Problem Solving

Developing a software application is a complex process that requires some guiding principles or methodologies.

George Pólya wrote How to Solve It, a book that has sold over a million copies. In this book he divides the problem solving task into four stages:

1.  Understanding the Problem
2.  Devising a Plan
3.  Carrying out the Plan
4.  Looking Back (evaluating your solution)

Top Down Design (a.k.a. stepwise refinement)

method for designing programmed solutions to complex problems.

seeks to reduce the complexity of a problem by organizing it in a manageable way.

Top-down design has three major steps:

1. Break the problem down into simpler subproblems
2. Solve each subproblem (possibly by using top-down design)
3. Combine the those solutions to form a solution to the problem

Consider building a house.

• Suppose you divide it into subtasks of building front and back halves.
• Not a good idea; each subtask smaller but no easier!
• Instead, divide it into subtasks such as framing, electrical, plumbing, etc.

• Are there identifiable, distinct, phases of the problem?
• Are there any aspects of the problem that are repetitive?
• Do certain parts of the problem resemble other?

• each subproblem may need to be further divided into subsubproblems or subsubsubproblems, etc.
• Continue dividing until each fragment of the problem is simple enough that its solution is obvious.
• Solutions are then devised to the small problems, and those solutions combined to form the overall solution.

Other examples of non-trivial tasks

• Writing term paper or book
• Developing a web page or web site
• Planning an awards banquet with expected 200 in attendance
• planning a spring break trip to Florida
• if you are a member of an Otterbein athletic team, beating Capital (or other major rival) in your sport

Software Development Lifecycle

This approach is echoed in what has become known as the Software Development Cycle, consisting of multiple phases:

1. Investigation
2. Analysis
3. Design
4. Development
5. Implementation
6. Maintenance
7. Retirement

Investigation is the process of determining the feasibility of a proposed system. This addresses such issues as:

• whether proposed system will meet client organization needs
• whether potential benefits of proposed system will outweigh its costs
• whether technology required by the proposed system is available and affordable

Analysis is the process of understanding the problem. Consult client to determine requirements, such as :

• what is the input?
• in what format should it be expected?
• what output is required?
• how should it be presented?
• Results of analysis are documented in written specification
• specification needs to be understandable to both client and developer

• Interest shifts from the problem to the solution.
• A solution is designed, based on the specifications.
• need to design the user interface, the database, the business logic (process)
Textual and graphical techniques are used to document design
• may also develop prototype product as part of analysis and design

• programmers write programs to carry out the design
• technical writers produce documentation on how to use the system
• testers extensively test the system (this actually occurs throughout analysis and design too) to make sure it works correctly

• carrying out the plan to transition from the old system to the new system
• training people who will use the new system
• installing the new system

Retirement occurs when the system has become outmoded and is replaced by a yet newer system

Algorithm

computer program is implementation of an algorithm : a step-by-step description of how the program's task will be accomplished. The task and algorithm may be very complex. A program is a set of instructions that tell the computer how to carry out the algorithm.

Programming Languages

In the beginning, there were machine languages.  Instructions coded as 1’s and 0’s.  OK for computer, hard to humans to do reliably

Assembly languages were developed, giving names to all the machine instructions.  Each assembly instruction corresponds to one machine instruction.  Better, but still hard for humans to do reliably.  Requires assembler to translate into machine language.

High level languages were developed.  Each language instruction corresponds to a (perhaps lengthy) sequence of machine instructions.  Much easier for people.

• FORTRAN: FORMula TRANslator.  Developed in 1950s for numerical applications.
• COBOL: COmmon Business Oriented Language.  Developed in 1950s for data processing.  English-like language.
• LISP : LISt Processor.  Developed in late 1950’s, this is the language for artificial intelligence applications.
• C: developed in late 1960s.  Used initially for telephone switching applications.  Successor to Fortran for numerical computing.
• Pascal: developed in 1970s as an educational language.
• C++: extension of C which includes object-oriented programming (OOP).  OOP is good because objects in the design/implementation will correspond to objects identified in the analysis/specification.  Developed in the 1980s
• Java: similar to C++, but developed in the 1990s to program smart appliances and also for programming WWW software.

There are so many because different problems and solutions can be expressed more efficiently using different vocabularies.  No single language includes all vocabularies.

All of them are equally powerful, however, as you will see next.

Theoretical basis for programming languages

Alan Turing, as one of his most important contributions to the field of computer science, developed a mathematical model of computation called the Turing Machine.

The Turing Machine has been shown to be capable of computing anything which is computable (i.e. programmable). Yes, there are things that cannot be programmed!

It has been shown that a programming language is equivalent to a Turing Machine in terms of the problems it can solve if it possesses three simple abilities.

1. Sequence
2. Selection
3. Iteration

Selection is the ability to make decisions, of which there are two varieties: deciding for or against and deciding either/or. For or against is a decision of whether to take some course of action, or none at all. Either/or is a decision between two possible courses of action.

Iteration is the ability to repeat an action in a loop.

All the programming languages listed above (and thousands of others) have all these capabilities, and so are equally as powerful as Turing Machines and each other!

Language choice is a matter of how efficiently a solution can be expressed, not whether it can be expressed.