# Index
### <a>F</a>
**Factorial,** [549-550](LiB0102.html#1370)
Feasibility check, for greedy algorithm, [138](LiB0032.html#362), [140](LiB0032.html#363)
Feasible sequence, [163](LiB0035.html#414)
Feasible set, [163](LiB0035.html#414)
Fermat, [447-448](LiB0083.html#1103)
Fibonacci Sequence, [12](LiB0009.html#44)
*k*th number in, [429](LiB0082.html#1036)
*n*th, [558-559](LiB0103.html#1393)
Finding largest key, in array, [498-501](LiB0091.html#1258)
**Finding Largest Key,** [345-346](LiB0072.html#821)
**Find Smallest and Largest Key,** [346-347](LiB0072.html#824)
**Find Smallest and Largest Keys by Pairing Keys,** [347-348](LiB0072.html#827)
Fine, T.L., [536](LiB0100.html#1339)
Finite, [436](LiB0083.html#1057)
First-fit strategy, [411-412](LiB0078.html#969)
Fischer, M.J., [383](LiB0076.html#895)
Fixed-length binary code, [169](LiB0036.html#428)
Floor, [511](LiB0093.html#1282)
Floyd, R.W., [102](LiB0026.html#276), [366](LiB0072.html#861)
**Floyd's Algorithm**
**for Shortest Paths,** [102-103](LiB0026.html#276)
**for Shortest Paths [2](LiB0008.html#18),** [103-104](LiB0026.html#278)
Fractional Knapsack problem, greedy approach to, [175-177](LiB0037.html#446)
Fredman, M.L., [115](LiB0028.html#305), [159](LiB0034.html#404)
Functions, [6](LiB0008.html#29), [513-514](LiB0093.html#1285). *See also* [Complexity function](LiB0112.html#1497)
complete quadratic, [25-26](LiB0010.html#75)
domain of, [514](LiB0094.html#1288)
Euler's totient, [441-442](LiB0083.html#1077)
Hash, [339](LiB0070.html#805)
probability, [531](LiB0100.html#1328)
promising, [192](LiB0039.html#481)
quadratic, [25-26](LiB0010.html#75)
range of, [514](LiB0094.html#1288)
Fundamental theorem of arithmetic, [425](LiB0081.html#1016)
Fussenegger, F., [366](LiB0072.html#861)
- 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