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The Resource Algorithmic problem solving, Roland Backhouse

Algorithmic problem solving, Roland Backhouse

Label
Algorithmic problem solving
Title
Algorithmic problem solving
Statement of responsibility
Roland Backhouse
Creator
Subject
Language
eng
Cataloging source
DLC
http://library.link/vocab/creatorDate
1948-
http://library.link/vocab/creatorName
Backhouse, Roland C.
Illustrations
illustrations
Index
index present
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/subjectName
  • Computer algorithms
  • Problem solving
Label
Algorithmic problem solving, Roland Backhouse
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Contents
pt. I Algorithmic Problem Solving -- ch. 1 Introduction -- 1.1. Algorithms -- 1.2. Algorithmic Problem Solving -- 1.3. Overview -- 1.4. Bibliographic Remarks -- ch. 2 Invariants -- 2.1. Chocolate Bars -- 2.1.1. The Solution -- 2.1.2. The Mathematical Solution -- 2.2. Empty Boxes -- 2.2.1. Review -- 2.3. The Tumbler Problem -- 2.3.1. Non-deterministic Choice -- 2.4. Tetrominoes -- 2.5. Summary -- 2.6. Bibliographic Remarks -- ch. 3 Crossing a River -- 3.1. Problems -- 3.2. Brute Force -- 3.2.1. Goat, Cabbage and Wolf -- 3.2.2. State-Space Explosion -- 3.2.3. Abstraction -- 3.3. Nervous Couples -- 3.3.1. What Is the Problem? -- 3.3.2. Problem Structure -- 3.3.3. Denoting States and Transitions -- 3.3.4. Problem Decomposition -- 3.3.5. A Review -- 3.4. Rule of Sequential Composition -- 3.5. The Bridge Problem -- 3.6. Conditional Statements -- 3.7. Summary -- 3.8. Bibliographic Remarks -- ch. 4 Games -- 4.1. Matchstick Games -- 4.2. Winning Strategies -- 4.2.1. Assumptions -- 4.2.2. Labelling Positions -- 4.2.3. Formulating Requirements -- 4.3. Subtraction-Set Games -- 4.4. Sums of Games -- 4.4.1. A Simple Sum Game -- 4.4.2. Maintain Symmetry! -- 4.4.3. More Simple Sums -- 4.4.4. Evaluating Positions -- 4.4.5. Using the Mex Function -- 4.5. Summary -- 4.6. Bibliographic Remarks -- ch. 5 Knights and Knaves -- 5.1. Logic Puzzles -- 5.2. Calculational Logic -- 5.2.1. Propositions -- 5.2.2. Knights and Knaves -- 5.2.3. Boolean Equality -- 5.2.4. Hidden Treasures -- 5.2.5. Equals for Equals -- 5.3. Equivalence and Continued Equalities -- 5.3.1. Examples of the Associativity of Equivalence -- 5.3.2. On Natural Language -- 5.4. Negation -- 5.4.1. Contraposition -- 5.4.2. Handshake Problems -- 5.4.3. Inequivalence -- 5.5. Summary -- 5.6. Bibliographic Remarks -- ch. 6 Induction -- 6.1. Example Problems -- 6.2. Cutting the Plane -- 6.3. Triominoes -- 6.4. Looking for Patterns -- 6.5. The Need for Proof -- 6.6. From Verification to Construction -- 6.7. Summary -- 6.8. Bibliographic Remarks -- ch. 7 Fake-Coin Detection -- 7.1. Problem Formulation -- 7.2. Problem Solution -- 7.2.1. The Basis -- 7.2.2. Induction Step -- 7.2.3. The Marked-Coin Problem -- 7.2.4. The Complete Solution -- 7.3. Summary -- 7.4. Bibliographic Remarks -- ch. 8 The Tower of Hanoi -- 8.1. Specification and Solution -- 8.1.1. The End of the World! -- 8.1.2. Iterative Solution -- 8.1.3. Why? -- 8.2. Inductive Solution -- 8.3. The Iterative Solution -- 8.4. Summary -- 8.5. Bibliographic Remarks -- ch. 9 Principles of Algorithm Design -- 9.1. Iteration, Invariants and Making Progress -- 9.2. A Simple Sorting Problem -- 9.3. Binary Search -- 9.4. Sam Loyd's Chicken-Chasing Problem -- 9.4.1. Cornering