Chapter 5. Problem Solving before Programming

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1 Christian Jacob 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 Chapter Overview

2 Page 2 Chapter 5: Problem Solving before Programming Christian Jacob 5.1 Problem-Solving Strategies Finding algorithmic solutions to programming problems is like solving 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 to already solved problems First Back TOC Prev Next Last

3 Page 3 Chapter 5: Problem Solving before Programming Christian Jacob Trial and error, hacking: This approach is, of course, less recommended at least for beginners. First Back TOC Prev Next Last

4 Page 4 Chapter 5: Problem Solving before Programming Christian Jacob 5.2 Algorithms as Paths Through Problem Spaces Algorithm: a precise specification of a behaviour intended to solve a well-defined problem Coding: the translation of an algorithm into a particular programming language Program: a step-by-step execution plan that a computer can perform as a sequence of simple steps or instructions First Back TOC Algorithms as Paths Through Problem Spaces Prev Next Last

5 Page 5 Chapter 5: Problem Solving before Programming Christian Jacob Sequences can have complex underlying structures. Example: sentences Dagwood likes his fast computer Name Verb Pronoun Adjective Noun Subject Predicate Object Sentence First Back TOC Algorithms as Paths Through Problem Spaces Prev Next Last

6 Page 6 Chapter 5: Problem Solving before Programming Christian Jacob 5.3 Givens, Goals, and Resources Givens: Goals: initial conditions of the problem (the way things are) desired state(s) (the way things should be) Any problem can be formulated at least as givens and goals. Resources: the means or methods that can transform a problem state into another, in order to move the solver from givens to goals in a step-by-step manner Differences in givens, goals, and resources make different problems (example: different levels of programming environments). First Back TOC Givens, Goals, and Resources Prev Next Last

7 Page 7 Chapter 5: Problem Solving before Programming Christian Jacob Examples: Game playing - Given: initial game setup - Goal: win! - Resources: possible moves Preparing a meal - Givens: available ingredients and cookin facilities - Goal: end up with something to eat - Resources: recipe, the cook s experience,... Note: Many of our daily problems are ill-defined: the givens, goals, resources, or combinations of the three, is unclear. Example: client application programmer programming language computer First Back TOC Givens, Goals, and Resources Prev Next Last

8 Page 8 Chapter 5: Problem Solving before Programming Christian Jacob 5.4 Analysing and Exploring Problem Spaces Problem space: a complete set of possible states, generated by exploring all the possible steps, or moves, which may or may not lead from a given state to a goal state. P F G C / F G C / P G C / P F F C / P G F G / P C P G C / F P F C / G P F G / C C / P F G G / P F C F / P G C P C / F G P G / F C P F / G C / P F G C First Back TOC Analysing and Exploring Problem Spaces Prev Next Last

9 Page 9 Chapter 5: Problem Solving before Programming Christian Jacob What should we know for a preliminary analysis of a problem? What are the givens? Do we really have all of them? - Are the givens specific to a particular situation? - Can we generalize? - Is there a notation that represents the givens and other states succinctly? What is the goal? - Is there are single goal, or are there several? - If there is a single goal, can it be split into pieces? - If there are several goals or subgoals, are they independent or are they connected? - Are there obstacles to overcome to reach a goal? How can they be overcome? - Are there any constraints on developing a solution? First Back TOC Analysing and Exploring Problem Spaces Prev Next Last

10 Page 10 Chapter 5: Problem Solving before Programming Christian Jacob What are the resources (moves, operators, procedures, rules, transformations)? - For each resource, are there constraints, or preconditions, to be addressed before applying it? - If so, are there other, possibly simpler, resources that meet the preconditions? - What are the variants? When you apply a resource, what changes? - What are the invariants? When you apply a resource, what stays the same? - Are there more powerful resources for this problem? - Would someone else know these resources? -... First Back TOC Analysing and Exploring Problem Spaces Prev Next Last

11 Page 11 Chapter 5: Problem Solving before Programming Christian Jacob 5.5 From Blind Search to Informed Search Example: the FOX-CORN-GOOSE problem Search tree (for two actions) P F G C / F G C / P G C / P F F C / P G F G / P C P F G C / P F G C / P G C / F P F G C / P F C / G P F G C / P F G / C First Back TOC From Blind Search to Informed Search Prev Next Last

12 Page 12 Chapter 5: Problem Solving before Programming Christian Jacob State space graph for the FOX-CORN-GOOSE problem P F G C / F G C / P G C / P F F C / P G F G / P C P G C / F P F C / G P F G / C C / P F G G / P F C F / P G C P C / F G P G / F C P F / G C / P F G C First Back TOC From Blind Search to Informed Search Prev Next Last

13 Page 13 Chapter 5: Problem Solving before Programming Christian Jacob 5.6 Analytical Reasoning Example: Planning a menu for a meal I. Preceding Courses: (1) A. Soup course: (4) 1. Cream of lettice (8) 2. Light sherry (8) B. Fish course: (4) 1. Filet of sole Veronique (5) II. Main Course: (1) A. Main dish: (2) 1. Cornish game hen à l orange (3) 2. Red wine (12) B. Accompanying dishes: (2) 1. Creamed spinach (3) 2. Wild rice (3) 3. Beverage: dry white wine (3) / (7) First Back TOC Analytical Reasoning Prev Next Last

14 Page 14 Chapter 5: Problem Solving before Programming Christian Jacob III. Following Courses: (1) A. Salad course: (5) 1. Assorted green (9) 2. Vinaigrette dressing (10) B. Dessert: (5) 1. Mandarin orange tart (10) 2. Sweet, heavier white whine (11) Laying out an algorithm or a problem solution is like planning a menu. The different parts of the problem solution are developed in a topdown fashion. An alternative approach would be to develop bottom-up (e.g., starting from the ingredients). First Back TOC Analytical Reasoning Prev Next Last

15 Page 15 Chapter 5: Problem Solving before Programming Christian Jacob 5.7 The Analogical Approach Patient Vomiting Abdominal pain Fever Pulse Drug successful A yes yes high elevated yes B yes yes no normal yes C yes no high normal no D no yes high elevated no E no no high elevated no F yes yes no elevated yes New patient yes yes low normal? First Back TOC The Analogical Approach Prev Next Last

16 Page 16 Chapter 5: Problem Solving before Programming Christian Jacob 5.8 References G. Blank and R. Barnes, The Universal Machine, Boston, MA: WCB/ McGraw-Hill, Chapters 2.1 through 2.5. First Back TOC References Prev Next Last

PUTTING ENGLISH TO WORK 1: Unit 8. In this unit you will learn:

PUTTING ENGLISH TO WORK 1: Unit 8 ORDERING FOOD In this unit you will learn: THESE LIFE SKILLS: Order food in a restaurant Take orders in a restaurant Read and understand a bill Please bring me some coffee.