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Problem Solving and Algorithm Design

Problem Solving and Algorithm Design. Problem Solving. Problem solving The act of finding a solution to a perplexing, distressing, vexing, or unsettled question. Problem Solving. G. Polya wrote How to Solve It: A New Aspect of Mathematical Method

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Problem Solving and Algorithm Design

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  1. Problem Solving and Algorithm Design

  2. Problem Solving • Problem solvingThe act of finding a solution to a perplexing, distressing, vexing, or unsettled question.

  3. Problem Solving • G. Polya wrote How to Solve It: A New Aspect of Mathematical Method • His “How to Solve It” list is quite general. • It’s written in the context of solving mathematical problems. • With simple wording changes the list becomes applicable to all types of problems.

  4. Ask Questions... • …to understand the problem: • What do I know about the problem? • What is the information that I have to process in order the find the solution? • What does the solution look like? • What sort of special cases exist? • How will I recognize that I have found the solution?

  5. Look for Familiar Things • You should never “reinvent the wheel”. • In computing, you see certain problems again and again in different guises. • A good programmer sees a task, or perhaps part of a task (a subtask), that has been solved before and plugs in the solution.

  6. Divide and Conquer • Break up a large problem into smaller units that can be handled more easily. • Abstraction plays an important role. • The divide-and-conquer approach can be applied over and over again until each subtask is manageable.

  7. Abstraction Abstraction - A mental model that removes complex details. This is a key concept. Abstraction will reappear throughout the course – be sure you understand it! 5

  8. Algorithms • Algorithm:A set of instructions for solving a problem or subproblem in a finite amount of time using a finite amount of data. • The instructions must be unambiguous.

  9. Example of an Algorithm • Preparing a Hollandaise sauce:

  10. Pseudocode • … uses a mixture of English and formatting to make the steps in the solution explicit.

  11. Developing an Algorithm • Since implementing the algorithm involves making it computer-readable, the plan must be in a suitable form. • The methodology (set of working methods) used to make the plan must begin with a problem statement and conclude with a plan that can be easily coded.

  12. Developing an Algorithm • Two methodologies are currently used, both based on the divide-and-conquer strategy: • Top-Down Design • (functional decomposition) • Object-Oriented Design • (OOD)

  13. Top-Down Design • … consists of breaking the problem into a set of subproblems called modules. • It creates a hierarchical structure of problems and subproblems (modules). • This process continues for as many levels as it takes to expand every task to the smallest details. • A step that needs to be expanded is an abstract step. • A step that needs no more expansion is a concrete step.

  14. Top-Down Design Figure 6.5 An example of top-down design

  15. Object-Oriented Design Object-oriented design is the process of planning a system of interacting objects for the purpose of solving a software problem. An object is an exemplar of a class. A class defines the abstract characteristics of a thing (object), including the thing's properties and the things it can do, or methods. One might say that a class is a blueprint that describes the nature of something.

  16. Object-Oriented Design An example: The class of Dog defines all possible dogs by listing the characteristics and behaviours they can have; the object Lassie is one particular dog, with particular versions of the characteristics. A Dog has fur; Lassie has brown-and-white fur.

  17. Object-Oriented Design Programming techniques may include features such as: • information hiding, • data abstraction, • encapsulation, • modularity, • polymorphism, • and inheritance.

  18. Testing the Algorithm • Regardless of the design methodology, the algorithm itself must be tested. • Testing at the algorithm development phase involves looking at each part of the design.

  19. Testing the Algorithm • Desk checking: Working through a design at a desk with a pencil and paper. • Walk-through: Manual simulation of the design by the team members, taking sample data values and simulating the design using the sample data. • Inspection: One person (not the designer) reads the design (handed out in advance) line by line while the others point out errors.

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