Loading...
Analysis of algorithms: an active learning approach
| Main Author: | |
|---|---|
| Format: | Printed Book |
| Published: |
New Delhi
Jones and Bartlett
2017
|
| Edition: | 2nd ed. |
| Subjects: |
Table of Contents:
- Chapter 1: Analysis Basics • What is Analysis? • Input Classes • Space Complexity • Exercises • What to Count and Consider • Cases to Consider • Exercises • Mathematical Background • Logarithms • Binary Trees • Probabilities • Summations • Exercises • Rates of Growth • Classification of Growth • Exercises • Tournament Method • Lower Bounds • Exercises • Analyzing Programs Chapter 2: Recursive Algorithms • Analyzing Recursive Algorithms • Exercises • Recurrence Relations • Approximating the Order of a Recurrence Relation • Exercises • Closest Pair • Exercises • Convex Hull • Exercises • Generating Permutations • Exercises • Recursion and Stacks • Programming Exercises Chapter 3: Searching and Selection Algorithms • Sequential Search • Worst-Case Analysis • Average-Case Analysis • Exercises • Binary Search • Worst-Case Analysis • Average-Case Analysis • Exercises • Selection • Exercises • Programming Exercise Chapter 4: Sorting Algorithms • Insertion Sort • Worst-Case Analysis • Average-Case Analysis • Exercises • Bubble Sort • Best-Case Analysis • Worst-Case Analysis • Average-Case Analysis • Exercises • Shellsort • Algorithm Analysis • The Effect of the Increment • Exercises • Radix Sort • Analysis • Exercises • Heapsort • Worst-Case Analysis • Average-Case Analysis • Exercises • Merge Sort • MergeLists Analysis • MergeSort Analysis • Exercises • Quicksort • Worst-Case Analysis • Average-Case Analysis • Exercises • External Polyphase Merge Sort • Number of Comparisons in Run Construction • Number of Comparisons in Run Merge • Number of Block Reads • Exercises • Additional Exercises • Programming Exercises Chapter 5: Numeric Algorithms • Calculating Polynomials • Horner’s Method • Preprocessed Coefficients • Exercises • Matrix Multiplication • Winograd’s Matrix Multiplication • Strassen’s Matrix Multiplication • Exercises • Linear Equations • Gauss–Jordan Method • Exercises Chapter 6: Formal Language Algorithms • Formal Language Basics • Lexical Ordering • Language Classifications • Exercises • Finite Auomata • Regular Languages • Regular Expression • Regular Grammars • Dererminate and Nondeterministic Finite Automata • Converting a Deterministic Finite Automaton into a Program • Exercises • Designing Finite Automata • Finite Automata Restrictions • Designing a Finite Automaton • Designing a Regular Grammar • Exercises • Finite Automata Equivalence and Limitations • Limits on Finite Automata • Exercises • Pushdown Automata • Creating a Deterministic Pushdown Automaton • Deterministic Context-Free Languages • Nondeterministic Pushdown Automata • Exercises • Context-Free Grammars • Context-Free Grammar Abilities • Designing Context-Free Grammars • Grammar Transformation • Greibach Normal Form • Converting a Context-Free Grammar into a Pushdown Automaton • Exercises • Limitations of Pushdown Automata • Exercises • Programming Language Compilation • Exercises Chapter 7: Matching Algorithms • String Machine •Finite Automata • Knuth–Morris–Pratt Algorithm • Boyer–Moore Algorithm • Exercises • Approximate String Matching • Analysis • Exercises • Programming Exercises Chapter 8: Graph Algorithms • Graph Background and Terminology • Terminology • Exercises • Data Structure Methods for Graphs • The Adjacency Matrix • The Adjacency List • Exercises • Depth-First and Breadth-First Traversal Algorithms • Depth-First Traversal • Breadth-First Traversal • Traversal Analysis • Exercises • Minimum Spanning Tree Algorithm • The Dijkstra–Prim Algorithm • The Kruskal Algorithm • Exercises • Shortest-Path Algorithm • Dijkstra’s Algorithm • Exercises • Biconnected Component Algorithm • Exercises • Partitioning Sets • Programming Exercises Chapter 9: Parallel Algorithms • Parallelism Introduction • Computer System Categories • Parallel Architectures • Principles for Parallelism Analysis • Exercises • The PRAM Model • Exercises • Simple Parallel Operations • Broadcasting Data in a CREW PRAM Model • Broadcasting Data in an EREW PRAM Model • Finding the Maximum Value in a List • Exercises • Parallel Searching • Exercises • Parallel Sorting • Linear Network Sort • Odd-Even Swap Sort • Other Parallel Sorts • Exercises • Parallel Numerical Algorithms • Matrix Multiplication on a Parallel Mesh • Matrix Multiplication in a CRCW PRAM Model • Solving Systems of Linear Equations with an SIMD Algorithm • Exercises • Parallel Graph Algorithms • All Pairs Shortest-Path Parallel Algorithm • Minimum Spanning Tree Parallel Algorithm • Exercises Chapter 10: Limits of Computation • Turing Machines • Turing Machines as Language Acceptors • Turing Machines as Function Calculators • Designing Turing Machines • Exercises • The Church–Turing Thesis • Turing Machine Variations • Two-Way Infinite Tape Turing Machines • Multiple Tape Turing Machines • Two-Dimensional Tape Turing Machines • Nondeterministic Turing Machines • A Universal Turing Machine • Exercises • The Limits of Turing Machines • Languages Not Recursively Enumerable • The Halting Problem • Exercise • What is NP? • Problem Reductions • NP-Complete Problems • Typical NP Problems • Graph Coloring • Bin Packing • Backpack Problem • Subset Sum Problem • CNF-Satisfiability Problem • Job Scheduling Problem • Exercises • What Makes Something NP? • Is P = NP? • Exercises • Testing Possible Solutions • Job Scheduling • Graph Coloring • Exercises Chapter 11: Other Algorithmic Techniques • Greedy Approximation Algorithms • Traveling Salesperson Approximations • Bin Packing Approximations • Backpack Approximation • Subset Sum Approximation • Graph Coloring Approximation • Exercises • Backtracking • Exercises • Branch and Bound • Exercises • Probabilistic Algorithms • Numerical Probabilistic Algorithms • Monte Carlo Algorithms • Las Vegas Algorithms • Sherwood Algorithms • Probabilistic Algorithm Comparison • Exercises • Dynamic Programming • Calculating Fibonacci Numbers and Binomial Coefficients • Dynamic Matrix Multiplication • Floyd’s All-Pairs Shortest Path Algorithm • A Dynamic Algorithm for the Backpack Problem • Exercises • Programming Exercises