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Sec. 11.3 Graph Traversals 383works regardless of whether the graph is directed or undirected. To ensure visitingall vertices, graphTraverse could be called as follows on a graph G:void graphTraverse(Graph G) {int v;for (v=0; v
384 Chap. 11 GraphsABABCCDDFFEE(a)(b)Figure 11.8 (a) A graph. (b) The depth-first search tree for the graph whenstarting at Vertex A.DFS processes each edge once in a directed graph. In an undirected graph,DFS processes each edge from both directions. Each vertex must be visited, butonly once, so the total cost is Θ(|V| + |E|).11.3.2 Breadth-First SearchOur second graph traversal algorithm is known as a breadth-first search (BFS).BFS examines all vertices connected to the start vertex before visiting vertices furtheraway. BFS is implemented similarly to DFS, except that a queue replacesthe recursion stack. Note that if the graph is a tree and the start vertex is at theroot, BFS is equivalent to visiting vertices level by level from top to bottom. Figure11.10 provides an implementation for the BFS algorithm. Figure 11.11 showsa graph and the corresponding breadth-first search tree. Figure 11.12 illustrates theBFS process for the graph of Figure 11.11(a).11.3.3 Topological SortAssume that we need to schedule a series of tasks, such as classes or constructionjobs, where we cannot start one task until after its prerequisites are completed. Wewish to organize the tasks into a linear order that allows us to complete them oneat a time without violating any prerequisites. We can model the problem using aDAG. The graph is directed because one task is a prerequisite of another — thevertices have a directed relationship. It is acyclic because a cycle would indicatea conflicting series of prerequisites that could not be completed without violatingat least one prerequisite. The process of laying out the vertices of a DAG in alinear order to meet the prerequisite rules is called a topological sort. Figure 11.14
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Data Structures and AlgorithmAnalys
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ivContents2.6.1 Direct Proof 372.6.
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viContents6.1 General Tree Definiti
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viiiContents10.5.2 B-Tree Analysis
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xContents15.7 Optimal Sorting 50115
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PrefaceWe study data structures so
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PrefacexvA sophomore-level class wh
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Prefacexviithe form ofcalls to meth
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PrefacexixFor the second edition, I
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1Data Structures and AlgorithmsHow
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Sec. 1.1 A Philosophy of Data Struc
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Sec. 1.1 A Philosophy of Data Struc
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Sec. 1.2 Abstract Data Types and Da
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Sec. 1.2 Abstract Data Types and Da
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Sec. 1.3 Design Patterns 13that tra
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Sec. 1.3 Design Patterns 15will cal
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Sec. 1.4 Problems, Algorithms, and
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Sec. 1.5 Further Reading 19vides po
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Sec. 1.6 Exercises 21than 10,000 of
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2Mathematical PreliminariesThis cha
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Sec. 2.1 Sets and Relations 25A seq
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Sec. 2.2 Miscellaneous Notation 27E
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Sec. 2.3 Logarithms 29Unfortunately
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Sec. 2.4 Summations and Recurrences
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Sec. 2.4 Summations and Recurrences
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Sec. 2.5 Recursion 35(a)(b)Figure 2
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Sec. 2.6 Mathematical Proof Techniq
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Sec. 2.8 Further Reading 45one inch
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Sec. 2.9 Exercises 47(c) For nonzer
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Sec. 2.9 Exercises 492.16 Write a r
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Sec. 2.9 Exercises 512.38 How many
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3Algorithm AnalysisHow long will it
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Sec. 3.1 Introduction 55efficient.
