©

Christian Jacob

Chapter Overview

Chapter 5

Problem Solving

before

Programming

5.1 Problem-Solving Strategies

5.2 Algorithms as Paths Through “Problem Spaces”

5.3 Givens, Goals, and Resources

5.4 Analysing and Exploring Problem Spaces

5.5 From Blind Search to Informed Search

5.6 Analytical Reasoning

5.7 The Analogical Approach

5.8 References

Page 2

Chapter 5: Problem Solving before Programming © Christian Jacob

Prev Next Last

oblems is like

o already solved

First Back TOC

5.1 Problem-Solving Strategies

Finding algorithmic solutions to programming prsolving mysteries in detective stories.

• Analytical problem-solving:

- the “Hercule Poirot” approach

- careful laying out of the evidence

- logically putting together little clues

• Analogical approach:

- the “Jane Marple” approach

- finding solutions by analogy or comparison tproblems

Page 3 Chapter 5: Problem Solving before Programming © Christian Jacob

Prev Next Last

— at least for

First Back TOC

• Trial and error, hacking:

This approach is, of course, less recommended beginners.

Page 4

Chapter 5: Problem Solving

before

Programming

© Christian Jacob

Prev Next Last

Problem

viour intended to

into a particular

at a computer can e steps or

First Back TOC Algorithms as Paths Through “Problem Spaces”

5.2 Algorithms as Paths Through “Spaces”

Algorithm: a precise specification of a behasolve a well-defined problem

Coding: the translation of an algorithmprogramming language

Program: a step-by-step execution plan thperform as a sequence of simplinstructions

Page 5

Chapter 5: Problem Solving

before

Programming

©

Christian Jacob

Prev Next Last

es.

computer

e Noun

First Back TOC Algorithms as Paths Through “Problem Spaces”

Sequences can have complex underlying structur

Example: sentences

Dagwood likes his fast

Name Verb Pronoun Adjectiv

Subject Predicate Object

Sentence

Page 6

Chapter 5: Problem Solving before Programming © Christian Jacob

Prev Next Last

s and goals.

transform a

givens to goals in a

different problems nments).

First Back TOC Givens, Goals, and Resources

5.3 Givens, Goals, and Resources

• Givens: initial conditions of the problem(the way things are)

• Goals: desired state(s)(the way things should be)

Any problem can be formulated at least as given

•

Resources

: the means or methods that canproblem state into another,in order to move the solver fromstep-by-step manner

Differences in givens, goals, and resources make (example: different levels of programming enviro

Page 7 Chapter 5: Problem Solving before Programming © Christian Jacob

Prev Next Last

lities

: the givens, goals, r.

ogramming

First Back TOC Givens, Goals, and Resources

Examples:

• Game playing

- Given: initial game setup

- Goal: win!

- Resources: possible moves

• Preparing a meal

- Givens: available ingredients and cookin faci

- Goal: end up with something to eat

- Resources: recipe, the cook’s experience, ...

Note

: Many of our daily problems are ill-definedresources, or combinations of the three, is

unclea

Example: client — application programmer — prlanguage — computer

Page 8 Chapter 5: Problem Solving before Programming © Christian Jacob

Prev Next Last

em Spaces

s, generated by or moves, which en state to a goal

F C / P G F G / P C

P F C / G P F G / C

G / P F C F / P G C

P G / F C P F / G C

/ P F G C

First Back TOC Analysing and Exploring Problem Spaces

5.4 Analysing and Exploring Probl

Problem space: a complete set of possible stateexploring all the possible steps,may or may not lead from a givstate.

P F G C /

F G C / P G C / P F

P G C / F

C / P F G

P C / F G

Page 9

Chapter 5: Problem Solving

before

Programming © Christian Jacob

Prev Next Last

of a problem?

them?

on?

s and other states

eces?

y independent or

oal? How can they

lution?

First Back TOC Analysing and Exploring Problem Spaces

What should we know for a preliminary analysis

• What are the givens? Do we really have all of

- Are the givens specific to a particular situati

- Can we generalize

?

