Problem Decomposition and Abstraction

1. Problem Decomposition and Abstraction

2. Problem Solving • Which one is easier: • Solving one big problem, or • Solving a number of small problems?

3. Problem Solving • Which one is easier: • Solving one big problem, or • Solving a number of small problems? • What are the advantages of small problems?

4. Problem Solving • Which one is easier: • Solving one big problem, or • Solving a number of small problems? • What are the advantages of small problems? • Easier to solve • Easier to ensure the solution is correct • In order to have a number of small problems • What do we need to do first?

5. Common Mistake • Dive into the details • (e.g. at the level of Java instructions) • Do not consider decomposing the problem first • “in English”

6. Tic-tac-toe We would like to build a tic-tac-toe game that a human can play against another How would you decompose the problem?

7. Problem Decomposition • Display the board • Make a move • Decide winner • Can these smaller problems be independently • solved? • tested?

8. Decide Winner Seems to be complicated, what can we do?

9. Decide Winner • Seems to be complicated, what can we do? • Decompose!

10. Decide Winner • Seems to be complicated, what can we do? • Decompose! • Check 3 rows • Check 3 columns • Check 2 diagonals • Can they be independently • Solved? • Tested?

11. Top-down Decomposition • Display the board • Make a move • Decide winner • Check 3 rows • Check 3 columns • Check 2 diagonals

12. Make a Move Decompose:

13. Make a Move • Decompose: • Ask for a move • Update the board

14. Top-down Decomposition • Display the board • Make a move • Ask for a move • Update the board • Decide winner • Check 3 rows • Check 3 columns • Check 2 diagonals Two levels of abstraction

15. When to stop decomposing a problem?

16. When to stop decomposing a problem? • Until you’re confident you can solve the smaller problems correctly • Different for different people

17. Make a Move Recall there are two human players Who makes a move?

18. Make a Move • Do we want • To break it down to • 2 smaller problems, each for a player • One problem that is • flexible for the 2 players • ?

19. Make a Move • Do we want • To break it down to • 2 smaller problems, each for a player • One problem that is • flexible for the 2 players • Prefer one problem that is flexible for 2 situations • The 2 smaller problems are very similar • Solving 2 similar problems is tedious • Rewriting almost the same instructions

20. Make a Move • makeAMove(player) • Similar to sqrt(x) • makeAMove can be used with different players • Problem abstraction • via parameters

21. Summary • Problem decomposition • Top-down • Decompose until you’re confident you can solve the small problems correctly.

22. Summary • Problem decomposition • Top-down • Decompose until you’re confident you can solve the small problems correctly. • Problem abstraction • Different levels of abstraction in top-down decomposition • More general to more specific • Increase abstraction via parameters • Allow the solution to be reused in different situations • Avoid repeatedly writing almost the same instructions