Introduction to the Design and Analysis of Algorithms

ISBN-10: 0132316811
ISBN-13: 9780132316811
Edition: 3rd 2012 (Revised)
Authors: Anany Levitin
List price: $164.40 Buy it from $55.95 Rent it from $41.10
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Description: Based on a new classification of algorithm design techniques and a clear delineation of analysis methods, Introduction to the Design and Analysis of Algorithms presents the subject in a coherent and innovative manner. Written in a student-friendly  More...

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Book details

List price: $164.40
Edition: 3rd
Copyright year: 2012
Publisher: Addison Wesley
Publication date: 9/29/2011
Binding: Paperback
Pages: 592
Size: 7.25" wide x 9.00" long x 0.75" tall
Weight: 1.870
Language: English

Based on a new classification of algorithm design techniques and a clear delineation of analysis methods, Introduction to the Design and Analysis of Algorithms presents the subject in a coherent and innovative manner. Written in a student-friendly style, the book emphasizes the understanding of ideas over excessively formal treatment while thoroughly covering the material required in an introductory algorithms course. Popular puzzles are used to motivate students' interest and strengthen their skills in algorithmic problem solving. Other learning-enhancement features include chapter summaries, hints to the exercises, and a detailed solution manual.

Anany Levitin is a professor of Computing Sciences at Villanova University. He is the author of a popular textbook on design and analysis of algorithms, which has been translated into Chinese, Greek, Korean, and Russian. He has also published papers on mathematical optimization theory, software engineering, data management, algorithm design techniques, and computer science education. Maria Levitin is an independent consultant specializing in web applications and data compression. She has previously worked for several leading software companies.

