# Index
### <a>L</a>
Lagrange, [443](LiB0083.html#1088)
Lambalgen, M. van, [540](LiB0100.html#1348)
Landis, E.M., [338](LiB0070.html#803)
Langston, M.A., [283](LiB0055.html#663)
Large-integer, [72](LiB0020.html#208)
**Large Integer Multiplication,** [74-76](LiB0020.html#213)
**Large Integer Multiplication [2](LiB0008.html#18),** [76-78](LiB0020.html#217)
Leaf, [190](LiB0039.html#477)
Least common multiple, [427](LiB0081.html#1025)
Left subtree, [116](LiB0028.html#307)
Lemmas, [522](LiB0096.html#1307)
Length, path, [97](LiB0026.html#266)
Linear recurrences
homogeneous, [553-562](LiB0102.html#1379)
nonhomogeneous, [562-567](LiB0103.html#1401)
Linear-time algorithms, [25](LiB0010.html#75)
LISP, [51](LiB0015.html#151)
List, definition of, [2-3](LiB0008.html#18)
Literal, [391](LiB0077.html#914)
In *x*, [524](LiB0097.html#1314)
Logarithms
common, [522](LiB0096.html#1307)
definition of, [522-523](LiB0096.html#1307)
natural, [524-526](LiB0097.html#1314)
properties of, [523-524](LiB0097.html#1311)
Logical (Boolean) variable, [391](LiB0077.html#914)
Longcor, W.H., [539](LiB0100.html#1346)
Loser, [345](LiB0072.html#821)
Lower bounds
for algorithms that remove most one inversion per comparison, [275-277](LiB0053.html#646)
for average-case behavior, [303-308](LiB0064.html#721)
definition of, [268](LiB0052.html#629)
exercises, [313](LiB0066.html#746), [316](LiB0066.html#754)
for searching only by comparison keys, [320-330](LiB0067.html#762)
for average-case behavior, [324-330](LiB0068.html#772)
for worst-case behavior, [322-324](LiB0068.html#767)
for sorting only by comparison keys, [297-300](LiB0060.html#698)
for worst-case behavior, [300-302](LiB0062.html#710)
- 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