Chapter 0 Mathematical Background¶
Chapter 1 Big Ideas of Algorithms¶
Chapter 2 Time Complexity¶
- 2.1. Best, Worst, and Average Cases
- 2.2. Faster Computer, or Faster Algorithm?
- 2.3. Asymptotic Analysis and Upper Bounds
- 2.4. Lower Bounds and \(\Theta\) Notation
- 2.5. Calculating Program Running Time
- 2.6. Analyzing Problems
- 2.7. Common Misunderstandings
- 2.8. Multiple Parameters
- 2.9. Space Bounds
- 2.10. Code Tuning and Empirical Analysis
- 2.11. Summation Techniques
- 2.12. Solving Recurrence Relations
- 2.13. Algorithm Analysis Summary Exercises
- 2.14. Algorithm Analysis Summary Exercises
Chapter 3 Linear Structures¶
- 3.1. Chapter Introduction: Lists
- 3.2. The List ADT
- 3.3. Array-Based List Implementation
- 3.4. Linked Lists
- 3.5. Comparison of List Implementations
- 3.6. Doubly Linked Lists
- 3.7. List Element Implementations
- 3.8. Stacks
- 3.9. Linked Stacks
- 3.10. Freelists
- 3.11. Implementing Recursion
- 3.12. Queues
- 3.13. Linked Queues
- 3.14. Linear Structure Summary Exercises
Chapter 4 Binary Trees¶
- 4.1. Binary Trees Chapter Introduction
- 4.2. Binary Trees
- 4.3. Binary Tree as a Recursive Data Structure
- 4.4. The Full Binary Tree Theorem
- 4.5. Binary Tree Traversals
- 4.6. Implementing Tree Traversals
- 4.7. Information Flow in Recursive Functions
- 4.7.1. Information Flow in Recursive Functions
- 4.7.2. Binary Tree Set Depth Exercise
- 4.7.3. Collect-and-return
- 4.7.4. Binary Tree Check Sum Exercise
- 4.7.5. Binary Tree Leaf Nodes Count Exercise
- 4.7.6. Binary Tree Sum Nodes Exercise
- 4.7.7. Combining Information Flows
- 4.7.8. Binary Tree Check Value Exercise
- 4.7.9. Combination Problems
- 4.7.10. Binary Tree Height Exercise
- 4.7.11. Binary Tree Get Difference Exercise
- 4.7.12. Binary Tree Has Path Sum Exercise
- 4.8. Binary Tree Node Implementations
- 4.9. Composite-based Expression Tree
- 4.10. Binary Tree Space Requirements
- 4.11. Binary Search Trees
- 4.12. Dictionary Implementation Using a BST
- 4.13. Binary Tree Guided Information Flow
- 4.14. Multiple Binary Trees
- 4.15. A Hard Information Flow Problem
- 4.16. Array Implementation for Complete Binary Trees
- 4.17. Heaps and Priority Queues
- 4.18. Trees versus Tries
- 4.19. 2-3 Trees
- 4.20. Binary Tree Chapter Summary
Chapter 5 Search Structures¶
Chapter 6 Sorting¶
- 6.1. Chapter Introduction: Sorting
- 6.2. Sorting Terminology and Notation
- 6.3. Insertion Sort
- 6.4. Bubble Sort
- 6.5. Selection Sort
- 6.6. The Cost of Exchange Sorting
- 6.7. Optimizing Sort Algorithms with Code Tuning
- 6.8. Shellsort
- 6.9. Mergesort Concepts
- 6.10. Implementing Mergesort
- 6.11. Quicksort
- 6.12. Heapsort
- 6.13. Binsort
- 6.14. Radix Sort
- 6.15. An Empirical Comparison of Sorting Algorithms
- 6.16. Lower Bounds for Sorting
- 6.17. Amortized Analysis
- 6.18. Sorting Summary Exercises
Chapter 7 Graphs¶
Chapter 8 Dynamic Programming¶
Chapter 9 Limits to Computing¶
- 9.1. Limits to Computing
- 9.2. Reductions
- 9.3. NP-Completeness
- 9.4. Circuit Satisfiability
- 9.5. Formula Satisfiability
- 9.6. 3-CNF Satisfiability
- 9.7. The Clique Problem
- 9.8. The Independent Set Problem
- 9.9. The Vertex Cover Problem
- 9.10. The Hamiltonian Cycle Problem
- 9.11. The Traveling Salesman Problem
- 9.12. NP-Completeness Proofs
- 9.13. Reduction of Circuit SAT to SAT
- 9.14. Reduction of SAT to 3-SAT
- 9.15. Reduction of 3-SAT to Clique
- 9.16. Reduction of Clique to Independent Set
- 9.17. Reduction of Independent Set to Vertex Cover
- 9.18. Reduction of 3-SAT to Hamiltonian Cycle
- 9.19. Reduction of Hamiltonian Cycle to Traveling Salesman
- 9.20. Coping with NP-Complete Problems
- 9.21. Unsolveable Problems
- 9.22. Turing Machines