the Prey -- 9.4.2. Catching the Prey -- 9.4.3. Optimality -- 9.5. Projects -- 9.6. Summary -- 9.7. Bibliographic Remarks -- ch. 10 The Bridge Problem -- 10.1. Lower and Upper Bounds -- 10.2. Outline Strategy -- 10.3. Regular Sequences -- 10.4. Sequencing Forward Trips -- 10.5. Choosing Settlers and Nomads -- 10.6. The Algorithm -- 10.7. Summary -- 10.8. Bibliographic Remarks -- ch. 11 Knight's Circuit -- 11.1. Straight-Move Circuits -- 11.2. Supersquares -- 11.3. Partitioning the Board -- 11.4. Summary -- 11.5. Bibliographic Remarks -- pt. II Mathematical Techniques -- ch. 12 The Language of Mathematics -- 12.1. Variables, Expressions and Laws -- 12.2. Sets -- 12.2.1. The Membership Relation -- 12.2.2. The Empty Set -- 12.2.3. Types/Universes -- 12.2.4. Union and Intersection -- 12.2.5. Set Comprehension -- 12.2.6. Bags -- 12.3. Functions -- 12.3.1. Function Application -- 12.3.2. Binary Operators -- 12.3.3. Operator Precedence -- 12.4. Types and Type Checking -- 12.4.1. Cartesian Product and Disjoint Sum -- 12.4.2. Function Types -- 12.5. Algebraic Properties -- 12.5.1. Symmetry -- 12.5.2. Zero and Unit -- 12.5.3. Idempotence -- 12.5.4. Associativity -- 12.5.5. Distributivity/Factorisation -- 12.5.6. Algebras -- 12.6. Boolean Operators -- 12.7. Binary Relations -- 12.7.1. Reflexivity -- 12.7.2. Symmetry -- 12.7.3. Converse -- 12.7.4. Transitivity -- 12.7.5. Anti-symmetry -- 12.7.6. Orderings -- 12.7.7. Equality -- 12.7.8. Equivalence Relations -- 12.8. Calculations -- 12.8.1. Steps in a Calculation -- 12.8.2. Relations between Steps -- 12.8.3. "If" and "Only If" -- 12.9. Exercises -- ch. 13 Boolean Algebra -- 13.1. Boolean Equality -- 13.2. Negation -- 13.3. Disjunction -- 13.4. Conjunction -- 13.5. Implication -- 13.5.1. Definitions and Basic Properties -- 13.5.2. Replacement Rules -- 13.6. Set Calculus -- 13.7. Exercises -- ch. 14 Quantifiers -- 14.1. DotDotDot and Sigmas -- 14.2. Introducing Quantifier Notation -- 14.2.1. Summation -- 14.2.2. Free and Bound Variables -- 14.2.3. Properties of Summation -- 14.2.4. Warning -- 14.3. Universal and Existential Quantification -- 14.3.1. Universal Quantification -- 14.3.2. Existential Quantification -- 14.4. Quantifier Rules -- 14.4.1. The Notation -- 14.4.2. Free and Bound Variables -- 14.4.3. Dummies -- 14.4.4. Range Part -- 14.4.5. Trading -- 14.4.6. Term Part -- 14.4.7. Distributivity Properties -- 14.5. Exercises -- ch. 15 Elements of Number Theory -- 15.1. Inequalities -- 15.2. Minimum and Maximum -- 15.3. The Divides Relation -- 15.4. Modular Arithmetic -- 1.5.4.1. Integer Division -- 15.4.2. Remainders and Modulo Arithmetic -- 15.5. Exercises -- ch. 16 Relations, Graphs and Path Algebras -- 16.1. Paths in a Directed Graph -- 16.2. Graphs and Relations -- 16.2.1. Relation Composition -- 16.2.2. Union of Relations -- 16.2.3. Transitive Closure -- 16.2.4. Reflexive Transitive Closure -- 16.3. Functional and Total Relations -- 16.4. Path-Finding Problems -- 16.4.1. Counting Paths -- 16.4.2. Frequencies -- 16.4.3. Shortest Distances -- 16.4.4. All Paths -- 16.4.5. Semirings and Operations on Graphs -- 16.5. Matrices -- 16.6. Closure Operators -- 16.7. Acyclic Graphs -- 16.7.1. Topological Ordering -- 16.8. Combinatorics -- 16.8.1. Basic Laws -- 16.8.2. Counting Choices -- 16.8.3. Counting Paths -- 16.9. Exercises
Control code
ocn680434847
Dimensions
24 cm
Extent
xiii, 414 p.
