# Index
### <a>I</a>
Identity element, [439](LiB0083.html#1069), [441](LiB0083.html#1077)
Implicitly, [194](LiB0039.html#486)
Index
as data type, [6](LiB0008.html#29)
of processor, [496](LiB0091.html#1254)
Induction
using to solve recurrences, [549-553](LiB0102.html#1370)
*vs.* substitution, [571](LiB0103.html#1420)
Induction base, [515-520](LiB0095.html#1290), [552](LiB0102.html#1376)
Induction hypothesis, [515-520](LiB0095.html#1290), [552](LiB0102.html#1376)
Induction step, [515-520](LiB0095.html#1290), [552](LiB0102.html#1376)
Infinity, [513](LiB0093.html#1285)
Initial condition, [550](LiB0102.html#1373)
In-order traversal, [334](LiB0070.html#795)
In-place sort, [57](LiB0016.html#167), [270](LiB0052.html#632)
Inputs, [5](LiB0008.html#28)
Input size, [17-18](LiB0009.html#56). *See also under specific algorithms*
definition of, [378](LiB0074.html#886)
intractability and, [378-382](LiB0074.html#886)
**Insertion Sort,** [270-271](LiB0052.html#632), [275](LiB0053.html#646), [277](LiB0054.html#650)
analysis of extra space usage, [272-273](LiB0053.html#639)
analysis summary, [273](LiB0053.html#641)
average-case time complexity analysis, [271-272](LiB0053.html#635)
exercises, [312-313](LiB0065.html#742)
*vs.* **Selection Sort,** [274](LiB0053.html#645)
worst-case time complexity analysis, [271](LiB0053.html#635)
Instance of problem, [3](LiB0008.html#21)
Integers, [420](LiB0080.html#992)
Interconnection networks, [491-494](LiB0090.html#1243)
Internal node, [285](LiB0056.html#669)
Internal search, [338](LiB0070.html#803)
**Interpolation Search,** [320](LiB0067.html#762), [330-333](LiB0068.html#788)
algorithm, [331](LiB0069.html#790)
robust, [332-333](LiB0069.html#792)
Intersection, [527](LiB0098.html#1321)
Intractability, [376-378](LiB0074.html#882)
categories, [378](LiB0074.html#886)
input size and, [378-382](LiB0074.html#886)
problems, [382-384](LiB0075.html#891)
Inversion, [276](LiB0054.html#648)
Isomorphic, [399](LiB0077.html#936)
Iverson, G.R., [539](LiB0100.html#1346)
- 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