# Index
### <a>A</a>
Note: Specific algorithms are in boldface.
Procedures are in italics.
螛(*n*2) algorithm, [26-31](LiB0011.html#78)
A(*n*). *See* [Average-case time complexity analysis](#averagecasetimecomplexityanalysis)
Abductive inference, [255-264](LiB0049.html#605)
**Best-First Search with Branch-and-Bound Pruning,** [263-264](LiB0050.html#617)
definition of, [255-256](LiB0049.html#605)
Abelian (commutative), [436](LiB0083.html#1057)
Abstract data type, [589](LiB0108.html#1465)
Acyclic graph
definition of, [97](LiB0026.html#266)
singly connected, [406](LiB0077.html#956)
**Add Array Members**
algorithm, [7](LiB0008.html#30)
every-case time complexity, [19](LiB0010.html#60)
input size, [17](LiB0009.html#56)
Addition
in computing modular powers, [439](LiB0083.html#1069)
of large integers, [72](LiB0020.html#208)
Address-space organization
message-passing architecture, [490](LiB0090.html#1236)
shared-address-space architecture, [490](LiB0090.html#1236)
Adel'son-Velskii, G.M., [338](LiB0070.html#803)
Adjacency matrix, [98](LiB0026.html#268)
Adjacent vertex, [98](LiB0026.html#268)
Adversary argument, [348-353](LiB0072.html#829)
Agrawal, A., [458](LiB0086.html#1144), [474](LiB0086.html#1191)
Akl, S., [505](LiB0091.html#1269)
Aldous, D., [539](LiB0100.html#1346)
Algorithms. *See also specific algorithms*
analysis of, [17-23](LiB0009.html#56), [24](LiB0010.html#73)
approximations. *See* [Approximation algorithms](#approximationalgorithms)
definition of, [2](LiB0008.html#18), [4](LiB0008.html#25)
deterministic, [201](LiB0041.html#501)
efficient, importance in developing, [9-17](LiB0008.html#35)
exercises, [42-46](LiB0012.html#130)
linear-time, [25](LiB0010.html#75)
nondeterministic algorithm, [387-388](LiB0077.html#907)
parallel. *See* [Parallel algorithms](LiB0125.html#1524)
polynomial-time. *See* [Polynomial-time algorithms](LiB0125.html#1527)
probabilistic, [200-201](LiB0040.html#499)
pseudopolynomial-time, [382](LiB0075.html#891)
quadratic-time sorting, [25](LiB0010.html#75)
sorting, decision trees for, [297-300](LiB0060.html#698)
writing, drawbacks to, [4](LiB0008.html#25)
Analysis of correctness, [24-25](LiB0010.html#73)
Apostol, T.M., [470](LiB0086.html#1182)
Approximation algorithms
for Bin-Packing problem, [410-416](LiB0078.html#967)
solutions from, [255](LiB0049.html#605)
for Traveling Salesperson problem, [406-411](LiB0077.html#956)
Arbitrary write protocol, [506](LiB0091.html#1271)
Arc (edge), [97](LiB0026.html#266)
Arithmetic, with large integers
addition, [72](LiB0020.html#208)
linear-time operations, [72](LiB0020.html#208)
multiplication, [72-78](LiB0020.html#208)
Arrays, [5](LiB0008.html#28)
Assignment of records, [269](LiB0052.html#631)
Asymptotic behavior, [28-29](LiB0011.html#88)
Asymptotic lower bound, [31](LiB0011.html#95)
Asymptotic upper bound, [29](LiB0011.html#89)
Average, [22](LiB0010.html#68)
Average-case time complexity analysis, [21-22](LiB0010.html#66)
**Binary Search Recursive,** [325-330](LiB0068.html#777)
**Insertion Sort,** [271-272](LiB0053.html#635)
lower bounds, [303-308](LiB0064.html#721)
**Quicksort,** [65-66](LiB0018.html#187)
AVL trees, [338](LiB0070.html#803)
- 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