Isbn
9780470684535
Isbn Type
(pbk. : alk. paper)
Lccn
2011022716
Other physical details
ill.
System control number
(OCoLC)680434847
Label
Algorithmic problem solving, Roland Backhouse
Publication
Bibliography note
Includes bibliographical references and index
Contents
pt. I Algorithmic Problem Solving -- ch. 1 Introduction -- 1.1. Algorithms -- 1.2. Algorithmic Problem Solving -- 1.3. Overview -- 1.4. Bibliographic Remarks -- ch. 2 Invariants -- 2.1. Chocolate Bars -- 2.1.1. The Solution -- 2.1.2. The Mathematical Solution -- 2.2. Empty Boxes -- 2.2.1. Review -- 2.3. The Tumbler Problem -- 2.3.1. Non-deterministic Choice -- 2.4. Tetrominoes -- 2.5. Summary -- 2.6. Bibliographic Remarks -- ch. 3 Crossing a River -- 3.1. Problems -- 3.2. Brute Force -- 3.2.1. Goat, Cabbage and Wolf -- 3.2.2. State-Space Explosion -- 3.2.3. Abstraction -- 3.3. Nervous Couples -- 3.3.1. What Is the Problem? -- 3.3.2. Problem Structure -- 3.3.3. Denoting States and Transitions -- 3.3.4. Problem Decomposition -- 3.3.5. A Review -- 3.4. Rule of Sequential Composition -- 3.5. The Bridge Problem -- 3.6. Conditional Statements -- 3.7. Summary -- 3.8. Bibliographic Remarks -- ch. 4 Games -- 4.1. Matchstick Games -- 4.2. Winning Strategies -- 4.2.1. Assumptions -- 4.2.2. Labelling Positions -- 4.2.3. Formulating Requirements -- 4.3. Subtraction-Set Games -- 4.4. Sums of Games -- 4.4.1. A Simple Sum Game -- 4.4.2. Maintain Symmetry! -- 4.4.3. More Simple Sums -- 4.4.4. Evaluating Positions -- 4.4.5. Using the Mex Function -- 4.5. Summary -- 4.6. Bibliographic Remarks -- ch. 5 Knights and Knaves -- 5.1. Logic Puzzles -- 5.2. Calculational Logic -- 5.2.1. Propositions -- 5.2.2. Knights and Knaves -- 5.2.3. Boolean Equality -- 5.2.4. Hidden Treasures -- 5.2.5. Equals for Equals -- 5.3. Equivalence and Continued Equalities -- 5.3.1. Examples of the Associativity of Equivalence -- 5.3.2. On Natural Language -- 5.4. Negation -- 5.4.1. Contraposition -- 5.4.2. Handshake Problems -- 5.4.3. Inequivalence -- 5.5. Summary -- 5.6. Bibliographic Remarks -- ch. 6 Induction -- 6.1. Example Problems -- 6.2. Cutting the Plane -- 6.3. Triominoes -- 6.4. Looking for Patterns -- 6.5. The Need for Proof -- 6.6. From Verification to Construction -- 6.7. Summary -- 6.8. Bibliographic Remarks -- ch. 7 Fake-Coin Detection -- 7.1. Problem Formulation -- 7.2. Problem Solution -- 7.2.1. The Basis -- 7.2.2. Induction Step -- 7.2.3. The Marked-Coin Problem -- 7.2.4. The Complete Solution -- 7.3. Summary -- 7.4. Bibliographic Remarks -- ch. 8 The Tower of Hanoi -- 8.1. Specification and Solution -- 8.1.1. The End of the World! -- 8.1.2. Iterative Solution -- 8.1.3. Why? -- 8.2. Inductive Solution -- 8.3. The Iterative Solution -- 8.4. Summary -- 8.5. Bibliographic Remarks -- ch. 9 Principles of Algorithm Design -- 9.1. Iteration, Invariants and Making Progress -- 9.2. A Simple Sorting Problem -- 9.3. Binary Search -- 9.4. Sam Loyd's Chicken-Chasing Problem -- 9.4.1. Cornering the Prey -- 9.4.2. Catching the Prey -- 9.4.3. Optimality -- 9.5. Projects -- 9.6. Summary -- 9.7. Bibliographic Remarks -- ch. 10 The Bridge Problem -- 10.1. Lower and Upper Bounds -- 10.2. Outline Strategy -- 10.3. Regular Sequences -- 10.4. Sequencing Forward Trips -- 10.5. Choosing Settlers and