a problem to output Algorithm = Input + Process + Output
- 2. Algorithm Characteristics of an Algorithm The following are the characteristics of an algorithm: • Input • Output • Unambiguity • Finiteness • Effectiveness • Language Independent
- 3. Algorithm Why do we need algorithm? • Scalability • Performance Any real time example
- 4. Algorithm Factors of Algorithm: Consider during Algorithm Design: • Modularity • Correctness • Maintainability • Functionality • Robustness • User friendly • Extensibility
- 5. Algorithm Categories of Algorithm: • Sort • Search • Insert • Delete • Update
- 6. Analysis of Algorithm 2 levels of Analysis 1. Priori Analysis Theoretical analysis Done before implementing the algorithm 2. Posterior Analysis Practical analysis Achieved by using any programming language How much running time and space
- 7. Asymptotic notations • The efficiency of an algorithm depends on the amount of time, storage and other resources required to execute the algorithm. • The efficiency is measured with the help of asymptotic notations. • Algorithm not have same performance for different input types • “The study of change in performance of the algorithm with the change in the order of the input size is defined as asymptotic analysis”.
- 8. Asymptotic notations • Mathematical notations • Describe running time of algorithm • There are mainly three asymptotic notations: 1. Big-O notation 2. Omega notation 3. Theta notation
- 9. Analysis of Algorithm It is determination of amount of time and space Generally perform following types of analysis: Worst case – Big Oh (MAX) Best case - Big Omega Average case – Big Theta Amortized – Overall cost