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Sec. 12.4 Further Reading 4251a3b42ce(a)561a23b5c46eprevcurr(b)Figure 12.18 Example of the Deutsch-Schorr-Waite garbage collection algorithm.(a) The initial multilist structure. (b) The multilist structure of (a) atthe instant when link node 5 is being processed by the garbage collection algorithm.A chain of pointers stretching from variable prev to the head node of thestructure has been (temporarily) created by the garbage collection algorithm.the left branch or the right branch of the link node being pointed to. At any giveninstant we have passed down only one path from the root, and we can follow thetrail of pointers back up. As we return (equivalent to popping the recursion stack),we set the pointer back to its original position so as to return the structure to itsoriginal condition. This is known as the Deutsch-Schorr-Waite garbage collectionalgorithm.12.4 Further ReadingFor information on LISP, see The Little LISPer by Friedman and Felleisen [FF89].Another good LISP reference is Common LISP: The Language by Guy L. Steele[Ste90]. For information on Emacs, which is both an excellent text editor anda programming environment, see the GNU Emacs Manual by Richard Stallman[Sta11b]. You can get more information about Java’s garbage collection systemfrom The Java Programming Language by Ken Arnold and James Gosling [AG06].For more details on sparse matrix representations, the Yale representation is describedby Eisenstat, Schultz and Sherman [ESS81]. The MATLAB sparse matrixrepresentation is described by Gilbert, Moler, and Schreiber [GMS91].
426 Chap. 12 Lists and Arrays Revisitedabc(a)deL1a(b)L1L2L3a b c d(c)L4Figure 12.19 Some example multilists.An introductory text on operating systems covers many topics relating to memorymanagement issues, including layout of files on disk and caching of informationin main memory. All of the topics covered here on memory management, bufferpools, and paging are relevant to operating system implementation. For example,see Operating Systems by William Stallings[Sta11a].12.5 Exercises12.1 For each of the following bracket notation descriptions, draw the equivalentmultilist in graphical form such as shown in Figure 12.2.(a) 〈a, b, 〈c, d, e〉, 〈f, 〈g〉, h〉〉(b) 〈a, b, 〈c, d, L1:e〉, L1〉(c) 〈L1:a, L1, 〈L2:b〉, L2, 〈L1〉〉12.2 (a) Show the bracket notation for the list of Figure 12.19(a).(b) Show the bracket notation for the list of Figure 12.19(b).(c) Show the bracket notation for the list of Figure 12.19(c).12.3 Given the linked representation of a pure list such as〈x 1 , 〈y 1 , y 2 , 〈z 1 , z 2 〉, y 4 〉, 〈w 1 , w 2 〉, x 4 〉,write an in-place reversal algorithm to reverse the sublists at all levels includingthe topmost level. For this example, the result would be a linkedrepresentation corresponding to〈x 4 , 〈w 2 , w 1 〉, 〈y 4 , 〈z 2 , z 1 〉, y 2 , y 1 〉, x 1 〉.12.4 What fraction of the values in a matrix must be zero for the sparse matrixrepresentation of Section 12.2 to be more space efficient than the standardtwo-dimensional matrix representation when data values require eight bytes,array indices require two bytes, and pointers require four bytes?12.5 Write a function to add an element at a given position to the sparse matrixrepresentation of Section 12.2.12.6 Write a function to delete an element from a given position in the sparsematrix representation of Section 12.2.
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Data Structures and AlgorithmAnalys
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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. 2.8 Further Reading 45one inch
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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. 3.10 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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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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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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7Internal SortingWe sort many thing
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Sec. 7.3 Shellsort 231Insertion Bub
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Sec. 7.4 Mergesort 233static
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Sec. 7.5 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. 7.10 Further Reading 257• Eq
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Sec. 7.11 Exercises 259algorithm to
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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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322 Chap. 9 Searching01HashTable100
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324 Chap. 9 Searching/** Insert rec
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328 Chap. 9 SearchingExample 9.9 Co
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330 Chap. 9 Searching/** Dictionary
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332 Chap. 9 SearchingThe cost for a
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334 Chap. 9 Searchingthat is not in
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338 Chap. 9 Searching9.16 Assume th
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10IndexingMany large-scale computin
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Sec. 10.1 Linear Indexing 343Linear
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Sec. 10.2 ISAM 347In−memoryTable
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Sec. 10.3 Tree-based Indexing 349Fi
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Sec. 10.4 2-3 Trees 351/** 2-3 tree
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Sec. 10.5 B-Trees 355private TTNode
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Sec. 10.6 Further Reading 365at mos
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Sec. 10.8 Projects 36710.7 Prove th
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PART IVAdvanced Data Structures369
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372 Chap. 11 Graphs04123147123(a)(b
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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 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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