Why do we need a problem solving method?

We need a problem solving method to answer the question, "How do you solve a problem, when you do not know how to solve the problem."

• If the problem is easy, you don't need a problem solving method.
• If the problem is hard, you just can't give up.

Here are the steps of a general problem-solving method.

• identify the problem
• define the problem
• design a solution
• implement a solution
• evaluate the results

A problem identification is a short description of the problem.

This is the most important part. Otherwise, you will be solving the wrong problem.

Who identifies the problem?

• you teacher
• your boss
• your customer
• you, if you are working for yourself
• you, if you are working on a subproblem of the problem
• ...and so on...

A subproblem is a part of a bigger problem. Where do subproblems arise?

The divide and conquer approach to problem solving goes as follows.

• The decomposition step is to break a larger problem into smaller problems (often, top-down design).
• Each of the smaller problems are solved, braking them into smaller problems if necessary.
• The composition step is to combine the solutions to the smaller problems to solve the larger problem (often, bottom-up implementation).

This is a top-down problem solving method. A top-down method, if one exists, is usually better than other methods.

• bottom-up approach
• inside-out approach
• shotgun approach
• do-nothing approach
• ready-fire-aim approach
• 0-step approach, also called point-and-grunt
• 1-step approach

Often a top-down multi-step problem solving approach works best.

Management of a large 20-story office building has been receiving complaints from people in the building that the elevators are too slow. Bentley, J. (1988). More programming pearls: confessions of a coder. Reading, MA: Addison-Wesley., p. 49.

How would you approach this problem? What are you going to do?

• Collect information.
• Make definitions.
• Learn about the problem (domain specific knowledge)
• Resolve ambiguities.

Finding the (reality) truth can be very difficult, as each stakeholder may slant their version of the (human) truth to be to their advantage.

Some things that first appear well defined are, on closer inspection, not well defined.

• When is 12:00 P.M.?
• When is 12:00 A.M.?

Legal contracts:

• 11:59 A.M., 12:01 P.M.
• 11:59 P.M., 12:01 A.M.

The Military: 0000-2359 (but most people would use 2400)

• 0000 hours (start of the day)
• 1200 hours (noon)
• 2400 hours (end of the day)

What is an interstate highway?

• I-81, I-77, and I-85, I-83 are interstate highways.
• How come Hawaii has interstate highways?

• Does a solution exist? (existence)
• Is there an effective solution? An effective solution is better than no solution.
• Is there an efficient solution? Which one is the best.

Software engineering and programming are required to implement software systems.

Although design is often best done top-down, implementation is often best done bottom-up.

Evaluating the implemented solution involves both verification and validation.

That is, it does what you said it would do (verification) and it solves the original problem (validation).

Note: In software programming, validation sometimes means that the user entered data that meets certain criteria.

Flashback: How might the elevator problem be solved?

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