## Course Outlines
We have used the manuscript several times in a one-semester algorithms course that meets three hours per week. The prerequisite include courses in college algebra, discrete structures, and data structures. In an ideal situation, the students remember the material in the mathematics prerequisites sufficiently well for them to be able to review Appendixes A and B on their own. However, we have found it necessary to review most of the material in these appendixes. Given this need, we cover the material in the following order:
- [Appendix A](LiB0093.html#1281): All
- [Chapter 1](LiB0008.html#16): All
- [Appendix B](LiB0102.html#1369): All
- [Chapter 2](LiB0014.html#141): [Sections 2.1](LiB0015.html#145)–[2.5](LiB0019.html#193), [2.8](LiB0022.html#234)
- [Chapter 3](LiB0024.html#252): [Sections 3.1](LiB0025.html#256)–[3.4](LiB0028.html#290), [3.6](LiB0030.html#331)
- [Chapter 4](LiB0032.html#359): [Sections 4.1](LiB0033.html#366), [4.2](LiB0034.html#399), [4.4](LiB0036.html#427)
- [Chapter 5](LiB0039.html#471): [Sections 5.1](LiB0039.html#474), [5.2](LiB0040.html#488), [5.4](LiB0042.html#507), [5.6](LiB0044.html#530), [5.7](LiB0045.html#537)
- [Chapter 6](LiB0047.html#565): [Sections 6.1](LiB0048.html#571), [6.2](LiB0049.html#591)
- [Chapter 7](LiB0052.html#627): [Sections 7.1](LiB0052.html#630)–[7.5](LiB0056.html#665), [7.7](LiB0060.html#697), [7.8.1](LiB0062.html#703), [7.8.2](LiB0063.html#711), [7.9](LiB0065.html#733)
- [Chapter 8](LiB0067.html#759): [Sections 8.1.1](LiB0068.html#768), [8.5.1](LiB0072.html#820), [8.5.2](LiB0072.html#825)
- [Chapter 9](LiB0074.html#880): Brief introduction to the concepts.
[Chapters 2](LiB0014.html#141)–[6](LiB0047.html#565) contain several sections, each solving a problem using the design method presented in the chapter. We cover the ones of most interest to us, but you are free to choose any of the sections.
If your students are able to review the appendixes on their own, you should be able to cover all of [Chapter 9](LiB0074.html#880). Although you still may not be able to cover any of [Chapters 10](LiB0080.html#989) and [11](LiB0089.html#1224), this material is quite accessible once students have studied the first nine chapters. Interested students should be able to read it independently.
- Table of Contents
- BackCover
- Foundations of Algorithms Using C++ Pseudocode, Third Edition
- Preface
- Chapter Contents
- Pedagogy
- Course Outlines
- Acknowledgments
- Errors
- Chapter 1: Algorithms - Efficiency, Analysis, and Order
- 1.2 The Importance of Developing Efficient Algorithms
- 1.3 Analysis of Algorithms
- 1.4 Order
- 1.5 Outline of This Book
- Exercises
- Chapter 2: Divide-and-Conquer
- 2.1 Binary Search
- 2.2 Mergesort
- 2.3 The Divide-and-Conquer Approach
- 2.4 Quicksort (Partition Exchange Sort)
- 2.5 Strassen's Matrix Multiplication Algorithm
- 2.6 Arithmetic with Large Integers
- 2.7 Determining Thresholds
- 2.8 When Not to Use Divide-and-Conquer
- Exercises
- Chapter 3: Dynamic Programming
- 3.1 The Binomial Coefficient
- 3.2 Floyd's Algorithm for Shortest Paths
- 3.3 Dynamic Programming and Optimization Problems
- 3.4 Chained Matrix Multiplication
- 3.5 Optimal Binary Search Trees
- 3.6 The Traveling Salesperson Problem
