Whole Picture

	Solving large problems is tough -- but approach them logically and you will succeed

Problem Solving

	Large problems share many properties:
			They are daunting -- there’s so much to do!
			We don’t know were to begin
			Not sure we know all of the tasks that must be done to produce a solution
			Not sure we know how to do all of the parts -- new knowledge may be required
			Not sure it is within our capability -- maybe an expert is needed

Problem Decomposition

	“Divide and conquer” is a political strategy, military strategy & IT strategy
	Top-level Plan --
			1. Describe (in any language) a series of steps that produce a solution
			2. For each step, solve it or decompose further
			3. For steps needing decomposition, repeat 2
			4. Assemble solutions and test correctness
			5. When solution fully assembled, evaluate

More Specifics

	We will step through the process, using Project 2 as an example:
			Problem decomposition is
			mostly common sense
			Process is not algorithmic
			Problem decomposition is
			to help you, so apply it as
			needed

1. Give Steps to a Solution

	Specify (in any language) a series of steps that produce a solution
			For a huge problem the steps may at first be vague, but they can be (& must be) made more precise as the whole picture emerges
			The goal is an algorithm(s), so …
			List & describe the inputs
			List & describe the outputs
			Be guided in figuring out the steps by the need to transform the inputs into the outputs

What Are Steps for PC?

What Are Steps for PC?

	Purple Concentrate:
			Build Basic GUI
			Set up control keys
			Build the Display Grid
			Build mouse-sensed KeyGrid
			Write functions for ctrl keys
			Set up customizing keys
			Primp design & make cool

PERT

	PERT is Program Evaluation & Review Technique … developed in 1950s
			Diagrams show the dependencies visually

2&3. Solve or Decompose

	For each step, solve it or decompose it further, i.e. apply same technique
			Most “top level” steps can’t be brained out, and need further decomposition
			“Top level” steps often seem huge, too
			The technique allows one to concentrate on only one problem at a time
			As before, focus on inputs, outputs, process to transform inputs into outputs

2&3. Solve or Decompose

	“Build mouse-sensed keypad”

2&3. Solve or Decompose

	“Build mouse-sensed keypad”
			Layout GIF 7x7 grid
			Setup to change grid color
			Build onClick e-handler
			…
			Define GIF prefetch array
			Prefetch brown & orange
			Build mouse e-handlers
			Update colors in e-handlers

4. Assemble Parts

	Assemble Solutions &Test Correctness
			Putting solutions together can be tough because of different assumptions made while solving the parts -- it always happens
			When working alone it is common to combine parts along the way and to test continuously
			Because of the need to test, pick a good order to solve the problems

4. Assemble Parts

	Proj2 solves & assembles parts together in a ‘good’ order

4. Assemble Parts

	Proj2 solves & assembles parts together in a ‘good’ order
			Most parts of Project 2 use
			the developing solution
			for testing -- that’s ‘good’
			Notice adding steps to
			test a solution may be wise
			Parts mismatch is common
			problem, but not in Proj2

Summary

	Large problems can be solved by the ‘divide and conquer’ technique
			The process is “top down” -- get a top level solution even if it is vague, imprecise
			Whenever you cannot produce a solution to a step directly, reapply the technique
			The start and first several steps will be daunting … but the process works!
			Get part of solution working quickly if possible