Introduction to algorithms:
"The leading introductory textbook and reference on algorithms"--
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| Main Authors: | , , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge, Massachusetts ; London, England
The MIT Press
[2022]
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| Edition: | Fourth edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | "The leading introductory textbook and reference on algorithms"-- |
| Item Description: | Includes bibliographical references and index Literaturverzeichnis: Seite 1227-1250 |
| Physical Description: | xx, 1291 Seiten Illustrationen, Diagramme |
| ISBN: | 9780262046305 026204630X |
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| 245 | 1 | 0 | |a Introduction to algorithms |c Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein |
| 250 | |a Fourth edition | ||
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Contents Preface xiii I Foundations Introduction 3 1 The Role of Algorithms in Computing 1.1 Algorithms 5 1.2 Algorithms as a technology 12 2 Getting Started 17 2.1 Insertionsort 17 2.2 Analyzing algorithms 25 2.3 Designing algorithms 34 3 Characterizing Running Times 49 3.1 O-notation, Ω-notation, and 0-notation 50 3.2 Asymptotic notation: formal definitions 53 3.3 Standard notations and common functions 63 4 Divide-and-Conquer 76 4.1 Multiplying square matrices 80 4.2 Strassen’s algorithm for matrix multiplication 85 4.3 The substitution method for solving recurrences 90 4.4 The recursion-tree method for solving recurrences 95 4.5 The master method for solving recurrences 101 4.6 Proof of the continuous master theorem 107 4.7 Akra-Bazzi recurrences 115 ★ ★ 5
VI Contents 5 ★ II Probabilistic Analysis and Randomized Algorithms 126 5.1 The hiring problem 126 5.2 Indicator random variables 130 5.3 Randomized algorithms 134 5.4 Probabilistic analysis and further uses of indicator random variables 140 Sorting and Order Statistics Introduction 6 7 8 157 Heapsort 161 6.1 Heaps 161 6.2 Maintaining the heap property 6.3 Building a heap 167 6.4 The heapsort algorithm 170 6.5 Priority queues 172 164 Quicksort 182 7.1 Description of quicksort 183 7.2 Performance of quicksort 187 13 A randomized version of quicksort 7.4 Analysis of quicksort 193 Sorting in Linear Time 205 8.1 Lower bounds for sorting 8.2 Counting sort 208 8.3 Radix sort 211 8.4 Bucket sort 215 191 205 Medians and Order Statistics 227 9.1 Minimum and maximum 228 9.2 Selection in expected linear time 230 9.3 Selection in worst-case linear time 236 III Data Structures Introduction 10 249 Elementary Data Structures 252 10.1 Simple array-based data structures: arrays, matrices, stacks, queues 252 10.2 Linked lists 258 10.3 Representing rooted trees 265
vii Contents 11 Hash Tables 272 11.1 Direct-address tables 273 11.2 Hash tables 275 11.3 Hash functions 282 11.4 Open addressing 293 11.5 Practical considerations 301 12 Binary Search Trees 312 12.1 What is a binary search tree? 312 12.2 Querying a binary search tree 316 12.3 Insertion and deletion 321 13 Red-Black Trees 331 13.1 Properties of red-black trees 13.2 Rotations 335 13.3 Insertion 338 13.4 Deletion 346 331 IV Advanced Design and Analysis Techniques Introduction 361 14 Dynamic Programming 362 14.1 Rod cutting 363 14.2 Matrix-chain multiplication 373 14.3 Elements of dynamic programming 382 14.4 Longest common subsequence 393 14.5 Optimal binary search trees 400 15 Greedy Algorithms 417 15.1 An activity-selection problem 418 15.2 Elements of the greedy strategy 426 15.3 Huffman codes 431 15.4 Offline caching 440 16 Amortized Analysis 448 16.1 Aggregate analysis 449 16.2 The accounting method 453 16.3 The potential method 456 16.4 Dynamic tables 460