New to the Third Edition
Preface
Introduction
What Is an Algorithm?
Exercises 1.1
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 1.2
Important Problem Types
Sorting
Searching
String Processing
Graph Problems
Combinatorial Problems
Geometric Problems
Numerical Problems
Exercises 1.3
Fundamental Data Structures
Linear Data Structures
Graphs
Trees
Sets and Dictionaries
Exercises 1.4
Summary
Fundamentals of the Analysis of Algorithm Efficiency
The Analysis Framework
Measuring an Input's Size
Units for Measuring Running Time
Orders of Growth
Worst-Case, Best-Case, and Average-Case Efficiencies
Recapitulation of the Analysis Framework
Exercises 2.1
Asymptotic Notations and Basic Efficiency Classes
Informal Introduction
O-notation
-notation
-notation
Useful Property Involving the Asymptotic Notations
Using Limits for Comparing Orders of Growth
Basic Efficiency Classes
Exercises 2.2
Mathematical Analysis of Nonrecursive Algorithms
Exercises 2.3
Mathematical Analysis of Recursive Algorithms
Exercises 2.4
Example: Computing the nth Fibonacci Number
Exercises 2.5
Empirical Analysis of Algorithms
Exercises 2.6
Algorithm Visualization
Summary
Brute Force and Exhaustive Search
Selection Sort and Bubble Sort
Selection Sort
Bubble Sort
Exercises 3.1
Sequential Search and Brute-Force String Matching
Sequential Search
Brute-Force String Matching
Exercises 3.2
Closest-Pair and Convex-Hull Problems by Brute Force
Closest-Pair Problem
Convex-Hull Problem
Exercises 3.3
Exhaustive Search
Traveling Salesman Problem
Knapsack Problem
Assignment Problem
Exercises 3.4
Depth-First Search and Breadth-First Search
Depth-First Search
Breadth-First Search
Exercises 3.5
Summary
Decrease-and-Conquer
Insertion Sort
Exercises 4.1
Topological Sorting
Exercises 4.2
Algorithms for Generating Combinatorial Objects
Generating Permutations
Generating Subsets
Exercises 4.3
Decrease-by-a-Constant-Factor Algorithms
Binary Search
Fake-Coin Problem
Russian Peasant Multiplication
Josephus Problem
Exercises 4.4
Variable-Size-Decrease Algorithms
Computing a Median and the Selection Problem
Interpolation Search
Searching and Insertion in a Binary Search Tree
The Game of Nim
Exercises 4.5
Summary
Divide-and-Conquer
Mergesort
Exercises 5.1
Quicksort
Exercises 5.2
Binary Tree Traversals and Related Properties
Exercises 5.3
Multiplication of Large Integers and Strassen's Matrix Multiplication
Multiplication of Large Integers
Strassen's Matrix Multiplication
Exercises 5.4
The Closest-Pair and Convex-Hull Problems by Divide-and-Conquer
The Closest-Pair Problem
Convex-Hull Problem
Exercises 5.5
Summary
Transform-and-Conquer
Presorting
Exercises 6.1
Gaussian Elimination
LU Decomposition
Computing a Matrix Inverse
Computing a Determinant
Exercises 6.2
Balanced Search Trees
AVL Trees
Trees
Exercises 6.3
Heaps and Heapsort
Notion of the Heap
Heapsort
Exercises 6.4
Horner's Rule and Binary Exponentiation
Horner's Rule
Binary Exponentiation
Exercises 6.5
Problem Reduction
Computing the Least Common Multiple
Counting Paths in a Graph
Reduction of Optimization Problems
Linear Programming
Reduction to Graph Problems
Exercises 6.6
Summary
Space and Time Trade-Offs
Sorting by Counting
Exercises 7.1
Input Enhancement in String Matching
Horspool's Algorithm
Boyer-Moore Algorithm
Exercises 7.2
Hashing
Open Hashing (Separate Chaining)
Closed Hashing (Open Addressing)
Exercises 7.3
B-Trees
Exercises 7.4
Summary
Dynamic Programming
Three Basic Examples
Exercises 8.1
The Knapsack Problem and Memory Functions
Memory Functions
Exercises 8.2
Optimal Binary Search Trees
Exercises 8.3
Warshall's and Floyd's Algorithms
Warshall's Algorithm
Floyd's Algorithm for the All-Pairs Shortest-Paths Problem
Exercises 8.4
Summary
Greedy Technique
Prim's Algorithm
Exercises 9.1
Kruskal's Algorithm
Disjoint Subsets and Union-Find Algorithms
Exercises 9.2
Dijkstra's Algorithm
Exercises 9.3
Huffman Trees and Codes
Exercises 9.4
Summary
Iterative Improvement
The Simplex Method
Geometric Interpretation of Linear Programming
An Outline of the Simplex Method
Further Notes on the Simplex Method
Exercises 10.1
The Maximum-Flow Problem
Exercises 10.2
Maximum Matching in Bipartite Graphs
Exercises 10.3
The Stable Marriage Problem
Exercises 10.4
Summary
Limitations of Algorithm Power
Lower-Bound Arguments
Trivial Lower Bounds
Information-Theoretic Arguments
Adversary Arguments
Problem Reduction
Exercises 11.1
Decision Trees
Decision Trees for Sorting
Decision Trees for Searching a Sorted Array
Exercises 11.2
P, NP, and NP-Complete Problems
P and NP Problems
NP-Complete Problems
Exercises 11.3
Challenges of Numerical Algorithms
Exercises 11.4
Summary
Coping with the Limitations of Algorithm Power
Backtracking
n-Queens Problem
Hamiltonian Circuit Problem
Subset-Sum Problem
General Remarks
Exercises 12.1
Branch-and-Bound
Assignment Problem
Knapsack Problem
Traveling Salesman Problem
Exercises 12.2
Approximation Algorithms for NP-Hard Problems
Approximation Algorithms for the Traveling Salesman Problem
Approximation Algorithms for the Knapsack Problem
Exercises 12.3
Algorithms for Solving Nonlinear Equations
Bisection Method
Method of False Position
Newton's Method
Exercises 12.4
Summary
Epilogue
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
Short Tutorial on Recurrence Relations
Sequences and Recurrence Relations

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