Chapter 7 Problem Solving and Algorithms

• This is probably the most important chapter of the book.
  • Learning the underlying technology is nice, but not critical.
  • Learning the technical skill of programming is a mechanical process.
  • Learning applications is useful but not critical.
• Learning how to solve problems, so that we can use all of the above is a critical issue.
  • Unfortunately, I am not sure I know how to teach this skill in class.
  • I learned it by working with my Dad almost every night and weekend on projects.
    • With him making fun of me when I did dumb things.... Thanks Dad!
  • I learned it in Boy Scouts
    • In the various challenges they threw at you as you progressed through the ranks.
  • I learned it in school, again by the challenges and problems.
• The book introduces Polya
  • He wrote a book called How to Solve It
  • This is a great reference, and worth a read.
    • Especially if you struggle as a problem solver.
    • But it is aimed at math problems.
    • And it is slightly strange.
• Polya's steps
  1. Understand the problem.
     • What are you asked to do? Show? Find?
     • Can you restate the problem in your own words?
     • Can you draw a picture/diagram?
     • Do you have enough information to find a solution?
     • Do you understand all of the words/terms?
     • Do you need to ask questions/seek clarification?
  2. Make a plan to solve the problem.
     • This is not necessarily the algorithm we are discussing, but that fits.
     • He lists a bunch of problem solving strategies.
     • And go from general to specific.
  3. Cary out the plan
     • If you have done a good job of planning, this should be easier.
     • But you may encounter problems.
     • Work through them.
  4. Evaluate your work
     • Did your plan work, could you have done better?
     • Use this to improve both your solution and your problem solving techniques.
• Some of Polya's Strategies include
  • Ask questions.
    • This is more to explore the problem space than anything.
    • I find if you can come up with a good question, you show you understand things.
    • NOT TRIVIAL QUESTIONS.
    • This takes real work.
  • Look for Familiar things
    • We (will soon) study classical algorithms to see how people have done things in the past.
    • If this applies, use it.
    • Don't reinvent the wheel.
  • Divide and Conquer
    • We will spend a lot of time on this in the future.
    • Can I break this into smaller problems? (YES)
    • Solve the smaller problems leads to a solution to the bigger problem.
• The computer problem solving process
  • We have looked at this before.
    1. Analyze the problem
       • Test
    2. Develop and Algorithm
       • Test
    3. Implement the Algorithm
       • Test
    4. Maintenance.
  • 
• Look at my Homework Assignment for 230
  • Why is each component part of this assignment?