viii Contents V Advanced Data Structures Introduction 17 477 Augmenting Data Structures 480 17.1 Dynamic order statistics 480 17.2 How to augment a data structure 17.3 Interval trees 489 486 18 B-Trees 497 18.1 Definition of В -trees 501 18.2 Basic operations on B-trees 504 18.3 Deleting a key from a B-tree 513 19 Data Structures for Disjoint Sets 520 19.1 Disjoint-set operations 520 19.2 Linked-list representation of disjoint sets 523 19.3 Disjoint-set forests 527 19.4 Analysis of union by rank with path compression ★ 531 VI Graph Algorithms Introduction 547 20 Elementary Graph Algorithms 549 20.1 Representations of graphs 549 20.2 Breadth-first search 554 20.3 Depth-first search 563 20.4 Topological sort 573 20.5 Strongly connected components 576 21 Minimum Spanning Trees 585 21.1 Growing a minimum spanning tree 586 21.2 The algorithms of Kruskal and Prim 591 22 Single-Source Shortest Paths 604 22.1 The Bellman-Ford algorithm 612 22.2 Single-source shortest paths in directed acyclic graphs 22.3 Dijkstra’s algorithm 620 22.4 Difference constraints and shortest paths 626 22.5 Proofs of shortest-paths properties 633 616
Contents VII їх 23 All-Pairs Shortest Paths 646 23.1 Shortest paths and matrix multiplication 648 23.2 The Floyd-Warshall algorithm 655 23.3 Johnson’s algorithm for sparse graphs 662 24 Maximum Flow 670 24.1 Flow networks 671 24.2 The Ford-Fulkerson method 676 24.3 Maximum bipartite matching 693 25 Matchings in Bipartite Graphs 704 25.1 Maximum bipartite matching (revisited) 705 25.2 The stable-marriage problem 716 25.3 The Hungarian algorithm for the assignment problem 723 Selected Topics Introduction 745 26 Parallel Algorithms 748 26.1 The basics of fork-join parallelism 750 26.2 Parallel matrix multiplication 770 26.3 Parallel merge sort 775 27 Online Algorithms 791 27.1 Waiting for an elevator 792 27.2 Maintaining a search list 795 27.3 Online caching 802 28 Matrix Operations 819 28.1 Solving systems of linear equations 819 28.2 Inverting matrices 833 28.3 Symmetric positive-definite matrices and least-squares approximation 838 29 Linear Programming 850 29.1 Linear programming formulations and algorithms 29.2 Formulating problems as linear programs 860 29.3 Duality 866 30 Polynomials and the FFT 877 30.1 Representing polynomials 879 30.2 The DFT and FFT 885 30.3 FFT circuits 894 853
x Contents 31 ★ 32 •k 33 VIII Number-Theoretic Algorithms 903 31.1 Elementary number-theoretic notions 904 31.2 Greatest common divisor 911 31.3 Modular arithmetic 916 31.4 Solving modular linear equations 924 31.5 The Chinese remainder theorem 928 31.6 Powers of an element 932 31.7 The RS A public-key cryptosystem 936 31.8 Primality testing 942 String Matching 957 32.1 The naive string-matching algorithm 960 32.2 The Rabin-Karp algorithm 962 32.3 String matching with finite automata 967 32.4 The Knuth-Morris-Pratt algorithm 975 32.5 Suffix arrays 985 Machine-Learning Algorithms 1003 33.1 Clustering 1005 33.2 Multiplicative-weights algorithms 33.3 Gradient descent 1022 1015 34 NP-Completeness 1042 34.1 Polynomial time 1048 34.2 Polynomial-time verification 1056 34.3 NP-completeness and reducibility 1061 34.4 NP-completeness proofs 1072 34.5 NP-complete problems 1080 35 Approximation Algorithms 1104 35.1 The vertex-cover problem 1106 35.2 The traveling-salesperson problem 1109 35.3 The set-covering problem 1115 35.4 Randomization and linear programming 1119 35.5 The subset-sum problem 1124 Appendix: Mathematical Background Introduction A 1139 Summations 1140 A.l Summation formulas and properties A.2 Bounding summations 1145 1140
