Analysis of Algorithm Part one analysis.ppt
- 1. Programming Fundamentals --> Ch1. Problem solving 1 Fundamentals of Algorithms Problem Solving
- 2. Fundamentals of Algorithmic Problem Solving
- 3. Programming Fundamentals --> Ch1. Problem solving 3 Problem Solving • Algorithm Step-by-step problem-solving process Solution achieved in finite amount of time Problem Solution by computer
- 4. Programming Fundamentals --> Ch1. Problem solving 4 Problem Solving Process • Phase 1 - Analyze the problem Outline the problem and its requirements Design (algorithm) to solve the problem ( Flow chart, pseudo code) Algorithm tracing • Phase 2 - Implement the algorithm Implement the algorithm in code (in Programming Language Program) Verify that the algorithm works • Phase 3 - Maintenance Use and modify the program if the requirements changes
- 5. Choosing between Exact and Approximate Problem Solving • The next principal decision is to choose between solving the problem exactly (exact algorithm) or solving the problem approximately (approximation algorithm). Exact algorithm Eg. extracting square roots, solving nonlinear equations, and evaluating definite integrals. Approximation algorithm Eg. Vertex Cover, Traveling Salesman Problem
- 6. Programming Fundamentals --> Ch1. Problem solving 6 Analyze the Problem (1) Design Algorithm • Pseudocode - is a mixture of a natural language and programming language constructs. Pseudo code is usually more precise than natural language. • Flow chart - a method of expressing an algorithm by a collection of connected geometric shapes containing descriptions of the algorithm’s steps
- 7. Programming Fundamentals --> Ch1. Problem solving 7 Flow Chart Symbols Start and End Input / output Selection Calculation Data Flow • A Flowchart is An algorithm graphical representation. Written as a combination of the following graphical notations:
- 8. Programming Fundamentals --> Ch1. Problem solving 8 • Pseudo-code: <Algorithm name> The comment lines “//” Begin <data definition> <actions> End
- 9. Programming Fundamentals --> Ch1. Problem solving 9 Analyze the Problem (1) Algorithm Tracing Draw flowchart Find all possible paths Check each path with appropriate input data Observed Outputs not conform to the expected ones error in the algorithm.
- 10. Proving an Algorithm’s Correctness/verification •Once an algorithm has been specified, you have to prove its correctness. i.e. you have to prove that the algorithm yields a required result for every legitimate input in a finite amount of time. Analyzing an Algorithm two kinds of analyzing the algorithm efficiency: • time efficiency- indicating how fast the algorithm runs • space efficiency-indicating how much extra memory it uses. •Range of inputs-These factors are not satisfactory then redesign the algorithm.
- 11. Programming Fundamentals --> Ch1. Problem solving 11 Computer Stage: after completing the program, the computer must do the following: 1.Compilation: 2.Execution: when the program become don’t has errors, the computer execute it to produce the output
- 12. Programming Fundamentals --> Ch1. Problem solving 12 Implement the algorithm • Errors are of three types: . syntax errors . run-time errors . logic errors • Syntax errors: detected by the C compiler . source code does not conform to one or more of C’s grammar rules . examples of syntax errors: undeclared variable, … • Often one mistake leads to multiple error messages – can be confusing
- 13. Programming Fundamentals --> Ch1. Problem solving 13 Implement the algorithm • Run-time errors. detected and displayed by computer during execution. - Occur when program directs computer to perform illegal operation. - will stop program execution and display message • Logic errors. - caused by faulty algorithm - sign of error: incorrect program output - cure: thorough testing and comparison with expected results A logic error is also referred to as a bug, so finding logic errors is called debugging.