Python-Based Data Structures and Algorithms
Python-Based Data Structures and Algorithms is a book that teaches readers how to use the Python programming language to
152 18 9MB
English Pages 1071 Year 2023
Table of contents :
Python-Based Data Structures and Algorithms
Preface
Python Programming 101 1
1.1 Chapter Goals
1.2 Creating Objects
1.2.1 Literal Values
1.2.2 Non-literal Object Creation
1.3 Calling Methods on Objects
1.4 Implementing a Class
1.4.1 Creating Objects and Calling Methods
1.4.2 The Dog Class
1.5 Operator Overloading
1.5.1 The Dog Class with Overloaded Addition
1.6 Importing Modules
1.7 Indentation in Python Programs
1.8 The Main Function
1.8.1 Python Program Structure
1.9 Reading from a File
1.9.1 A Text File with Single Line Records
1.9.2 Reading and Processing Single Line Records
1.9.3 Pattern for Reading Single Line Records from a File
1.10 Reading Multi-line Records from a File
1.10.1 A Text File with Multiple Line Records
1.10.2 Reading and Processing Multi-line Records
1.10.3 Pattern for Reading Multi-line Records from a File
1.11 A Container Class
1.12 Polymorphism
1.12.1 Graphics Command Classes
1.13 The Accumulator Pattern
1.13.1 List of Squares
1.13.2 A Graphics Program
1.14 Implementing a GUI with Tkinter
1.14.1 A GUI Drawing Application
1.15 XML Files
1.15.1 The Truck XML File
1.15.2 The GoToCommand with XML Creation Code
1.15.3 Writing Graphics Commands to an XML File
1.16 Reading XML Files
1.16.1 Using an XML Parser
1.17 Chapter Summary
1.18 Review Questions
1.19 Programming Problems
Computational Complexity 2
2.1 Chapter Goals
2.2 Computer Architecture
2.2.1 Running a Program
2.3 Accessing Elements in a Python List
2.3.1 List Access Timing
2.3.2 A Plot XML Sample
2.4 Big-Oh Notation
2.5 The PyList Append Operation
2.5.1 Inefficient Append
2.6 A Proof by Induction
2.7 Making the PyList Append Efficient
2.7.1 Efficient Append
2.8 Commonly Occurring Computational Complexities
2.9 More Asymptotic Notation
2.9.1 Big-Oh Asymptotic Upper Bound
2.9.2 Asymptotic Lower Bound
2.9.3 Theta Asymptotic Tight Bound
2.10 Amortized Complexity
2.10.1 A PyList Class
2.10.2 Proof of Append Complexity
2.11 Chapter Summary
2.12 Review Questions
2.13 Programming Problems
Recursion 3
3.1 Chapter Goals
3.2 Scope
3.2.1 Local Scope
3.2.2 Enclosing Scope
3.2.3 Global Scope
3.2.4 Built-In Scope
3.2.5 LEGB
3.3 The Run-Time Stack and the Heap
3.4 Writing a Recursive Function
3.4.1 Sum of Integers
3.4.2 Recursive Sum of Integers
3.4.3 No Else Needed
3.5 Tracing the Execution of a Recursive Function
3.6 Recursion in Computer Graphics
3.6.1 Recursive Spiral
3.7 Recursion on Lists and Strings
3.7.1 List Recursion
3.7.2 Reversing a List
3.7.4 Another Version of Reverse
3.8 Using Type Reflection
3.8.1 Reflection Reverse
3.9 Chapter Summary
3.10 Review Questions
3.11 Programming Problems
Sequences 4
4.1 Chapter Goals
4.2 Lists
4.2.1 The PyList Datatype
4.2.2 The PyList Constructor
4.2.3 PyList Get and Set
4.2.4 PyList Concatenate
4.2.5 PyList Append
4.2.6 PyList Insert
4.2.7 PyList Delete
4.2.8 PyList Equality Test
4.2.9 PyList Iteration
4.2.10 PyList Length
4.2.11 PyList Membership
4.2.12 PyList String Conversion
4.2.13 PyList String Representation
4.3 Cloning Objects
4.4 Item Ordering
4.4.1 The Point Class
4.4.2 Calling the Sort Method
4.5 Selection Sort
4.5.2 The Selection Sort Code
4.6 Merge Sort
