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Sec. 9.6 Exercises 3379.9 Write an algorithm to implement the move-to-front self-organizing list heuristic,assuming that the list is implemented using an array. In particular, writea function MoveToFront that takes as input a value to be searched for andwhich adjusts the list appropriately. If the value is not already in the list, addit to the beginning of the list.9.10 Write an algorithm to implement the transpose self-organizing list heuristic,assuming that the list is implemented using an array. In particular, writea function Transpose that takes as input a value to be searched for andwhich adjusts the list appropriately. If the value is not already in the list, addit to the end of the list.9.11 Write functions for computing union, intersection, and set difference on arbitrarilylong bit vectors used to represent set membership as described inSection 9.3. Assume that for each operation both vectors are of equal length.9.12 Compute the probabilities for the following situations. These probabilitiescan be computed analytically, or you may write a computer program to generatethe probabilities by simulation.(a) Out of a group of 23 students, what is the probability that 2 studentsshare the same birthday?(b) Out of a group of 100 students, what is the probability that 3 studentsshare the same birthday?(c) How many students must be in the class for the probability to be at least50% that there are 2 who share a birthday in the same month?9.13 Assume that you are hashing key K to a hash table of n slots (indexed from0 to n − 1). For each of the following functions h(K), is the function acceptableas a hash function (i.e., would the hash program work correctly forboth insertions and searches), and if so, is it a good hash function? FunctionRandom(n) returns a random integer between 0 and n − 1, inclusive.(a) h(k) = k/n where k and n are integers.(b) h(k) = 1.(c) h(k) = (k + Random(n)) mod n.(d) h(k) = k mod n where n is a prime number.9.14 Assume that you have a seven-slot closed hash table (the slots are numbered0 through 6). Show the final hash table that would result if you used thehash function h(k) = k mod 7 and linear probing on this list of numbers:3, 12, 9, 2. After inserting the record with key value 2, list for each emptyslot the probability that it will be the next one filled.9.15 Assume that you have a ten-slot closed hash table (the slots are numbered 0through 9). Show the final hash table that would result if you used the hashfunction h(k) = k mod 10 and quadratic probing on this list of numbers:3, 12, 9, 2, 79, 46. After inserting the record with key value 46, list for eachempty slot the probability that it will be the next one filled.
338 Chap. 9 Searching9.16 Assume that you have a ten-slot closed hash table (the slots are numbered0 through 9). Show the final hash table that would result if you used thehash function h(k) = k mod 10 and pseudo-random probing on this list ofnumbers: 3, 12, 9, 2, 79, 44. The permutation of offsets to be used by thepseudo-random probing will be: 5, 9, 2, 1, 4, 8, 6, 3, 7. After inserting therecord with key value 44, list for each empty slot the probability that it willbe the next one filled.9.17 What is the result of running sfold from Section 9.4.1 on the followingstrings? Assume a hash table size of 101 slots.(a) HELLO WORLD(b) NOW HEAR THIS(c) HEAR THIS NOW9.18 Using closed hashing, with double hashing to resolve collisions, insert thefollowing keys into a hash table of thirteen slots (the slots are numbered0 through 12). The hash functions to be used are H1 and H2, defined below.You should show the hash table after all eight keys have been inserted.Be sure to indicate how you are using H1 and H2 to do the hashing. FunctionRev(k) reverses the decimal digits of k, for example, Rev(37) = 73;Rev(7) = 7.H1(k) = k mod 13.H2(k) = (Rev(k + 1) mod 11).Keys: 2, 8, 31, 20, 19, 18, 53, 27.9.19 Write an algorithm for a deletion function for hash tables that replaces therecord with a special value indicating a tombstone. Modify the functionshashInsert and hashSearch to work correctly with tombstones.9.20 Consider the following permutation for the numbers 1 to 6:2, 4, 6, 1, 3, 5.Analyze what will happen if this permutation is used by an implementation ofpseudo-random probing on a hash table of size seven. Will this permutationsolve the problem of primary clustering? What does this say about selectinga permutation for use when implementing pseudo-random probing?9.7 Projects9.1 Implement a binary search and the quadratic binary search of Section 9.1.Run your implementations over a large range of problem sizes, timing theresults for each algorithm. Graph and compare these timing results.
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Data Structures and AlgorithmAnalys
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ivContents2.6.1 Direct Proof 372.6.
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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 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. 3.3 A Faster Computer, or a Fa
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Sec. 3.4 Asymptotic Analysis 633.4
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Sec. 3.8 Multiple Parameters 77the
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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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Sec. 4.7 Projects 1414.16 Re-implem
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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. 7.5 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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266 Chap. 8 File Processing and Ext
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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. 12.3 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. 12.3 Memory Management 421is e
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Sec. 12.3 Memory Management 423AaBc
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Sec. 12.6 Projects 42712.7 Write a
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13Advanced Tree StructuresThis chap
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14Analysis TechniquesOften it is ea
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Sec. 14.2 Recurrence Relations 4671
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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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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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500 Chap. 15 Lower BoundsFigure 15.
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502 Chap. 15 Lower Boundsnot only t
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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 513on
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Sec. 16.2 Randomized Algorithms 515
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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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