# Index
### <a>N</a>
Natural logarithms, [524-526](LiB0097.html#1314)
Neapolitan, R.E., [256](LiB0050.html#607), [264](LiB0050.html#619), [406](LiB0077.html#956), [540](LiB0100.html#1348)
Neumann, John von, [486](LiB0089.html#1227)
Node, [210](LiB0043.html#522)
Nondeterministic algorithm, [387-388](LiB0077.html#907)
Nonhomogeneous linear recurrence, with constant coefficients, [562-567](LiB0103.html#1401)
Nonincreasing first fit, [412](LiB0078.html#972)
Nonnegative integer, [12](LiB0009.html#44)
Nonpromising node, [191](LiB0039.html#479), [234](LiB0047.html#568)
Nonuniform memory access (NUMA), [480](LiB0087.html#1211), [481](LiB0088.html#1214)
Notation, [511-513](LiB0093.html#1282)
*NP*
definition of, [389-390](LiB0077.html#910)
exercises, [416-418](LiB0078.html#981)
sets of, [386-390](LiB0077.html#905)
*NP*-complete, [376](LiB0074.html#882), [394-395](LiB0077.html#922)
complementary problems, [400-401](LiB0077.html#940)
Cook's Theorem, [394](LiB0077.html#922)
definition of, [394](LiB0077.html#922)
graph isomorphism problem, [399-400](LiB0077.html#936)
problems, handling of, [390-401](LiB0077.html#911)
state of, [398](LiB0077.html#933)
*NP*-easy, [404](LiB0077.html#952)
*NP*-equivalent, [405](LiB0077.html#955)
*NP*-hard, [402-404](LiB0077.html#948)
problems, handling of, [406-416](LiB0077.html#956)
*NP* theory, [384-386](LiB0076.html#897)
*n*-Queens problem, [196-200](LiB0040.html#489)
***n*th Fibonacci Term Iterative,** [92](LiB0024.html#255)
input size, [17-18](LiB0009.html#56)
*vs.* Algorithm [1](LiB0008.html#17).6, [15-17](LiB0009.html#50)
***n*th Fibonacci Term Recursive,** [12](LiB0009.html#44)
input size, [17-18](LiB0009.html#56)
*vs.* Algorithm [1](LiB0008.html#17).7, [16](LiB0009.html#52)
NUMA (nonuniform memory access), [480](LiB0087.html#1211), [481](LiB0088.html#1214)
Number, [6](LiB0008.html#29)
Number-theoretic algorithms
**Compute Modular Power,** [454-456](LiB0085.html#1130)
definition of, [419](LiB0080.html#991)
**Euclid's Algorithm,** [428-434](LiB0082.html#1031)
exercises, [480-483](LiB0087.html#1211)
**Polynomial Determine Prime,** [464-474](LiB0086.html#1166)
**Solve Modular Linear Equation,** [453](LiB0084.html#1127)
Number theory
composite numbers, [420-421](LiB0080.html#992)
definition of, [419](LiB0080.html#991)
greatest common divisor, [421-424](LiB0081.html#999), [427-434](LiB0081.html#1025)
least common multiple, [427](LiB0081.html#1025)
prime factorization, [424-426](LiB0081.html#1011)
prime numbers, [420-421](LiB0080.html#992)
*numdigits,* [311-312](LiB0065.html#740)
- 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