4.6.1 The Merge Sort Code
4.7 Quicksort
4.7.1 The Quicksort Code
4.8 Two-Dimensional Sequences
4.8.1 The Board Class
4.8.2 The X, O, and Dummy Classes
4.9 The Minimax Algorithm
4.10 Linked Lists
4.10.1 The Node Class
4.10.2 The LinkedList Constructor
4.10.3 LinkedList Get and Set
4.10.4 LinkedList Concatenate
4.10.5 LinkedList Append
4.10.6 LinkedList Insert
4.10.7 Other Linked List Operations
4.11 Stacks and Queues
4.11.1 The Stack Class Code
4.11.2 Infix Expression Evaluation
4.11.3 Radix Sort
4.11.4 The CharAt Function
4.12 Chapter Summary
4.13 Review Questions
4.14 Programming Problems
Sets and Maps 5
5.1 Chapter Goals
5.2 Playing Sudoku
5.3 Sets
5.4 Hashing
5.5 The HashSet Class
5.5.1 The HashSet Constructor
5.5.2 Storing an Item
5.5.3 Collision Resolution
5.5.4 HashSet Add Helper Function
5.5.5 The Load Factor
5.5.6 HashSet Add
5.5.7 Deleting an Item
5.5.8 HashSet Remove Helper Function
5.5.9 HashSet Remove
5.5.10 Finding an Item
5.5.11 HashSet Membership
5.5.12 Iterating Over a Set
5.5.13 Other Set Operations
5.5.14 HashSet Difference Update
5.5.15 HashSet Difference
5.6 Solving Sudoku
5.6.1 The Sudoku Reduce Function
5.7 Maps
5.7.1 The HashMap Class
5.7.2 HashSet Get Item
5.7.3 The HashMap Class
5.8 Memoization
5.8.1 A Memoized Fibonacci Function
5.9 Correlating Two Sources of Information
5.10 Chapter Summary
5.11 Review Questions
5.12 Programming Problems
Trees 6
6.1 Chapter Goals
6.2 Abstract Syntax Trees and Expressions
6.2.1 Constructing ASTs
6.3 Prefix and Postfix Expressions
6.3.1 AST Tree Traversal
6.4 Parsing Prefix Expressions
6.4.1 The Prefix Expression Grammar
6.4.2 A Prefix Expression Parser
6.4.3 The Postfix Expression Grammar
6.5 Binary Search Trees
6.5.1 The BinarySearchTree Class
6.6 Search Spaces
6.6.1 Depth-First Search Algorithm
6.6.2 Sudoku Depth-First Search
6.6.3 Calling Sudoku’s Solve Function
6.7 Chapter Summary
6.8 Review Questions
6.9 Programming Problems
Graphs 7
7.1 Chapter Goals
7.2 Graph Notation
7.3 Searching a Graph
7.3.1 Iterative Depth First Search of a Graph
7.4 Kruskal’s Algorithm
7.4.1 Proof of Correctness
7.4.2 Kruskal’s Complexity Analysis
7.4.3 The Partition Data Structure
7.5 Dijkstra’s Algorithm
7.5.1 Dijkstra’s Complexity Analysis
7.6 Graph Representations
7.6.1 A Graph XML File
7.6.2 A Vertex Class
7.6.3 An Edge Class
7.7 Chapter Summary
7.8 Review Questions
7.9 Programming Problems
Membership Structures 8
8.1 Chapter Goals
8.2 Bloom Filters
8.2.1 The Hashing Functions
8.2.2 The Bloom Filter Size
8.2.3 Drawbacks of a Bloom Filter
8.3 The Trie Datatype
8.3.1 The Trie Class
8.3.2 Inserting into a Trie
8.3.3 Membership in a Trie
8.3.4 Comparing Tries and Bloom Filters
8.4 Chapter Summary
8.5 Review Questions
8.6 Programming Problems
Heaps 9
9.1 Chapter Goals
9.2 Key Ideas
9.3 Building a Heap
9.3.1 The buildFrom Method
9.4 The Heapsort Algorithm Version 1
9.4.1 The addToHeap Method
9.5 Analysis of Version 1 Phase I
9.6 Phase II
9.6.1 The siftDownFromTo Method
9.7 Analysis of Phase II
9.8 The Heapsort Algorithm Version 2
9.9 Analysis of Heapsort Version 2
9.10 Comparison to Other Sorting Algorithms
9.11 Chapter Summary
9.12 Review Questions
9.13 Programming Problems
Balanced Binary Search Trees 10
10.1 Chapter Goals
10.2 Binary Search Trees
10.2.1 Binary Search Tree Insert
10.3 AVL Trees
10.3.1 Definitions
10.3.2 Implementation Alternatives
10.3.3 AVLNode with Stored Balance