Contents Xl В Sets, Etc. 1153 B.l Sets 1153 В .2 Relations 1158 B.3 Functions 1161 B.4 Graphs 1164 B.5 Trees 1169 C Counting and Probability 1178 C.l Counting 1178 C.2 Probability 1184 C.3 Discrete random variables 1191 C.4 The geometric and binomial distributions 1196 C.5 The tails of the binomial distribution 1203 ★ D Matrices 1214 D.l Matrices and matrix operations D.2 Basic matrix properties 1219 Bibliography Index 1251 1227 1214 |
| adam_txt |
Contents Preface xiii I Foundations Introduction 3 1 The Role of Algorithms in Computing 1.1 Algorithms 5 1.2 Algorithms as a technology 12 2 Getting Started 17 2.1 Insertionsort 17 2.2 Analyzing algorithms 25 2.3 Designing algorithms 34 3 Characterizing Running Times 49 3.1 O-notation, Ω-notation, and 0-notation 50 3.2 Asymptotic notation: formal definitions 53 3.3 Standard notations and common functions 63 4 Divide-and-Conquer 76 4.1 Multiplying square matrices 80 4.2 Strassen’s algorithm for matrix multiplication 85 4.3 The substitution method for solving recurrences 90 4.4 The recursion-tree method for solving recurrences 95 4.5 The master method for solving recurrences 101 4.6 Proof of the continuous master theorem 107 4.7 Akra-Bazzi recurrences 115 ★ ★ 5
VI Contents 5 ★ II Probabilistic Analysis and Randomized Algorithms 126 5.1 The hiring problem 126 5.2 Indicator random variables 130 5.3 Randomized algorithms 134 5.4 Probabilistic analysis and further uses of indicator random variables 140 Sorting and Order Statistics Introduction 6 7 8 157 Heapsort 161 6.1 Heaps 161 6.2 Maintaining the heap property 6.3 Building a heap 167 6.4 The heapsort algorithm 170 6.5 Priority queues 172 164 Quicksort 182 7.1 Description of quicksort 183 7.2 Performance of quicksort 187 13 A randomized version of quicksort 7.4 Analysis of quicksort 193 Sorting in Linear Time 205 8.1 Lower bounds for sorting 8.2 Counting sort 208 8.3 Radix sort 211 8.4 Bucket sort 215 191 205 Medians and Order Statistics 227 9.1 Minimum and maximum 228 9.2 Selection in expected linear time 230 9.3 Selection in worst-case linear time 236 III Data Structures Introduction 10 249 Elementary Data Structures 252 10.1 Simple array-based data structures: arrays, matrices, stacks, queues 252 10.2 Linked lists 258 10.3 Representing rooted trees 265
vii Contents 11 Hash Tables 272 11.1 Direct-address tables 273 11.2 Hash tables 275 11.3 Hash functions 282 11.4 Open addressing 293 11.5 Practical considerations 301 12 Binary Search Trees 312 12.1 What is a binary search tree? 312 12.2 Querying a binary search tree 316 12.3 Insertion and deletion 321 13 Red-Black Trees 331 13.1 Properties of red-black trees 13.2 Rotations 335 13.3 Insertion 338 13.4 Deletion 346 331 IV Advanced Design and Analysis Techniques Introduction 361 14 Dynamic Programming 362 14.1 Rod cutting 363 14.2 Matrix-chain multiplication 373 14.3 Elements of dynamic programming 382 14.4 Longest common subsequence 393 14.5 Optimal binary search trees 400 15 Greedy Algorithms 417 15.1 An activity-selection problem 418 15.2 Elements of the greedy strategy 426 15.3 Huffman codes 431 15.4 Offline caching 440 16 Amortized Analysis 448 16.1 Aggregate analysis 449 16.2 The accounting method 453 16.3 The potential method 456 16.4 Dynamic tables 460
