Algorithms and Data Structures The Basic Toolbox

This concise introduction is ideal for readers familiar with programming and basic mathematical language. It uses pictures, words and high-level pseudocode to explain algorithms and presents efficient implementations using real programming languages.

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Bibliographic Details
Main Authors Mehlhorn, Kurt, Sanders, Peter
Format eBook Book
LanguageEnglish
Published Berlin, Heidelberg Springer Nature 2008
Springer
Springer Berlin / Heidelberg
Springer Berlin Heidelberg
Edition1
Subjects
Algorithm Analysis and Problem Complexity
Artificial Intelligence
Computer algorithms
Computer programming, programs, data
Computer Science
Data Structures
Data structures (Computer science)
Programming Techniques
Online AccessGet full text
ISBN9783540779780
3540779787
9783540779773
3540779779
DOI10.1007/978-3-540-77978-0

Cover

Table of Contents:
  • Intro -- Preface -- Contents -- 1 Appetizer: Integer Arithmetics -- 2 Introduction -- 3 Representing Sequences by Arrays and Linked Lists -- 4 Hash Tables and Associative Arrays -- 5 Sorting and Selection -- 6 Priority Queues -- 7 Sorted Sequences -- 8 Graph Representation -- 9 Graph Traversal -- 10 Shortest Paths -- 11 Minimum Spanning Trees -- 12 Generic Approaches to Optimization -- A Appendix -- References -- Index
  • Intro -- Appetizer: Integer Arithmetics -- Addition -- Multiplication: The School Method -- Result Checking -- A Recursive Version of the School Method -- Karatsuba Multiplication -- Algorithm Engineering -- The Programs -- Proofs of Lemma 1.5 and Theorem 1.7 -- Implementation Notes -- Historical Notes and Further Findings -- Introduction -- Asymptotic Notation -- The Machine Model -- Pseudocode -- Designing Correct Algorithms and Programs -- An Example -- Binary Search -- Basic Algorithm Analysis -- Average-Case Analysis -- Randomized Algorithms -- Graphs -- P and NP -- Implementation Notes -- Historical Notes and Further Findings -- Representing Sequences by Arrays and Linked Lists -- Linked Lists -- Unbounded Arrays -- *Amortized Analysis -- Stacks and Queues -- Lists Versus Arrays -- Implementation Notes -- Historical Notes and Further Findings -- Hash Tables and Associative Arrays -- Hashing with Chaining -- Universal Hashing -- Hashing with Linear Probing -- Chaining Versus Linear Probing -- *Perfect Hashing -- Implementation Notes -- Historical Notes and Further Findings -- Sorting and Selection -- Simple Sorters -- Mergesort -- an O( nlogn) Sorting Algorithm -- A Lower Bound -- Quicksort -- Selection -- Breaking the Lower Bound -- *External Sorting -- Implementation Notes -- Historical Notes and Further Findings -- Priority Queues -- Binary Heaps -- Addressable Priority Queues -- *External Memory -- Implementation Notes -- Historical Notes and Further Findings -- Sorted Sequences -- Binary Search Trees -- (a,b)-Trees and Red--Black Trees -- More Operations -- Amortized Analysis of Update Operations -- Augmented Search Trees -- Implementation Notes -- Historical Notes and Further Findings -- Graph Representation -- Unordered Edge Sequences -- Adjacency Arrays -- Static Graphs -- Adjacency Lists -- Dynamic Graphs
  • The Adjacency Matrix Representation -- Implicit Representations -- Implementation Notes -- Historical Notes and Further Findings -- Graph Traversal -- Breadth-First Search -- Depth-First Search -- Implementation Notes -- Historical Notes and Further Findings -- Shortest Paths -- From Basic Concepts to a Generic Algorithm -- Directed Acyclic Graphs -- Nonnegative Edge Costs (Dijkstra's Algorithm) -- *Average-Case Analysis of Dijkstra's Algorithm -- Monotone Integer Priority Queues -- Arbitrary Edge Costs (Bellman--Ford Algorithm) -- All-Pairs Shortest Paths and Node Potentials -- Shortest-Path Queries -- Implementation Notes -- Historical Notes and Further Findings -- Minimum Spanning Trees -- Cut and Cycle Properties -- The Jarník--Prim Algorithm -- Kruskal's Algorithm -- The Union--Find Data Structure -- *External Memory -- Applications -- Implementation Notes -- Historical Notes and Further Findings -- Generic Approaches to Optimization -- Linear Programming -- a Black-Box Solver -- Greedy Algorithms -- Never Look Back -- Dynamic Programming -- Building It Piece by Piece -- Systematic Search -- When in Doubt, Use Brute Force -- Local Search -- Think Globally, Act Locally -- Evolutionary Algorithms -- Implementation Notes -- Historical Notes and Further Findings -- Appendix -- Mathematical Symbols -- Mathematical Concepts -- Basic Probability Theory -- Useful Formulae -- References -- Index