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Sec. 3.1 Introduction 57n! 2 n2n 25
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Sec. 3.2 Best, Worst, and Average C
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Sec. 3.3 A Faster Computer, or a Fa
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Sec. 3.4 Asymptotic Analysis 633.4
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Sec. 3.4 Asymptotic Analysis 65If s
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Sec. 3.5 Calculating the Running Ti
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Sec. 3.7 Common Misunderstandings 7
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Sec. 3.8 Multiple Parameters 77the
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Sec. 3.9 Space Bounds 79A data stru
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Sec. 3.10 Speeding Up Your Programs
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Sec. 3.11 Empirical Analysis 833.11
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Sec. 3.13 Exercises 853.13 Exercise
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Sec. 3.13 Exercises 87(f) sum = 0;f
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Sec. 3.14 Projects 893.24 Prove tha
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4Lists, Stacks, and QueuesIf your p
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Sec. 4.1 Lists 95list ADT. Interfac
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Sec. 4.1 Lists 97for (L.moveToStart
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Sec. 4.1 Lists 99public void moveTo
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Sec. 4.1 Lists 101/** Singly linked
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Sec. 4.1 Lists 103headcurrtailhead2
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Sec. 4.1 Lists 105/** Set curr at l
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Sec. 4.1 Lists 107curr...23 10 12(a
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Sec. 4.1 Lists 109/** Singly linked
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Sec. 4.1 Lists 111Array-based lists
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Sec. 4.1 Lists 113headcurrtail20 23
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Sec. 4.1 Lists 115/** Insert "it" a
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Sec. 4.2 Stacks 117The principle be
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Sec. 4.2 Stacks 119/** Array-based
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Sec. 4.2 Stacks 121top1top2Figure 4
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Sec. 4.2 Stacks 123you might want t
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Sec. 4.3 Queues 125/** Queue ADT */
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Sec. 4.3 Queues 127frontfront20 512
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Sec. 4.3 Queues 129/** Array-based
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Sec. 4.4 Dictionaries 1314.3.3 Comp
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Sec. 4.4 Dictionaries 133not get at
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Sec. 4.4 Dictionaries 135/** Contai
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Sec. 4.4 Dictionaries 137}/** @retu
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Sec. 4.6 Exercises 139(b) L2.append
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Sec. 4.7 Projects 1414.16 Re-implem
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Sec. 4.7 Projects 143‘a’ ‘b
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146 Chap. 5 Binary TreesABCDEFGHIFi
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148 Chap. 5 Binary TreesAny number
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150 Chap. 5 Binary Trees/** ADT for
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152 Chap. 5 Binary Treestends to be
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154 Chap. 5 Binary Trees5.3 Binary
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156 Chap. 5 Binary TreesABCDEFGHIFi
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158 Chap. 5 Binary Treesto its call
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160 Chap. 5 Binary Trees5.3.2 Space
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162 Chap. 5 Binary Trees012345 678
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164 Chap. 5 Binary Trees12037422442
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166 Chap. 5 Binary Trees37244273240
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168 Chap. 5 Binary Treessubroot105
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170 Chap. 5 Binary Treesin the case
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172 Chap. 5 Binary Treessynonymous
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174 Chap. 5 Binary Trees/** Heapify
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176 Chap. 5 Binary TreesRH1H2Figure
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178 Chap. 5 Binary Trees5.6 Huffman
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180 Chap. 5 Binary TreesLetter C D
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182 Chap. 5 Binary Trees/** Huffman
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184 Chap. 5 Binary Trees/** Build a
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186 Chap. 5 Binary Treesa reverse p
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188 Chap. 5 Binary Trees18 bits, mo
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190 Chap. 5 Binary Trees5.12 Write
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192 Chap. 5 Binary Trees(c) What is
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194 Chap. 5 Binary Trees5.7 Complet
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196 Chap. 6 Non-Binary TreesRootRAn
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198 Chap. 6 Non-Binary TreesRABCD E
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200 Chap. 6 Non-Binary Trees/** Gen
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202 Chap. 6 Non-Binary Treesspond t
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204 Chap. 6 Non-Binary Treesditiona
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206 Chap. 6 Non-Binary Treeslence o
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208 Chap. 6 Non-Binary TreesR’RA
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210 Chap. 6 Non-Binary TreesRRABABC
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212 Chap. 6 Non-Binary Trees(a)(b)F
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214 Chap. 6 Non-Binary Treestwo chi
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216 Chap. 6 Non-Binary Treeschild v
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218 Chap. 6 Non-Binary TreesCAFBEHG
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220 Chap. 6 Non-Binary Treestree af
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7Internal SortingWe sort many thing
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Sec. 7.2 Three Θ(n 2 ) Sorting Alg
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Sec. 7.3 Shellsort 231Insertion Bub
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Sec. 7.4 Mergesort 233static
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Sec. 7.4 Mergesort 235static
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Sec. 7.5 Quicksort 237Quicksort is
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Sec. 7.5 Quicksort 239static
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Sec. 7.5 Quicksort 241is still unli
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Sec. 7.6 Heapsort 243subarray, only
