Instruction Manual for Introduction to the Design and Analysis of Algorithms 3rd Edition by Anany Levitin ISBN 0132316811 9780132316811

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ISBN 10: 0132316811
ISBN 13: 9780132316811
Author: Anany Levitin

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.

Introduction to the Design and Analysis of Algorithms 3rd Table of contents:

New to the Third Edition
Preface
Introduction

Chapter 1: Introduction to Algorithms

1.1 What Is an Algorithm?
  Exercises 1.1
1.2 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
1.3 Important Problem Types
  Sorting
  Searching
  String Processing
  Graph Problems
  Combinatorial Problems
  Geometric Problems
  Numerical Problems
  Exercises 1.3
1.4 Fundamental Data Structures
  Linear Data Structures
  Graphs
  Trees
  Sets and Dictionaries
  Exercises 1.4
Summary

Chapter 2: Fundamentals of the Analysis of Algorithm Efficiency

2.1 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
2.2 Asymptotic Notations and Basic Efficiency Classes
  Informal Introduction
  O-notation, Ω-notation, Θ-notation
  Useful Property Involving the Asymptotic Notations
  Using Limits for Comparing Orders of Growth
  Basic Efficiency Classes
  Exercises 2.2
2.3 Mathematical Analysis of Nonrecursive Algorithms
  Exercises 2.3
2.4 Mathematical Analysis of Recursive Algorithms
  Exercises 2.4
2.5 Example: Computing the nth Fibonacci Number
  Exercises 2.5
2.6 Empirical Analysis of Algorithms
  Exercises 2.6
2.7 Algorithm Visualization
Summary

Chapter 3: Brute Force and Exhaustive Search

3.1 Selection Sort and Bubble Sort
  Selection Sort
  Bubble Sort
  Exercises 3.1
3.2 Sequential Search and Brute-Force String Matching
  Sequential Search
  Brute-Force String Matching
  Exercises 3.2
3.3 Closest-Pair and Convex-Hull Problems by Brute Force
  Closest-Pair Problem
  Convex-Hull Problem
  Exercises 3.3
3.4 Exhaustive Search
  Traveling Salesman Problem
  Knapsack Problem
  Assignment Problem
  Exercises 3.4
3.5 Depth-First Search and Breadth-First Search
  Depth-First Search
  Breadth-First Search
  Exercises 3.5
Summary

Chapter 4: Decrease-and-Conquer

4.1 Insertion Sort
  Exercises 4.1
4.2 Topological Sorting
  Exercises 4.2
4.3 Algorithms for Generating Combinatorial Objects
  Generating Permutations
  Generating Subsets
  Exercises 4.3
4.4 Decrease-by-a-Constant-Factor Algorithms
  Binary Search
  Fake-Coin Problem
  Russian Peasant Multiplication
  Josephus Problem
  Exercises 4.4
4.5 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

Chapter 5: Divide-and-Conquer

5.1 Mergesort
  Exercises 5.1
5.2 Quicksort
  Exercises 5.2
5.3 Binary Tree Traversals and Related Properties
  Exercises 5.3
5.4 Multiplication of Large Integers and Strassen’s Matrix Multiplication
  Multiplication of Large Integers
  Strassen’s Matrix Multiplication
  Exercises 5.4
5.5 The Closest-Pair and Convex-Hull Problems by Divide-and-Conquer
  The Closest-Pair Problem
  Convex-Hull Problem
  Exercises 5.5
Summary

Chapter 6: Transform-and-Conquer

6.1 Presorting
  Exercises 6.1
6.2 Gaussian Elimination
  LU Decomposition
  Computing a Matrix Inverse
  Computing a Determinant
  Exercises 6.2
6.3 Balanced Search Trees
  AVL Trees
  2-3 Trees
  Exercises 6.3
6.4 Heaps and Heapsort
  Notion of the Heap
  Heapsort
  Exercises 6.4
6.5 Horner’s Rule and Binary Exponentiation
  Horner’s Rule
  Binary Exponentiation
  Exercises 6.5
6.6 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

Chapter 7: Space and Time Trade-Offs

7.1 Sorting by Counting
  Exercises 7.1
7.2 Input Enhancement in String Matching
  Horspool’s Algorithm
  Boyer-Moore Algorithm
  Exercises 7.2
7.3 Hashing
  Open Hashing (Separate Chaining)
  Closed Hashing (Open Addressing)
  Exercises 7.3
7.4 B-Trees
  Exercises 7.4
Summary

Chapter 8: Dynamic Programming

8.1 Three Basic Examples
  Exercises 8.1
8.2 The Knapsack Problem and Memory Functions
  Memory Functions
  Exercises 8.2
8.3 Optimal Binary Search Trees
  Exercises 8.3
8.4 Warshall’s and Floyd’s Algorithms
  Warshall’s Algorithm
  Floyd’s Algorithm for the All-Pairs Shortest-Paths Problem
  Exercises 8.4
Summary

Chapter 9: Greedy Technique

9.1 Prim’s Algorithm
  Exercises 9.1
9.2 Kruskal’s Algorithm
  Disjoint Subsets and Union-Find Algorithms
  Exercises 9.2
9.3 Dijkstra’s Algorithm
  Exercises 9.3
9.4 Huffman Trees and Codes
  Exercises 9.4
Summary

Chapter 10: Iterative Improvement

10.1 The Simplex Method
  Geometric Interpretation of Linear Programming
  An Outline of the Simplex Method
  Further Notes on the Simplex Method
  Exercises 10.1
10.2 The Maximum-Flow Problem
  Exercises 10.2
10.3 Maximum Matching in Bipartite Graphs
  Exercises 10.3
10.4 The Stable Marriage Problem
  Exercises 10.4
Summary

Chapter 11: Limitations of Algorithm Power

11.1 Lower-Bound Arguments
  Trivial Lower Bounds
  Information-Theoretic Arguments
  Adversary Arguments
  Problem Reduction
  Exercises 11.1
11.2 Decision Trees
  Decision Trees for Sorting
  Decision Trees for Searching a Sorted Array
  Exercises 11.2
11.3 P, NP, and NP-Complete Problems
  P and NP Problems
  NP-Complete Problems
  Exercises 11.3
11.4 Challenges of Numerical Algorithms
  Exercises 11.4
Summary

Chapter 12: Coping with the Limitations of Algorithm Power

12.1 Backtracking
  n-Queens Problem
  Hamiltonian Circuit Problem
  Subset-Sum Problem
  General Remarks
  Exercises 12.1
12.2 Branch-and-Bound
  Assignment Problem
  Knapsack Problem
  Traveling Salesman Problem
  Exercises 12.2
12.3 Approximation Algorithms for NP-Hard Problems
  Approximation Algorithms for the Traveling Salesman Problem
  Approximation Algorithms for the Knapsack Problem
  Exercises 12.3
12.4 Algorithms for Solving Nonlinear Equations
  Bisection Method
  Method of False Position
  Newton’s Method
  Exercises 12.4
Summary
Epilogue

Appendices

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

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