viii Contents V Advanced Data Structures Introduction 17 477 Augmenting Data Structures 480 17.1 Dynamic order statistics 480 17.2 How to augment a data structure 17.3 Interval trees 489 486 18 B-Trees 497 18.1 Definition of В -trees 501 18.2 Basic operations on B-trees 504 18.3 Deleting a key from a B-tree 513 19 Data Structures for Disjoint Sets 520 19.1 Disjoint-set operations 520 19.2 Linked-list representation of disjoint sets 523 19.3 Disjoint-set forests 527 19.4 Analysis of union by rank with path compression ★ 531 VI Graph Algorithms Introduction 547 20 Elementary Graph Algorithms 549 20.1 Representations of graphs 549 20.2 Breadth-first search 554 20.3 Depth-first search 563 20.4 Topological sort 573 20.5 Strongly connected components 576 21 Minimum Spanning Trees 585 21.1 Growing a minimum spanning tree 586 21.2 The algorithms of Kruskal and Prim 591 22 Single-Source Shortest Paths 604 22.1 The Bellman-Ford algorithm 612 22.2 Single-source shortest paths in directed acyclic graphs 22.3 Dijkstra’s algorithm 620 22.4 Difference constraints and shortest paths 626 22.5 Proofs of shortest-paths properties 633 616
Contents VII їх 23 All-Pairs Shortest Paths 646 23.1 Shortest paths and matrix multiplication 648 23.2 The Floyd-Warshall algorithm 655 23.3 Johnson’s algorithm for sparse graphs 662 24 Maximum Flow 670 24.1 Flow networks 671 24.2 The Ford-Fulkerson method 676 24.3 Maximum bipartite matching 693 25 Matchings in Bipartite Graphs 704 25.1 Maximum bipartite matching (revisited) 705 25.2 The stable-marriage problem 716 25.3 The Hungarian algorithm for the assignment problem 723 Selected Topics Introduction 745 26 Parallel Algorithms 748 26.1 The basics of fork-join parallelism 750 26.2 Parallel matrix multiplication 770 26.3 Parallel merge sort 775 27 Online Algorithms 791 27.1 Waiting for an elevator 792 27.2 Maintaining a search list 795 27.3 Online caching 802 28 Matrix Operations 819 28.1 Solving systems of linear equations 819 28.2 Inverting matrices 833 28.3 Symmetric positive-definite matrices and least-squares approximation 838 29 Linear Programming 850 29.1 Linear programming formulations and algorithms 29.2 Formulating problems as linear programs 860 29.3 Duality 866 30 Polynomials and the FFT 877 30.1 Representing polynomials 879 30.2 The DFT and FFT 885 30.3 FFT circuits 894 853
x Contents 31 ★ 32 •k 33 VIII Number-Theoretic Algorithms 903 31.1 Elementary number-theoretic notions 904 31.2 Greatest common divisor 911 31.3 Modular arithmetic 916 31.4 Solving modular linear equations 924 31.5 The Chinese remainder theorem 928 31.6 Powers of an element 932 31.7 The RS A public-key cryptosystem 936 31.8 Primality testing 942 String Matching 957 32.1 The naive string-matching algorithm 960 32.2 The Rabin-Karp algorithm 962 32.3 String matching with finite automata 967 32.4 The Knuth-Morris-Pratt algorithm 975 32.5 Suffix arrays 985 Machine-Learning Algorithms 1003 33.1 Clustering 1005 33.2 Multiplicative-weights algorithms 33.3 Gradient descent 1022 1015 34 NP-Completeness 1042 34.1 Polynomial time 1048 34.2 Polynomial-time verification 1056 34.3 NP-completeness and reducibility 1061 34.4 NP-completeness proofs 1072 34.5 NP-complete problems 1080 35 Approximation Algorithms 1104 35.1 The vertex-cover problem 1106 35.2 The traveling-salesperson problem 1109 35.3 The set-covering problem 1115 35.4 Randomization and linear programming 1119 35.5 The subset-sum problem 1124 Appendix: Mathematical Background Introduction A 1139 Summations 1140 A.l Summation formulas and properties A.2 Bounding summations 1145 1140
Contents Xl В Sets, Etc. 1153 B.l Sets 1153 В .2 Relations 1158 B.3 Functions 1161 B.4 Graphs 1164 B.5 Trees 1169 C Counting and Probability 1178 C.l Counting 1178 C.2 Probability 1184 C.3 Discrete random variables 1191 C.4 The geometric and binomial distributions 1196 C.5 The tails of the binomial distribution 1203 ★ D Matrices 1214 D.l Matrices and matrix operations D.2 Basic matrix properties 1219 Bibliography Index 1251 1227 1214 |
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| author | Cormen, Thomas H. Leiserson, Charles Eric Rivest, Ronald Linn 1947- Stein, Clifford 1965- |