10.3.4 AVL Tree Iterative Insert
10.3.5 Rotations
10.3.6 AVL Tree Recursive Insert
10.3.7 The Recursive Insert AVL Tree Class Declaration
10.3.8 Maintaining Balance Versus Height
10.3.9 AVLNode with Stored Height
10.3.10 Deleting an Item from an AVL Tree
10.4 Splay Trees
10.4.1 Splay Rotations
10.5 Iterative Splaying
10.6 Recursive Splaying
10.7 Performance Analysis
10.8 Chapter Summary
10.9 Review Questions
10.10 Programming Problems
B-Trees 11
11.1 Chapter Goals
11.2 Relational Databases
11.2.1 The Feed Table
11.2.2 The FeedAttribType Table
11.2.3 The FeedAttribute Table
11.2.4 A Temporary Table
11.2.5 Programming the Joining of Tables
11.2.6 The readRecord Function
11.2.7 Efficient Join
11.3 B-Tree Organization
11.4 The Advantages of B-Trees
11.5 B-Tree Implementation
11.6 B-Tree Insert
11.7 B-Tree Delete
11.8 Chapter Summary
11.9 Review Questions
11.10 Programming Problems
Heuristic Search 12
12.1 Chapter Goals
12.2 Depth First Search
12.2.1 Iterative Depth First Search of a Graph
12.2.2 Maze Representation
12.2.3 DFS Example
12.3 Breadth First Search
12.3.1 BFS Example
12.4 Hill Climbing
12.4.1 Hill Climbing Example
12.4.2 Closed Knight’s Tour
12.4.3 The N-Queens Problem
12.5 Best First Search
12.5.1 Best First Example
12.6 A* Search
12.6.1 A* Example
12.7 Minimax Revisited
12.8 Chapter Summary
12.9 Review Questions
12.10 Programming Problems
Appendix A: Integer Operators 13
Appendix B: Float Operators 14
Appendix C: String Operators and Methods
Appendix D: List Operators and Methods
Appendix E: Dictionary Operators and Methods
Appendix F:Turtle Methods 18
Appendix G:TurtleScreen Methods 19
20.1 The Draw Program
20.2 The Scope Program
20.3 The Sort Animation
20.4 The PlotData Program
20.5 The Tic Tac Toe Application
20.6 The Connect Four Front-End
Index
Python-Based Data Structures and Algorithms
Preface
Python Programming 101 1
1.1 Chapter Goals
1.2 Creating Objects
1.2.1 Literal Values
1.2.2 Non-literal Object Creation
1.3 Calling Methods on Objects
1.4 Implementing a Class
1.4.1 Creating Objects and Calling Methods
1.4.2 The Dog Class
1.5 Operator Overloading
1.5.1 The Dog Class with Overloaded Addition
1.6 Importing Modules
1.7 Indentation in Python Programs
1.8 The Main Function
1.8.1 Python Program Structure
1.9 Reading from a File
1.9.1 A Text File with Single Line Records
1.9.2 Reading and Processing Single Line Records
1.9.3 Pattern for Reading Single Line Records from a File
1.10 Reading Multi-line Records from a File
1.10.1 A Text File with Multiple Line Records
1.10.2 Reading and Processing Multi-line Records
1.10.3 Pattern for Reading Multi-line Records from a File
1.11 A Container Class
1.12 Polymorphism
1.12.1 Graphics Command Classes
1.13 The Accumulator Pattern
1.13.1 List of Squares
1.13.2 A Graphics Program
1.14 Implementing a GUI with Tkinter
1.14.1 A GUI Drawing Application
1.15 XML Files
1.15.1 The Truck XML File
1.15.2 The GoToCommand with XML Creation Code
1.15.3 Writing Graphics Commands to an XML File
1.16 Reading XML Files
1.16.1 Using an XML Parser
1.17 Chapter Summary
1.18 Review Questions
1.19 Programming Problems
Computational Complexity 2
2.1 Chapter Goals
2.2 Computer Architecture
2.2.1 Running a Program
2.3 Accessing Elements in a Python List
2.3.1 List Access Timing
2.3.2 A Plot XML Sample
2.4 Big-Oh Notation
2.5 The PyList Append Operation
2.5.1 Inefficient Append