- Is there a

notation

that represents the givensuccinctly?

• What is the

goal

?

- Is there are single goal, or are there several?

- If there is a single goal, can it be split into pi

- If there are several goals or subgoals, are theare they connected?

- Are there obstacles to overcome to reach a gbe overcome?

- Are there any constraints on developing a so

Page 10 Chapter 5: Problem Solving before Programming © Christian Jacob

Prev Next Last

cedures, rules,

reconditions, to be

ces that meet the

source, what

esource, what stays

roblem?

First Back TOC Analysing and Exploring Problem Spaces

• What are the resources (moves, operators, protransformations)?

- For each resource, are there constraints, or paddressed before applying it?

- If so, are there other, possibly simpler, resourpreconditions?

- What are the variants? When you apply a rechanges?

- What are the invariants? When you apply a rthe same?

- Are there more powerful resources for this p

- Would someone else know these resources?

- ...

Page 11

Chapter 5: Problem Solving

before

Programming

© Christian Jacob

Prev Next Last

Search

P F G C / P F G / C

F G / P C

First Back TOC From Blind Search to Informed Search

5.5 From Blind Search to Informed

Example: the FOX-CORN-GOOSE problem

Search tree (for two actions)

P F G C /

F G C / P

P F G C / P F G C / P G C / F P F G C / P F C / G

G C / P F F C / P G

Page 12

Chapter 5: Problem Solving

before Programming © Christian Jacob

Prev Next Last

blem

F G / P C

P F G / C

F / P G C

P F / G C

First Back TOC From Blind Search to Informed Search

State space graph for the FOX-CORN-GOOSE pro

P F G C /

F G C / P G C / P F F C / P G

P G C / F P F C / G

C / P F G G / P F C

P C / F G P G / F C

/ P F G C

Page 13

Chapter 5: Problem Solving

before

Programming

©

Christian Jacob

Prev Next Last

(1)

(4)

(8)(8)

(4)(5)

(1)

(2)(3)

(12)

(2)(3)(3)

(3) / (7)

First Back TOC Analytical Reasoning

5.6 Analytical Reasoning

Example: Planning a menu for a meal

I. Preceding Courses:

A. Soup course:1. Cream of lettice2. Light sherry

B. Fish course:

1. Filet of sole Veronique

II.

Main Course:

A.

Main dish:

1.

Cornish game hen à l’orange

2. Red wine

B.

Accompanying dishes:

1.

Creamed spinach

2.

Wild rice

3. Beverage : dry white wine

Page 14 Chapter 5: Problem Solving before Programming © Christian Jacob

Prev Next Last

(1)

(5)

(9)(10)

(5)

(10)(11)

like planning a

eveloped in a top-

ttom-up

First Back TOC Analytical Reasoning

III. Following Courses:

A. Salad course:1. Assorted green2. Vinaigrette dressing

B. Dessert:1. Mandarin orange tart2. Sweet, heavier white whine

Laying out an algorithm or a problem solution ismenu.

The different parts of the problem solution are d

down

fashion.

An alternative approach would be to develop

bo

(e.g., starting from the ingredients).

Page 15 Chapter 5: Problem Solving before Programming © Christian Jacob

Prev Next Last

rugcessful

yes

yes

no

no

no

yes

?

First Back TOC The Analogical Approach

5.7 The Analogical Approach

Patient VomitingAbdominal

painFever Pulse

Dsuc

A yes yes high elevated

B yes yes no

normal

C

yes

no high normal

D no yes high elevated

E no no high elevated

F

yes yes

no elevated

Newpatient

yes yes low normal

Page 16 Chapter 5: Problem Solving before Programming © Christian Jacob

Prev Next Last

, Boston, MA: WCB/

First Back TOC References

5.8 References

• G. Blank and R. Barnes, The Universal MachineMcGraw-Hill, 1998. Chapters 2.1 through 2.5.