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| id | DE-604.BV047874708 |
| illustrated | Illustrated |
| index_date | 2024-07-03T19:21:00Z |
| indexdate | 2025-02-24T09:01:10Z |
| institution | BVB |
| isbn | 9780262046305 026204630X |
| language | English |
| lccn | 2021037260 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-033257157 |
| oclc_num | 1285368737 |
| open_access_boolean | |
| owner | DE-739 DE-83 DE-188 DE-92 DE-20 DE-473 DE-BY-UBG DE-860 DE-573 DE-824 DE-19 DE-BY-UBM DE-898 DE-BY-UBR DE-703 DE-1046 DE-861 DE-29T DE-384 DE-706 DE-355 DE-BY-UBR DE-4325 |
| owner_facet | DE-739 DE-83 DE-188 DE-92 DE-20 DE-473 DE-BY-UBG DE-860 DE-573 DE-824 DE-19 DE-BY-UBM DE-898 DE-BY-UBR DE-703 DE-1046 DE-861 DE-29T DE-384 DE-706 DE-355 DE-BY-UBR DE-4325 |
| physical | xx, 1291 Seiten Illustrationen, Diagramme |
| publishDate | 2022 |
| publishDateSearch | 2022 |
| publishDateSort | 2022 |
| publisher | The MIT Press |
| record_format | marc |
| spelling | Cormen, Thomas H. Verfasser (DE-588)12942661X aut Introduction to algorithms Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein Fourth edition Cambridge, Massachusetts ; London, England The MIT Press [2022] © 2022 xx, 1291 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Literaturverzeichnis: Seite 1227-1250 "The leading introductory textbook and reference on algorithms"-- Computer programming Computer algorithms Datenstruktur (DE-588)4011146-5 gnd rswk-swf Informatik (DE-588)4026894-9 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Algorithmische Programmierung (DE-588)4293504-0 gnd rswk-swf Algorithmische Programmierung (DE-588)4293504-0 s DE-604 Datenstruktur (DE-588)4011146-5 s Algorithmus (DE-588)4001183-5 s Informatik (DE-588)4026894-9 s Leiserson, Charles Eric Verfasser (DE-588)140222847 aut Rivest, Ronald Linn 1947- Verfasser (DE-588)140222960 aut Stein, Clifford 1965- Verfasser (DE-588)1253530661 aut Erscheint auch als Online-Ausgabe 978-0-262-36750-9 (DE-604)BV047913937 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033257157&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cormen, Thomas H. Leiserson, Charles Eric Rivest, Ronald Linn 1947- Stein, Clifford 1965- Introduction to algorithms Computer programming Computer algorithms Datenstruktur (DE-588)4011146-5 gnd Informatik (DE-588)4026894-9 gnd Algorithmus (DE-588)4001183-5 gnd Algorithmische Programmierung (DE-588)4293504-0 gnd |
| subject_GND | (DE-588)4011146-5 (DE-588)4026894-9 (DE-588)4001183-5 (DE-588)4293504-0 |
| title | Introduction to algorithms |
| title_auth | Introduction to algorithms |
| title_exact_search | Introduction to algorithms |
| title_exact_search_txtP | Introduction to algorithms |
| title_full | Introduction to algorithms Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein |
| title_fullStr | Introduction to algorithms Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein |
| title_full_unstemmed | Introduction to algorithms Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein |
| title_short | Introduction to algorithms |
| title_sort | introduction to algorithms |
| topic | Computer programming Computer algorithms Datenstruktur (DE-588)4011146-5 gnd Informatik (DE-588)4026894-9 gnd Algorithmus (DE-588)4001183-5 gnd Algorithmische Programmierung (DE-588)4293504-0 gnd |
| topic_facet | Computer programming Computer algorithms Datenstruktur Informatik Algorithmus Algorithmische Programmierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033257157&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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