2.6 A Proof by Induction
2.7 Making the PyList Append Efficient
2.7.1 Efficient Append
2.8 Commonly Occurring Computational Complexities
2.9 More Asymptotic Notation
2.9.1 Big-Oh Asymptotic Upper Bound
2.9.2 Asymptotic Lower Bound
2.9.3 Theta Asymptotic Tight Bound
2.10 Amortized Complexity
2.10.1 A PyList Class
2.10.2 Proof of Append Complexity
2.11 Chapter Summary
2.12 Review Questions
2.13 Programming Problems
Recursion 3
3.1 Chapter Goals
3.2 Scope
3.2.1 Local Scope
3.2.2 Enclosing Scope
3.2.3 Global Scope
3.2.4 Built-In Scope
3.2.5 LEGB
3.3 The Run-Time Stack and the Heap
3.4 Writing a Recursive Function
3.4.1 Sum of Integers
3.4.2 Recursive Sum of Integers
3.4.3 No Else Needed
3.5 Tracing the Execution of a Recursive Function
3.6 Recursion in Computer Graphics
3.6.1 Recursive Spiral
3.7 Recursion on Lists and Strings
3.7.1 List Recursion
3.7.2 Reversing a List
3.7.4 Another Version of Reverse
3.8 Using Type Reflection
3.8.1 Reflection Reverse
3.9 Chapter Summary
3.10 Review Questions
3.11 Programming Problems
Sequences 4
4.1 Chapter Goals
4.2 Lists
4.2.1 The PyList Datatype
4.2.2 The PyList Constructor
4.2.3 PyList Get and Set
4.2.4 PyList Concatenate
4.2.5 PyList Append
4.2.6 PyList Insert
4.2.7 PyList Delete
4.2.8 PyList Equality Test
4.2.9 PyList Iteration
4.2.10 PyList Length
4.2.11 PyList Membership
4.2.12 PyList String Conversion
4.2.13 PyList String Representation
4.3 Cloning Objects
4.4 Item Ordering
4.4.1 The Point Class
4.4.2 Calling the Sort Method
4.5 Selection Sort
4.5.2 The Selection Sort Code
4.6 Merge Sort
4.6.1 The Merge Sort Code
4.7 Quicksort
4.7.1 The Quicksort Code
4.8 Two-Dimensional Sequences
4.8.1 The Board Class
4.8.2 The X, O, and Dummy Classes
4.9 The Minimax Algorithm
4.10 Linked Lists
4.10.1 The Node Class
4.10.2 The LinkedList Constructor
4.10.3 LinkedList Get and Set
4.10.4 LinkedList Concatenate
4.10.5 LinkedList Append
4.10.6 LinkedList Insert
4.10.7 Other Linked List Operations
4.11 Stacks and Queues
4.11.1 The Stack Class Code
4.11.2 Infix Expression Evaluation
4.11.3 Radix Sort
4.11.4 The CharAt Function
4.12 Chapter Summary
4.13 Review Questions
4.14 Programming Problems
Sets and Maps 5
5.1 Chapter Goals
5.2 Playing Sudoku
5.3 Sets
5.4 Hashing
5.5 The HashSet Class
5.5.1 The HashSet Constructor
5.5.2 Storing an Item
5.5.3 Collision Resolution
5.5.4 HashSet Add Helper Function
5.5.5 The Load Factor
5.5.6 HashSet Add
5.5.7 Deleting an Item
5.5.8 HashSet Remove Helper Function
5.5.9 HashSet Remove
5.5.10 Finding an Item
5.5.11 HashSet Membership
5.5.12 Iterating Over a Set
5.5.13 Other Set Operations
5.5.14 HashSet Difference Update
5.5.15 HashSet Difference
5.6 Solving Sudoku
5.6.1 The Sudoku Reduce Function
5.7 Maps
5.7.1 The HashMap Class
5.7.2 HashSet Get Item
5.7.3 The HashMap Class
5.8 Memoization
5.8.1 A Memoized Fibonacci Function
5.9 Correlating Two Sources of Information
5.10 Chapter Summary
5.11 Review Questions
5.12 Programming Problems
Trees 6
6.1 Chapter Goals
6.2 Abstract Syntax Trees and Expressions
6.2.1 Constructing ASTs
6.3 Prefix and Postfix Expressions
6.3.1 AST Tree Traversal
6.4 Parsing Prefix Expressions
6.4.1 The Prefix Expression Grammar
6.4.2 A Prefix Expression Parser
6.4.3 The Postfix Expression Grammar
6.5 Binary Search Trees
6.5.1 The BinarySearchTree Class
6.6 Search Spaces
6.6.1 Depth-First Search Algorithm
6.6.2 Sudoku Depth-First Search