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Sec. 7.7 Binsort and Radix Sort 245
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Sec. 7.8 An Empirical Comparison of
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Sec. 7.9 Lower Bounds for Sorting 2
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Sec. 7.9 Lower Bounds for Sorting 2
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Sec. 7.10 Further Reading 257• Eq
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Sec. 7.11 Exercises 259algorithm to
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Sec. 7.12 Projects 2617.18 Which of
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266 Chap. 8 File Processing and Ext
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302 Chap. 9 Searchingintroduced in
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304 Chap. 9 Searchingvalue in L gre
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306 Chap. 9 SearchingWe now show th
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308 Chap. 9 Searchingrecords by exp
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310 Chap. 9 SearchingThis is potent
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312 Chap. 9 Searchingand the total
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314 Chap. 9 SearchingThis method of
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316 Chap. 9 Searchingbirthday is si
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318 Chap. 9 Searching45674567319692
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320 Chap. 9 Searching01000953012330
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322 Chap. 9 Searching01HashTable100
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324 Chap. 9 Searching/** Insert rec
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326 Chap. 9 Searching09050090501100
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328 Chap. 9 SearchingExample 9.9 Co
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330 Chap. 9 Searching/** Dictionary
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Page 362 and 363: Sec. 10.1 Linear Indexing 343Linear
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Sec. 13.1 Tries 433000xxxx00xxxxx0x
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Sec. 13.2 Balanced Trees 4353737244
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Sec. 13.2 Balanced Trees 437that is
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Sec. 13.2 Balanced Trees 439GPDSASP
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Sec. 13.4 Further Reading 45313.3.4
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Sec. 13.6 Projects 455(c) Show the
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Sec. 13.6 Projects 45713.11 Select
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14Analysis TechniquesOften it is ea
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Sec. 14.1 Summation Techniques 463w
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Sec. 14.1 Summation Techniques 465B
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Sec. 14.2 Recurrence Relations 4671
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Sec. 14.2 Recurrence Relations 469n
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Sec. 14.2 Recurrence Relations 471E
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Sec. 14.2 Recurrence Relations 473N
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Sec. 14.2 Recurrence Relations 475T
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Sec. 14.3 Amortized Analysis 477(ch
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Sec. 14.4 Further Reading 479compar
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Sec. 14.5 Exercises 48114.14 For th
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Sec. 14.6 Projects 48314.24 Use mat
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486 Chap. 15 Lower Boundsthe concep
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488 Chap. 15 Lower Boundsat least o
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490 Chap. 15 Lower BoundsABCGDEFFig
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492 Chap. 15 Lower BoundsProof 1: T
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494 Chap. 15 Lower BoundsFigure 15.
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496 Chap. 15 Lower BoundsTo minimiz
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498 Chap. 15 Lower BoundsThis recur
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500 Chap. 15 Lower BoundsFigure 15.
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502 Chap. 15 Lower Boundsnot only t
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504 Chap. 15 Lower Bounds1234Figure
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506 Chap. 15 Lower Bounds(a) Assume
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16Patterns of AlgorithmsThis chapte
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Sec. 16.1 Dynamic Programming 511Dy
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Sec. 16.1 Dynamic Programming 513on
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Sec. 16.2 Randomized Algorithms 515
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Sec. 16.3 Numerical Algorithms 523
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Sec. 16.3 Numerical Algorithms 525t
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Sec. 16.3 Numerical Algorithms 527B
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Sec. 16.3 Numerical Algorithms 529o
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Sec. 16.3 Numerical Algorithms 531o
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Sec. 16.6 Projects 533value depth5
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536 Chap. 17 Limits to ComputationT
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540 Chap. 17 Limits to ComputationS
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542 Chap. 17 Limits to Computationa
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544 Chap. 17 Limits to Computation3
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548 Chap. 17 Limits to Computationp
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550 Chap. 17 Limits to ComputationE
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552 Chap. 17 Limits to Computation1
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554 Chap. 17 Limits to ComputationM
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556 Chap. 17 Limits to Computationw
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558 Chap. 17 Limits to Computationx
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560 Chap. 17 Limits to Computationt
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562 Chap. 17 Limits to Computationm
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564 Chap. 17 Limits to Computation(
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Bibliography[AG06] Ken Arnold and J
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BIBLIOGRAPHY 569[GI91] Zvi Galil an
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BIBLIOGRAPHY 571[SJH93] Clifford A.
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Index80/20 rule, 309, 333abstract d
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INDEX 575image space, 430key space,
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INDEX 577building, 172-177for memor
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INDEX 579octree, 451Ω notation, 65
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INDEX 581comparing algorithms, 224-
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