Problem Decomposition and Abstraction

Problem Decomposition and Abstraction

Problem Solving

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

Problem Solving

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

What are the advantages of small problems?

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?

Common Mistake

Dive into the details (e.g. at the level of Java instructions)

Do not consider decomposing the problem first “in English”

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?

Problem Decomposition

1. Display the board2. Make a move3. Decide winner

Can these smaller problems be independently solved? tested?

Decide Winner

Seems to be complicated, what can we do?

Decide Winner

Seems to be complicated, what can we do? Decompose!

Decide Winner

Seems to be complicated, what can we do? Decompose!

a. Check 3 rowsb. Check 3 columnsc. Check 2 diagonals

Can they be independently Solved? Tested?

Top-down Decomposition

1. Display the board2. Make a move3. Decide winner

a. Check 3 rowsb. Check 3 columnsc. Check 2 diagonals

Make a Move

Decompose:

Make a Move

Decompose: Ask for a move Update the board

Top-down Decomposition

1. Display the board2. Make a move

a. Ask for a moveb. Update the board

3. Decide winnera. Check 3 rowsb. Check 3 columnsc. Check 2 diagonals

Two levels of abstraction

When to stop decomposing a problem?

When to stop decomposing a problem?

Until you’re confident you can solve the smaller problems correctly Different for different people

Make a Move

Recall there are two human players

Who makes a move?

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

?

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

Make a Move

makeAMove(player) Similar to sqrt(x) makeAMove can be used with different players

Problem abstraction via parameters

Summary

Problem decomposition Top-down

Decompose until you’re confident you can solve the small problems correctly.

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