6.6.3 Calling Sudoku’s Solve Function
6.7 Chapter Summary
6.8 Review Questions
6.9 Programming Problems
Graphs 7
7.1 Chapter Goals
7.2 Graph Notation
7.3 Searching a Graph
7.3.1 Iterative Depth First Search of a Graph
7.4 Kruskal’s Algorithm
7.4.1 Proof of Correctness
7.4.2 Kruskal’s Complexity Analysis
7.4.3 The Partition Data Structure
7.5 Dijkstra’s Algorithm
7.5.1 Dijkstra’s Complexity Analysis
7.6 Graph Representations
7.6.1 A Graph XML File
7.6.2 A Vertex Class
7.6.3 An Edge Class
7.7 Chapter Summary
7.8 Review Questions
7.9 Programming Problems
Membership Structures 8
8.1 Chapter Goals
8.2 Bloom Filters
8.2.1 The Hashing Functions
8.2.2 The Bloom Filter Size
8.2.3 Drawbacks of a Bloom Filter
8.3 The Trie Datatype
8.3.1 The Trie Class
8.3.2 Inserting into a Trie
8.3.3 Membership in a Trie
8.3.4 Comparing Tries and Bloom Filters
8.4 Chapter Summary
8.5 Review Questions
8.6 Programming Problems
Heaps 9
9.1 Chapter Goals
9.2 Key Ideas
9.3 Building a Heap
9.3.1 The buildFrom Method
9.4 The Heapsort Algorithm Version 1
9.4.1 The addToHeap Method
9.5 Analysis of Version 1 Phase I
9.6 Phase II
9.6.1 The siftDownFromTo Method
9.7 Analysis of Phase II
9.8 The Heapsort Algorithm Version 2
9.9 Analysis of Heapsort Version 2
9.10 Comparison to Other Sorting Algorithms
9.11 Chapter Summary
9.12 Review Questions
9.13 Programming Problems
Balanced Binary Search Trees 10
10.1 Chapter Goals
10.2 Binary Search Trees
10.2.1 Binary Search Tree Insert
10.3 AVL Trees
10.3.1 Definitions
10.3.2 Implementation Alternatives
10.3.3 AVLNode with Stored Balance
10.3.4 AVL Tree Iterative Insert
10.3.5 Rotations
10.3.6 AVL Tree Recursive Insert
10.3.7 The Recursive Insert AVL Tree Class Declaration
10.3.8 Maintaining Balance Versus Height
10.3.9 AVLNode with Stored Height
10.3.10 Deleting an Item from an AVL Tree
10.4 Splay Trees
10.4.1 Splay Rotations
10.5 Iterative Splaying
10.6 Recursive Splaying
10.7 Performance Analysis
10.8 Chapter Summary
10.9 Review Questions
10.10 Programming Problems
B-Trees 11
11.1 Chapter Goals
11.2 Relational Databases
11.2.1 The Feed Table
11.2.2 The FeedAttribType Table
11.2.3 The FeedAttribute Table
11.2.4 A Temporary Table
11.2.5 Programming the Joining of Tables
11.2.6 The readRecord Function
11.2.7 Efficient Join
11.3 B-Tree Organization
11.4 The Advantages of B-Trees
11.5 B-Tree Implementation
11.6 B-Tree Insert
11.7 B-Tree Delete
11.8 Chapter Summary
11.9 Review Questions
11.10 Programming Problems
Heuristic Search 12
12.1 Chapter Goals
12.2 Depth First Search
12.2.1 Iterative Depth First Search of a Graph
12.2.2 Maze Representation
12.2.3 DFS Example
12.3 Breadth First Search
12.3.1 BFS Example
12.4 Hill Climbing
12.4.1 Hill Climbing Example
12.4.2 Closed Knight’s Tour
12.4.3 The N-Queens Problem
12.5 Best First Search
12.5.1 Best First Example
12.6 A* Search
12.6.1 A* Example
12.7 Minimax Revisited
12.8 Chapter Summary
12.9 Review Questions
12.10 Programming Problems
Appendix A: Integer Operators 13
Appendix B: Float Operators 14
Appendix C: String Operators and Methods
Appendix D: List Operators and Methods
Appendix E: Dictionary Operators and Methods
Appendix F:Turtle Methods 18
Appendix G:TurtleScreen Methods 19
20.1 The Draw Program
20.2 The Scope Program
20.3 The Sort Animation
20.4 The PlotData Program
20.5 The Tic Tac Toe Application
20.6 The Connect Four Front-End
Index
