Chapter 1: The Role of Algorithms in Computing Section 1-1:
Algorithms
Section 1-2:
Algorithms as a Technology
Chapter 2: Getting StartedSection 2-1:
Insertion Sort
Section 2-2:
Analyzing Algorithms
Section 2-3:
Designing Algorithms
Chapter 3: Growth of FunctionsSection 3-1:
Asymptotic Notation
Section 3-2:
Standard Notations and Common Functions
Chapter 4: Divide-and-ConquerSection 4-1:
The Maximum-Subarray Problem
Section 4-2:
Strassen's Algorithm for Matrix Multiplication
Section 4-3:
The Substitution Method for Solving Recurrences
Section 4-4:
The Recursion-tree Method for Solving Recurrences
Section 4-5:
The Master Method for Solving Recurrences
Section 4-6:
Proof of the Master Theorem
Chapter 5: Probabilistic Analysis and Randomized AlgorithmsSection 5-1:
The Hiring Problem
Section 5-2:
Indicator Random Variables
Section 5-3:
Randomized Algorithms
Section 5-4:
Probabilistic Analysis and Further uses of Indicaor Random Variables
Section 6-1:
Heaps
Section 6-2:
Maintaining the Heap Property
Section 6-3:
Building a Heap
Section 6-4:
The Heapsort Algorithm
Section 6-5:
Priority Queues
Section 7-1:
Description of Quicksort
Section 7-2:
Performance of Quicksort
Section 7-3:
A Randomized Version of Quicksort
Section 7-4:
Analysis of Quicksort
Chapter 8: Sorting in Linear TimeSection 8-1:
Lower Bounds for Sorting
Section 8-2:
Counting Sort
Section 8-3:
Radix Sort
Section 8-4:
Bucker Sort
Chapter 9: Medians and Order StatisticsSection 9-1:
Minimum and Maximum
Section 9-2:
Selection in Expected Linear Time
Section 9-3:
Selection in Worst-Case Linear Time
Chapter 10: Elementary Data StructuresSection 10-1:
Stacks and Queues
Section 10-2:
Linked List
Section 10-3:
Implementing Pointers and Objects
Section 10-4:
Representing Rooted Trees
Section 11-1:
Direct-Address Tables
Section 11-2:
Hash Tables
Section 11-3:
Hash Functions
Section 11-4:
Open Addressing
Section 11-5:
Perfect Hashing
Chapter 12: Binary Search TreesSection 12-1:
What is a Binary Search Tree?
Section 12-2:
Querying a Binary Search Tree
Section 12-3:
Insertion and Deletion
Section 12-4:
Randomly Built Binary Search Trees
Chapter 13: Red-Black TreesSection 13-1:
Properties of red-black trees
Section 13-2:
Rotations
Section 13-3:
Insertion
Section 13-4:
Deletion
Chapter 14: Augmenting Data StructuresSection 14-1:
Dynamic order Statistics
Section 14-2:
How To Augment a Data Structure
Section 14-3:
Interval Trees
Chapter 15: Dynamic Programming Section 15-1:
Rod Cuttting
Section 15-2:
Matrix-Chain Multiplication
Section 15-3:
Elements of Dynamic Programing
Section 15-4:
Longest Common Subsequence
Section 15-5:
Optimal Binary Search Trees
Chapter 16: Greedy AlgorithmsSection 16-1:
An Activity-Selection Problem
Section 16-2:
Elements of the Greedy Strategy
Section 16-3:
Huffman Codes
Section 16-4:
Matroids and Greedy Methods
Section 16-5:
A Task-Scheduling Problem as a Matroid
Chapter 17: Amortized AnalysisSection 17-1:
Aggregate Analysis
Section 17-2:
The Accounting Method
Section 17-3:
The Potential Method
Section 17-4:
Dynamic Tables
Section 18-1:
Definition of B-Trees
Section 18-2:
Basic Operation on B-trees
Section 18-3:
Deleting a Key from a B-tree
Chapter 19: Fibonacci HeapsSection 19-2:
Mergeable-heap Operations
Section 19-3:
Descreasing a key and deleting a Node
Section 19-4:
Bounding the Maximum Degree
Chapter 20: Van Emde Boas TreesSection 20-1:
