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PART I: Algorithmic Problem Solving
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PART I: Algorithmic Problem Solving
by Roland Backhouse
Algorithmic Problem Solving
Coverpage
Titlepage
Copyright
Contents
Preface
PART I: Algorithmic Problem Solving
CHAPTER 1: Introduction
1.1 Algorithms
1.2 Algorithmic Problem Solving
1.3 Overview
1.4 Bibliographic Remarks
CHAPTER 2: Invariants
2.1 Chocolate Bars
2.2 Empty Boxes
2.3 The Tumbler Problem
2.4 Tetrominoes
2.5 Summary
2.6 Bibliographic Remarks
CHAPTER 3: Crossing a River
3.1 Problems
3.2 Brute Force
3.3 Nervous Couples
3.4 Rule of Sequential Composition
3.5 The Bridge Problem
3.6 Conditional Statements
3.7 Summary
3.8 Bibliographic Remarks
CHAPTER 4: Games
4.1 Matchstick Games
4.2 Winning Strategies
4.3 Subtraction-Set Games
4.4 Sums of Games
4.5 Summary
4.6 Bibliographic Remarks
CHAPTER 5: Knights and Knaves
5.1 Logic Puzzles
5.2 Calculational Logic
5.3 Equivalence and Continued Equalities
5.4 Negation
5.5 Summary
5.6 Bibliographic Remarks
CHAPTER 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
CHAPTER 7: Fake-Coin Detection
7.1 Problem Formulation
7.2 Problem Solution
7.3 Summary
7.4 Bibliographic Remarks
CHAPTER 8: The Tower of Hanoi
8.1 Specification and Solution
8.2 Inductive Solution
8.3 The Iterative Solution
8.4 Summary
8.5 Bibliographic Remarks
CHAPTER 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
9.5 Projects
9.6 Summary
9.7 Bibliographic Remarks
CHAPTER 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
CHAPTER 11: Knight’s Circuit
11.1 Straight-Move Circuits
11.2 Supersquares
11.3 Partitioning the Board
11.4 Summary
11.5 Bibliographic Remarks
PART II: Mathematical Techniques
CHAPTER 12: The Language of Mathematics
12.1 Variables, Expressions and Laws
12.2 Sets
12.3 Functions
12.4 Types and Type Checking
12.5 Algebraic Properties
12.6 Boolean Operators
12.7 Binary Relations
12.8 Calculations
12.9 Exercises
CHAPTER 13: Boolean Algebra
13.1 Boolean Equality
13.2 Negation
13.3 Disjunction
13.4 Conjunction
13.5 Implication
13.6 Set Calculus
13.7 Exercises
CHAPTER 14: Quantifiers
14.1 DotDotDot and Sigmas
14.2 Introducing Quantifier Notation
14.3 Universal and Existential Quantification
14.4 Quantifier Rules
14.5 Exercises
CHAPTER 15: Elements of Number Theory
15.1 Inequalities
15.2 Minimum and Maximum
15.3 The Divides Relation
15.4 Modular Arithmetic
15.5 Exercises
CHAPTER 16: Relations, Graphs and Path Algebras
16.1 Paths in a Directed Graph
16.2 Graphs and Relations
16.3 Functional and Total Relations
16.4 Path-Finding Problems
16.5 Matrices
16.6 Closure Operators
16.7 Acyclic Graphs
16.8 Combinatorics
16.9 Exercises
Solutions to Exercises
References
Index
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CHAPTER 1: Introduction
Part I
Algorithmic Problem Solving
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