- Exercises
- Chapter 4: The Greedy Approach
- 4.1 Minimum Spanning Trees
- 4.2 Dijkstra's Algorithm for Single-Source Shortest Paths
- 4.3 Scheduling
- 4.4 Huffman Code
- 4.5 The Greedy Approach versus Dynamic Programming: The Knapsack Problem
- Exercises
- Chapter 5: Backtracking
- 5.2 The n-Queens Problem
- 5.3 Using a Monte Carlo Algorithm to Estimate the Efficiency of a Backtracking Algorithm
- 5.4 The Sum-of-Subsets Problem
- 5.5 Graph Coloring
- 5.6 The Hamiltonian Circuits Problem
- 5.7 The 0-1 Knapsack Problem
- Exercises
- Chapter 6: Branch-and-Bound
- 6.1 Illustrating Branch-and-Bound with the 0 - 1 Knapsack problem
- 6.2 The Traveling Salesperson Problem
- 6.3 Abductive Inference (Diagnosis)
- Exercises
- Chapter 7: Introduction to Computational Complexity - The Sorting Problem
- 7.2 Insertion Sort and Selection Sort
- 7.3 Lower Bounds for Algorithms that Remove at Most One Inversion per Comparison
- 7.4 Mergesort Revisited
- 7.5 Quicksort Revisited
- 7.6 Heapsort
- 7.6.1 Heaps and Basic Heap Routines
- 7.6.2 An Implementation of Heapsort
- 7.7 Comparison of Mergesort, Quicksort, and Heapsort
- 7.8 Lower Bounds for Sorting Only by Comparison of Keys
- 7.8.1 Decision Trees for Sorting Algorithms
- 7.8.2 Lower Bounds for Worst-Case Behavior
- 7.8.3 Lower Bounds for Average-Case Behavior
- 7.9 Sorting by Distribution (Radix Sort)
- Exercises
- Chapter 8: More Computational Complexity - The Searching Problem
- 8.1 Lower Bounds for Searching Only by Comparisons of Keys
- 8.2 Interpolation Search
- 8.3 Searching in Trees
- 8.4 Hashing
- 8.5 The Selection Problem: Introduction to Adversary Arguments
- Exercises
- Chapter 9: Computational Complexity and Interactability - An Introduction to the Theory of NP
- 9.2 Input Size Revisited
- 9.3 The Three General Problem Categories
- 9.4 The Theory of NP
- 9.5 Handling NP-Hard Problems
- Exercises
- Chapter 10: Number-Theoretic Algorithms
- 10.1 Number Theory Review
- 10.2 Computing the Greatest Common Divisor
- 10.3 Modular Arithmetic Review
- 10.4 Solving Modular Linear Equations
- 10.5 Computing Modular Powers
- 10.6 Finding Large Prime Numbers
- 10.7 The RSA Public-Key Cryptosystem
- Exercises
- Chapter 11: Introduction to Parallel Algorithms
- 11.1 Parallel Architectures
- 11.2 The PRAM Model
- Exercises
- Appendix A: Review of Necessary Mathematics
- A.2 Functions
- A.3 Mathematical Induction
- A.4 Theorems and Lemmas
- A.5 Logarithms
- A.6 Sets
- A.7 Permutations and Combinations
- A.8 Probability
- Exercises
- Appendix B: Solving Recurrence Equations - With Applications to Analysis of Recursive Algorithms
- B.2 Solving Recurrences Using the Characteristic Equation
- B.3 Solving Recurrences by Substitution
- B.4 Extending Results for n, a Power of a Positive Constant b, to n in General
- B.5 Proofs of Theorems
- Exercises
- Appendix C: Data Structures for Disjoint Sets
- References
- Index
- Index_B
- Index_C
- Index_D
- Index_E
- Index_F
- Index_G
- Index_H
- Index_I
- Index_J
- Index_K
- Index_L
- Index_M
- Index_N
- Index_O
- Index_P
- Index_Q
- Index_R
- Index_S
- Index_T
- Index_U
- Index_V
- Index_W-X
- Index_Y
- Index_Z
- List of Figures
- List of Tables
- List of Algorithms, Examples, and Theorems
- List of Sidebars