Preliminary Approaches
Section 20-2:
A Recursive Structure
Section 20-3:
The van Emde Boas Tree
Chapter 21: Data Structures for Disjoint SetsSection 21-1:
Disjoint-Set Operations
Section 21-2:
Linked-list Representations of Disjoint Sets
Section 21-3:
Disjoint-set Forests
Section 21-4:
Analysis of Union by rank with path Compression
Chapter 22: Elementary Graph AlgorithmsSection 22-1:
Representations of Graphs
Section 22-2:
Breadth-first search
Section 22-3:
Depth-first Search
Section 22-4:
Topological Sort
Section 22-5:
Strongly Connected Components
Chapter 23: Minimum Spanning TreesSection 23-1:
Growing a Minimum Spanning Tree
Section 23-2:
The Algorithms of Kruskal and Prim
Exercise 1
Exercise 8
Exercise 9
Exercise 10
Exercise 11
Chapter 24: Single-Source Shortest PathsSection 24-1:
The Bellman-Ford Algorithm
Section 24-2:
Single-Source Shortest paths in Directed Acyclic Graphs Section 24-3:
Dijkstra's Algorithm
Section 24-4:
Difference Constraints and Shortest paths
Section 24-5:
Proofs of shortest-paths Properties
Exercise 1
Exercise 2
Exercise 4
Exercise 5
Exercise 6
Chapter 25: All-Pairs Shortest PathsCOMING SOON
Section 26-1:
Flow Networks
Section 26-2:
The Ford-Fulkerson Method
Section 26-3:
Maximum Bipartite Matching Section 26-4:
Push-Relabel AlgorithmsSection 26-5:
The Relabel-to-Front AlgorithmExercise 1
Exercise 2
Exercise 3
Exercise 5
Exercise 7
Chapter 27: Multithreaded AlgorithmsSection 27-1:
The Basis of dynamic Multithreading
Section 27-2:
Multithreaded Matrix Multiplication
Section 27-3:
Multithreated Merge Sort
Chapter 28: Matrix OperationsSection 28-1:
Solving systems of Linear Equations
Section 28-2:
Inverting Matrices
Section 28-3:
Symmetric Positive-Definitive Matrices and least-Squares Approximation
Chapter 29: Linear ProgrammingSection 29-1:
Standard and Slack forms
Section 29-2:
Formulating Problems as Linear Programs
Section 29-3:
The Simplex Algorithm
Section 29-4:
Duality
Section 29-5:
The Initial Basic Feasible Solution
Chapter 30: Polynomials and The FFTSection 30-1:
Representing Polynomials
Section 30-2:
The DFT and FFT
Section 30-3:
Efficient FFT Implementations
Chapter 31: Number-Theoretic AlgorithmsSection 31-1:
Elementary Number-Theoretic Notions
Section 31-2:
Greatest Common Divisor
Section 31-3:
Modular Arithmetic
Section 31-4:
Solving Modular Linear Equations
Section 31-5:
The Chinese Remainder Theorem
Section 31-6:
Powers of an Element
Section 31-7:
The RSA public-key cyrptosystem
Section 31-8:
Primarily Testing Section 31-9:
Integer Factorization
Chapter 32: String MatchingSection 32-1:
The Naive String-Matching Algorithm
Section 32-2:
The Rabin-Karp Algorithm
Section 32-3:
String Matching with Finite Automata
Section 32-4:
The Knuth-Morris-Pratt Algorithm
Chapter 33: Computational Geometry COMING SOON
Chapter 34: NP-CompletenessSection 34-1:
Polynomial Time
Section 34-2:
Polynomial-time verificationSection 34-3:
NP-Completeness and ReducibilitySection 34-4:
NP-Completeness ProofsSection 34-5:
NP-Complete Problems
Chapter 35: Approximation AlgorithmsCOMING SOON
Section A-1:
Summation Formulas and Properties
Section A-2:
Bounding Summations
Chapter B: Sets, Etc.COMING SOON
Chapter C: Counting and ProbabilityCOMING SOON
Section D-1:
Matrices and Matrix operations
Section D-2:
Basic Matrix Properties
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