Nomads -- 10.6. The Algorithm -- 10.7. Summary -- 10.8. Bibliographic Remarks -- ch. 11 Knight's Circuit -- 11.1. Straight-Move Circuits -- 11.2. Supersquares -- 11.3. Partitioning the Board -- 11.4. Summary -- 11.5. Bibliographic Remarks -- pt. II Mathematical Techniques -- ch. 12 The Language of Mathematics -- 12.1. Variables, Expressions and Laws -- 12.2. Sets -- 12.2.1. The Membership Relation -- 12.2.2. The Empty Set -- 12.2.3. Types/Universes -- 12.2.4. Union and Intersection -- 12.2.5. Set Comprehension -- 12.2.6. Bags -- 12.3. Functions -- 12.3.1. Function Application -- 12.3.2. Binary Operators -- 12.3.3. Operator Precedence -- 12.4. Types and Type Checking -- 12.4.1. Cartesian Product and Disjoint Sum -- 12.4.2. Function Types -- 12.5. Algebraic Properties -- 12.5.1. Symmetry -- 12.5.2. Zero and Unit -- 12.5.3. Idempotence -- 12.5.4. Associativity -- 12.5.5. Distributivity/Factorisation -- 12.5.6. Algebras -- 12.6. Boolean Operators -- 12.7. Binary Relations -- 12.7.1. Reflexivity -- 12.7.2. Symmetry -- 12.7.3. Converse -- 12.7.4. Transitivity -- 12.7.5. Anti-symmetry -- 12.7.6. Orderings -- 12.7.7. Equality -- 12.7.8. Equivalence Relations -- 12.8. Calculations -- 12.8.1. Steps in a Calculation -- 12.8.2. Relations between Steps -- 12.8.3. "If" and "Only If" -- 12.9. Exercises -- ch. 13 Boolean Algebra -- 13.1. Boolean Equality -- 13.2. Negation -- 13.3. Disjunction -- 13.4. Conjunction -- 13.5. Implication -- 13.5.1. Definitions and Basic Properties -- 13.5.2. Replacement Rules -- 13.6. Set Calculus -- 13.7. Exercises -- ch. 14 Quantifiers -- 14.1. DotDotDot and Sigmas -- 14.2. Introducing Quantifier Notation -- 14.2.1. Summation -- 14.2.2. Free and Bound Variables -- 14.2.3. Properties of Summation -- 14.2.4. Warning -- 14.3. Universal and Existential Quantification -- 14.3.1. Universal Quantification -- 14.3.2. Existential Quantification -- 14.4. Quantifier Rules -- 14.4.1. The Notation -- 14.4.2. Free and Bound Variables -- 14.4.3. Dummies -- 14.4.4. Range Part -- 14.4.5. Trading -- 14.4.6. Term Part -- 14.4.7. Distributivity Properties -- 14.5. Exercises -- ch. 15 Elements of Number Theory -- 15.1. Inequalities -- 15.2. Minimum and Maximum -- 15.3. The Divides Relation -- 15.4. Modular Arithmetic -- 1.5.4.1. Integer Division -- 15.4.2. Remainders and Modulo Arithmetic -- 15.5. Exercises -- ch. 16 Relations, Graphs and Path Algebras -- 16.1. Paths in a Directed Graph -- 16.2. Graphs and Relations -- 16.2.1. Relation Composition -- 16.2.2. Union of Relations -- 16.2.3. Transitive Closure -- 16.2.4. Reflexive Transitive Closure -- 16.3. Functional and Total Relations -- 16.4. Path-Finding Problems -- 16.4.1. Counting Paths -- 16.4.2. Frequencies -- 16.4.3. Shortest Distances -- 16.4.4. All Paths -- 16.4.5. Semirings and Operations on Graphs -- 16.5. Matrices -- 16.6. Closure Operators -- 16.7. Acyclic Graphs -- 16.7.1. Topological Ordering -- 16.8. Combinatorics -- 16.8.1. Basic Laws -- 16.8.2. Counting Choices -- 16.8.3. Counting Paths -- 16.9. Exercises
Control code
ocn680434847
Dimensions
24 cm
Extent
xiii, 414 p.
Isbn
9780470684535
Isbn Type
(pbk. : alk. paper)
Lccn
2011022716
Other physical details
ill.
System control number
(OCoLC)680434847

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