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Sec. 4.1 Lists 107curr...23 10 12(a)...curr2... 23 10 12 ...it1(b)Figure 4.10 The linked list removal process. (a) The linked list before removingthe node with value 10. (b) The linked list after removal. 1 marks the list nodebeing removed. it is set to point to the element. 2 marks the next field ofthe preceding list node, which is set to point to the node following the one beingdeleted.the node before it, because that is what we really want). This takes Θ(n) time inthe average and worst cases. Implementation of method moveToPos is similar inthat finding the ith position requires marching down i positions from the head ofthe list, taking Θ(i) time.Implementations for the remaining operations each require Θ(1) time.FreelistsThe new operator is relatively expensive to use. Garbage collection is also expensive.Section 12.3 discusses how general-purpose memory managers are implemented.The expense comes from the fact that free-store routines must be capableof handling requests to and from free store with no particular pattern, as well asmemory requests of vastly different sizes. This, combined with unpredictable freeingof space by the garbage collector, makes them inefficient compared to whatmight be implemented for more controlled patterns of memory access.List nodes are created and deleted in a linked list implementation in a waythat allows the Link class programmer to provide simple but efficient memorymanagement routines. Instead of making repeated calls to new, the Link classcan handle its own freelist. A freelist holds those list nodes that are not currentlybeing used. When a node is deleted from a linked list, it is placed at the head of thefreelist. When a new element is to be added to a linked list, the freelist is checkedto see if a list node is available. If so, the node is taken from the freelist. If thefreelist is empty, the standard new operator must then be called.Freelists are particularly useful for linked lists that periodically grow and thenshrink. The freelist will never grow larger than the largest size yet reached by the
108 Chap. 4 Lists, Stacks, and Queueslinked list. Requests for new nodes (after the list has shrunk) can be handled bythe freelist. Another good opportunity to use a freelist occurs when a program usesmultiple lists. So long as they do not all grow and shrink together, the free list canlet link nodes move between the lists.In the implementation shown here, the link class is augmented with methodsget and release. Figure 4.11 shows the reimplementation for the Link class tosupport these methods. Note how simple they are, because they need only removeand add an element to the front of the freelist, respectively. The freelist methodsget and release both run in Θ(1) time, except in the case where the freelist isexhausted and the new operation must be called. Figure 4.12 shows the necessarymodifications to members of the linked list class to make use of the freelist versionof the link class.The freelist variable declaration uses the keyword static. This creates asingle variable shared among all instances of the Link nodes. In this way, a singlefreelist shared by all Link nodes.4.1.3 Comparison of List ImplementationsNow that you have seen two substantially different implementations for lists, it isnatural to ask which is better. In particular, if you must implement a list for sometask, which implementation should you choose?Array-based lists have the disadvantage that their size must be predeterminedbefore the array can be allocated. Array-based lists cannot grow beyond their predeterminedsize. Whenever the list contains only a few elements, a substantialamount of space might be tied up in a largely empty array. Linked lists have theadvantage that they only need space for the objects actually on the list. There isno limit to the number of elements on a linked list, as long as there is free-storememory available. The amount of space required by a linked list is Θ(n), while thespace required by the array-based list implementation is Ω(n), but can be greater.Array-based lists have the advantage that there is no wasted space for an individualelement. Linked lists require that an extra pointer be added to every listnode. If the element size is small, then the overhead for links can be a significantfraction of the total storage. When the array for the array-based list is completelyfilled, there is no storage overhead. The array-based list will then be more spaceefficient, by a constant factor, than the linked implementation.A simple formula can be used to determine whether the array-based list orlinked list implementation will be more space efficient in a particular situation.Call n the number of elements currently in the list, P the size of a pointer in storageunits (typically four bytes), E the size of a data element in storage units (thiscould be anything, from one bit for a Boolean variable on up to thousands of bytesor more for complex records), and D the maximum number of list elements thatcan be stored in the array. The amount of space required for the array-based list is
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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. 2.8 Further Reading 45one inch
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3Algorithm AnalysisHow long will it
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Sec. 3.1 Introduction 55efficient.
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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. 7.10 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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Sec. 7.12 Projects 2637.6 It has be
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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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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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332 Chap. 9 SearchingThe cost for a
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334 Chap. 9 Searchingthat is not in
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336 Chap. 9 SearchingA good introdu
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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. 10.5 B-Trees 361331012 233348
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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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374 Chap. 11 Graphs0 1 2 3 40201 11
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376 Chap. 11 Graphstime. This is a
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378 Chap. 11 GraphsIt is reasonably
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380 Chap. 11 Graphs}/** @return an
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382 Chap. 11 Graphs}/** Set the wei
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384 Chap. 11 GraphsABABCCDDFFEE(a)(
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386 Chap. 11 Graphs/** Breadth firs
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388 Chap. 11 Graphs/** Recursive to
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390 Chap. 11 GraphsA103B2205D11C15E
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392 Chap. 11 Graphs/** Dijkstra’s
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394 Chap. 11 GraphsA7 5CB91 26ED 21
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396 Chap. 11 GraphsPrim’s algorit
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398 Chap. 11 GraphsInitialA B C D E
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400 Chap. 11 Graphs(a) IF an undire
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402 Chap. 11 Graphs11.8 Projects11.
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12Lists and Arrays RevisitedSimple
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Sec. 12.1 Multilists 407L1L2L3bcdL4
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Sec. 12.2 Matrix Representations 40
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Sec. 12.3 Memory Management 413/**
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Sec. 12.3 Memory Management 417Tag
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Sec. 12.3 Memory Management 419tend
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Sec. 12.4 Further Reading 4251a3b42
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Sec. 12.6 Projects 42712.7 Write a
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13Advanced Tree StructuresThis chap
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Sec. 13.2 Balanced Trees 437that is
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14Analysis TechniquesOften it is ea
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Sec. 14.1 Summation Techniques 463w
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Sec. 14.2 Recurrence Relations 4671
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Sec. 14.2 Recurrence Relations 469n
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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 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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