Introduction to the Design and Analysis of Algorithms

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.

Table of Contents:
Table of Contents New to the Third Edition Preface Introduction 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 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 -notation -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 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 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 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 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 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 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 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 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 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 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 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