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Algorithms and Problem Solving-1 Algorithms and Problem Solving.

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1 Algorithms and Problem Solving-1 Algorithms and Problem Solving

2 Algorithms and Problem Solving-2 Problem Solving Programming is a process of problem solving Problem solving techniques –Analyze the problem –Outline the problem requirements –Design steps (algorithm) to solve the problem Algorithm: –Step-by-step problem-solving process –Solution achieved in finite amount of time

3 Algorithms and Problem Solving-3 Problem Solving Process Step 1 - Analyze the problem –Outline the problem and its requirements –Design steps (algorithm) to solve the problem Step 2 - Implement the algorithm –Implement the algorithm in code –Verify that the algorithm works Step 3 - Maintenance –Use and modify the program if the problem domain changes

4 Algorithms and Problem Solving-4 Analyze the Problem Thoroughly understand the problem Understand problem requirements –Does program require user interaction? –Does program manipulate data? –What is the output? If the problem is complex, divide it into subproblems –Analyze each subproblem as above

5 Algorithms and Problem Solving-5 What is an algorithm? The idea behind the computer program Stays the same independent of –Which kind of hardware it is running on –Which programming language it is written in Solves a well-specified problem in a general way Is specified by –Describing the set of instances (input) it must work on –Describing the desired properties of the output

6 Algorithms and Problem Solving-6 Before a computer can perform a task, it must have an algorithm that tells it what to do. Informally: “An algorithm is a set of steps that define how a task is performed.” Formally: “An algorithm is an ordered set of unambiguous executable steps, defining a terminating process.” –Ordered set of steps: structure! –Executable steps: doable! –Unambiguous steps: follow the directions! –Terminating: must have an end!

7 Algorithms and Problem Solving-7 The definition of an algorithm

8 Algorithms and Problem Solving-8 Important Properties of Algorithms Correct –always returns the desired output for all legal instances of the problem. Unambiguous Precise Efficient –Can be measured in terms of Time Space –Time tends to be more important

9 Algorithms and Problem Solving-9 Algorithms can be represented in different ways: A single algorithm can be represented in many ways: –Formulas: F = (9/5)C + 32 –Words: Multiply the Celsius by 9/5 and add 32. –Flow Charts. –Pseudo-code. In each case, the algorithm stays the same; the implementation differs!

10 Algorithms and Problem Solving-10 A program is a representation of an algorithm designed for computer applications. –Process: Activity of executing a program, or execute the algorithm represented by the program –  Process: Activity of executing an algorithm.

11 Algorithms and Problem Solving-11 Expressing Algorithms English description Pseudo-code High-level programming language More precise More easily expressed

12 Algorithms and Problem Solving-12 Pseudocode is a notational system where ideas can be expressed in enough detail to be represented as an algorithm. Pseudocode is like a programming language but its rules are less stringent. Written as a combination of English and programming constructs –Based on selection (if, switch) and iteration (while, repeat) constructs in high-level programming languages Design using these high level primitives –Independent of actual programming language

13 Algorithms and Problem Solving-13 Example: The sequential search algorithm in pseudocode

14 Algorithms and Problem Solving-14 Algorithm discovery The Two Steps of Program Development: –1. Discover the algorithm. –2. Represent the algorithm as a program. Step 2 is the easy step! Step 1 can be very difficult! To discover an algorithm is to solve the problem!

15 Algorithms and Problem Solving-15 Problem Solving is an art and a creative process Problem solving techniques are not unique to Computer Science. The CS field has joined with other fields to try to solve problems better. Ideally, there should be an algorithm to find/develop algorithms. However, this is not the case as some problems do not have algorithmic solutions. Problem solving remains an art!

16 Algorithms and Problem Solving-16 Problem Solving Strategies Working backwards –Reverse-engineer –Once you know it can be done, it is much easier to do –What are some examples? Look for a related problem that has been solved before –Java design patterns –Sort a particular list such as: David, Alice, Carol and Bob to find a general sorting algorithm Stepwise Refinement –Break the problem into several sub-problems –Solve each subproblem separately –Produces a modular structure K.I.S.S. = Keep It Simple Stupid!

17 Algorithms and Problem Solving-17 Stepwise Refinement Stepwise refinement is a top-down methodology in that it progresses from the general to the specific. Bottom-up methodologies progress from the specific to the general. –These approaches complement each other Solutions produced by stepwise refinement posses a natural modular structure - hence its popularity in algorithmic design.

18 Algorithms and Problem Solving-18 Object-Oriented Design Methodology Four stages to the decomposition process –Brainstorming –Filtering –Scenarios –Responsibility algorithms

19 Algorithms and Problem Solving-19 Class-Responsibility-Collaboration (CRC) Cards

20 Algorithms and Problem Solving-20 Brainstorming A group problem-solving technique that involves the spontaneous contribution of ideas from all members of the group –All ideas are potential good ideas –Think fast and furiously first, and ponder later –A little humor can be a powerful force Brainstorming is designed to produce a list of candidate classes

21 Algorithms and Problem Solving-21 Filtering Determine which are the core classes in the problem solution There may be two classes in the list that have many common attributes and behaviors There may be classes that really don’t belong in the problem solution

22 Algorithms and Problem Solving-22 Scenarios Assign responsibilities to each class There are two types of responsibilities –What a class must know about itself (knowledge) –What a class must be able to do (behavior) Encapsulation is the bundling of data and actions in such a way that the logical properties of the data and actions are separated from the implementation details

23 Algorithms and Problem Solving-23 Responsibility Algorithms The algorithms must be written for the responsibilities –Knowledge responsibilities usually just return the contents of one of an object’s variables –Action responsibilities are a little more complicated, often involving calculations

24 Algorithms and Problem Solving-24 Computer Example Let’s repeat the problem-solving process for creating an address list Brainstorming and filtering –Circling the nouns and underlining the verbs Page 171

25 Computer Example First pass at a list of classes

26 Computer Example Filtered list

27 Algorithms and Problem Solving-27 CRC Cards

28 Algorithms and Problem Solving-28 Responsibility Algorithms

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