Introduction to the Design and Analysis of Algorithms, 3rd edition
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Overview
Introduction to the Design and Analysis of Algorithms presents the subject in a coherent and innovative manner. The text examines new algorithm design techniques and methods for analysis and includes puzzles and other learnerfocused features to help you strengthen your algorithmic problemsolving skills.
Published by Pearson (July 14th 2021)  Copyright © 2012
ISBN13: 9780137541133
Table of contents
1. Introduction
What Is an Algorithm?
Exercises
Fundamentals of Algorithmic Problem Solving
Understanding the Problem
Ascertaining the Capabilities of the Computational Device
Choosing between Exact and Approximate Problem Solving
Algorithm Design Techniques
Designing an Algorithm and Data Structures
Methods of Specifying an Algorithm
Proving an Algorithm's Correctness
Analyzing an Algorithm
Coding an Algorithm
Exercises
Important Problem Types
Sorting
Searching
String Processing
Graph Problems
Combinatorial Problems
Geometric Problems
Numerical Problems
Exercises
Fundamental Data Structures
Linear Data Structures
Graphs
Trees
Sets and Dictionaries
Exercises
Summary
2. Fundamentals of the Analysis of Algorithm Efficiency
The Analysis Framework
Measuring an Input's Size
Units for Measuring Running Time
Orders of Growth
WorstCase, BestCase, and AverageCase Efficiencies
Recapitulation of the Analysis Framework
Exercises
Asymptotic Notations and Basic Efficiency Classes
Informal Introduction
Onotation
notation
notation
Useful Property Involving the Asymptotic Notations
Using Limits for Comparing Orders of Growth
Basic Efficiency Classes
Exercises
Mathematical Analysis of Nonrecursive Algorithms
Exercises
Mathematical Analysis of Recursive Algorithms
Exercises
Example: Computing the nth Fibonacci Number
Exercises
Empirical Analysis of Algorithms
Exercises
Algorithm Visualization
Summary
3. Brute Force and Exhaustive Search
Selection Sort and Bubble Sort
Selection Sort
Bubble Sort
Exercises
Sequential Search and BruteForce String Matching
Sequential Search
BruteForce String Matching
Exercises
ClosestPair and ConvexHull Problems by Brute Force
ClosestPair Problem
ConvexHull Problem
Exercises
Exhaustive Search
Traveling Salesman Problem
Knapsack Problem
Assignment Problem
Exercises
DepthFirst Search and BreadthFirst Search
DepthFirst Search
BreadthFirst Search
Exercises
Summary
4. DecreaseandConquer
Insertion Sort
Exercises
Topological Sorting
Exercises
Algorithms for Generating Combinatorial Objects
Generating Permutations
Generating Subsets
Exercises
DecreasebyaConstantFactor Algorithms
Binary Search
FakeCoin Problem
Russian Peasant Multiplication
Josephus Problem
Exercises
VariableSizeDecrease Algorithms
Computing a Median and the Selection Problem
Interpolation Search
Searching and Insertion in a Binary Search Tree
The Game of Nim
Exercises
Summary
5. DivideandConquer
Mergesort
Exercises
Quicksort
Exercises
Binary Tree Traversals and Related Properties
Exercises
Multiplication of Large Integers and
Strassen's Matrix Multiplication
Multiplication of Large Integers
Strassen's Matrix Multiplication
Exercises
The ClosestPair and ConvexHull Problems
by DivideandConquer
The ClosestPair Problem
ConvexHull Problem
Exercises
Summary
6. TransformandConquer
Presorting
Exercises
Gaussian Elimination
LU Decomposition
Computing a Matrix Inverse
Computing a Determinant
Exercises
Balanced Search Trees
AVL Trees
 Trees
Exercises
Heaps and Heapsort
Notion of the Heap
Heapsort
Exercises
Horner's Rule and Binary Exponentiation
Horner's Rule
Binary Exponentiation
Exercises
Problem Reduction
Computing the Least Common Multiple
Counting Paths in a Graph
Reduction of Optimization Problems
Linear Programming
Reduction to Graph Problems
Exercises
Summary
7. Space and Time TradeOffs
Sorting by Counting
Exercises
Input Enhancement in String Matching
Horspool's Algorithm
BoyerMoore Algorithm
Exercises
Hashing
Open Hashing (Separate Chaining)
Closed Hashing (Open Addressing)
Exercises
BTrees
Exercises
Summary
8. Dynamic Programming
Three Basic Examples
Exercises
The Knapsack Problem and Memory Functions
Memory Functions
Exercises
Optimal Binary Search Trees
Exercises
Warshall's and Floyd's Algorithms
Warshall's Algorithm
Floyd's Algorithm for the AllPairs ShortestPaths Problem
Exercises
Summary
9. Greedy Technique
Prim's Algorithm
Exercises
Kruskal's Algorithm
Disjoint Subsets and UnionFind Algorithms
Exercises
Dijkstra's Algorithm
Exercises
Huffman Trees and Codes
Exercises
Summary
10. Iterative Improvement
The Simplex Method
Geometric Interpretation of Linear Programming
An Outline of the Simplex Method
Further Notes on the Simplex Method
Exercises
The MaximumFlow Problem
Exercises
Maximum Matching in Bipartite Graphs
Exercises
The Stable Marriage Problem
Exercises
Summary
11. Limitations of Algorithm Power
LowerBound Arguments
Trivial Lower Bounds
InformationTheoretic Arguments
Adversary Arguments
Problem Reduction
Exercises
Decision Trees
Decision Trees for Sorting
Decision Trees for Searching a Sorted Array
Exercises
P, NP, and NPComplete Problems
P and NP Problems
NPComplete Problems
Exercises
Challenges of Numerical Algorithms
Exercises
Summary
12. Coping with the Limitations of Algorithm Power
Backtracking
nQueens Problem
Hamiltonian Circuit Problem
SubsetSum Problem
General Remarks
Exercises
BranchandBound
Assignment Problem
Knapsack Problem
Traveling Salesman Problem
Exercises
Approximation Algorithms for NPHard Problems
Approximation Algorithms for the Traveling Salesman Problem
Approximation Algorithms for the Knapsack Problem
Exercises
Algorithms for Solving Nonlinear Equations
Bisection Method
Method of False Position
Newton's Method
Exercises
Summary
Epilogue
APPENDIX: A
Useful Formulas for the Analysis of Algorithms
Properties of Logarithms
Combinatorics
Important Summation Formulas
Sum Manipulation Rules
Approximation of a Sum by a Definite Integral
Floor and Ceiling Formulas
Miscellaneous
APPENDIX: B
Short Tutorial on Recurrence Relations
Sequences and Recurrence Relations
Methods for Solving Recurrence Relations
Common Recurrence Types in Algorithm Analysis
References
Hints to Exercises
Index
Your questions answered
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