A Practical Introduction to Data Structures and Algorithm Analysis

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Sec. 14.5 Exercises 50114.4 Use subtract-and-guess or divide-and-guess to find the closed form solutionfor the following summation. You must first find a pattern from which todeduce a potential closed form solution, and then prove that the proposedsolution is correct.n∑i/2 ii=114.5 Use the shifting method to solve the summationn∑i 2 .i=114.6 Use the shifting method to solve the summationn∑2 i .i=114.7 Use the shifting method to solve the summationn∑i2 n−i .i=114.8 Consider the following code fragment.sum = 0; inc = 0;for (i=1; i
502 Chap. 14 Analysis Techniques14.11 Give and prove the closed-form solution for the recurrence relation T(n) =T(n − 1) + 1, T(1) = 1.14.12 Give and prove the closed-form solution for the recurrence relation T(n) =T(n − 1) + c, T(1) = c.14.13 Prove by induction that the closed-form solution for the recurrence relationT(n) = 2T(n/2) + n; T(2) = 1is in Ω(n log n).14.14 For the following recurrence, give a closed-form solution. You should notgive an exact solution, but only an asymptotic solution (i.e., using Θ notation).You may assume that n is a power of 2. Prove that your answer iscorrect.T(n) = T(n/2) + √ n for n > 1; T(1) = 1.14.15 Using the technique of expanding the recurrence, find the exact closed-formsolution for the recurrence relationT(n) = 2T(n/2) + n; T(2) = 2.You may assume that n is a power of 2.14.16 Section 5.5 provides an asymptotic analysis for the worst-case cost of functionbuildHeap. Give an exact worst-case analysis for buildHeap.14.17 For each of the following recurrences, find and then prove (using induction)an exact closed-form solution. When convenient, you may assume that n isa power of 2.(a) T(n) = T(n − 1) + n/2 for n > 1; T(1) = 1.(b) T(n) = 2T(n/2) + n for n > 2; T(2) = 2.14.18 Use Theorem 14.1 to prove that binary search requires Θ(log n) time.14.19 Recall that when a hash table gets to be more than about one half full, itsperformance quickly degrades. One solution to this problem is to reinsertall elements of the hash table into a new hash table that is twice as large.Assuming that the (expected) average case cost to insert into a hash table isΘ(1), prove that the average cost to insert is still Θ(1) when this reinsertionpolicy is used.14.20 Given a 2-3 tree with N nodes, prove that inserting M additional nodes requiresO(M + N) node splits.
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xviPrefacemake the examples as clea
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xviiiPrefaceOne of the most importa
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xxPrefaceOthers at Prentice Hall wh
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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 13Data Typ
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Sec. 1.3 Design Patterns 151.3.3 Co
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Sec. 1.4 Problems, Algorithms, and
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Sec. 1.5 Further Reading 194. It mu
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Sec. 1.6 Exercises 21If you want to
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Sec. 1.6 Exercises 231.12 Imagine t
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2Mathematical PreliminariesThis cha
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Sec. 2.1 Sets and Relations 27examp
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Sec. 2.2 Miscellaneous Notation 29x
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Sec. 2.3 Logarithms 31positive inte
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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 37factorial of n
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Sec. 2.6 Mathematical Proof Techniq
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Sec. 2.7 Estimating 47Example 2.17
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Sec. 2.8 Further Reading 49typical
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Sec. 2.9 Exercises 51(f) {〈2, 1
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Sec. 2.9 Exercises 532.17 Prove by
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Sec. 2.9 Exercises 552.38 When buyi
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3Algorithm AnalysisHow long will it
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Sec. 3.1 Introduction 59compiled wi
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Sec. 3.1 Introduction 61Example 3.3
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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 67comp
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Sec. 3.4 Asymptotic Analysis 69fast
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Sec. 3.4 Asymptotic Analysis 71Exam
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Sec. 3.4 Asymptotic Analysis 73Rule
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Sec. 3.5 Calculating the Running Ti
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Sec. 3.5 Calculating the Running Ti
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Sec. 3.6 Analyzing Problems 79binar
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Sec. 3.7 Common Misunderstandings 8
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Sec. 3.9 Space Bounds 83pixel. Assu
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Sec. 3.9 Space Bounds 85A classic e
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Sec. 3.10 Speeding Up Your Programs
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Sec. 3.11 Empirical Analysis 893.11
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Sec. 3.13 Exercises 913.3 Arrange t
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Sec. 3.13 Exercises 93(f) sum = 0;f
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Sec. 3.14 Projects 95a summation fo
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4Lists, Stacks, and QueuesIf your p
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Sec. 4.1 Lists 101The next step is
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Sec. 4.1 Lists 103mentations, asser
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Sec. 4.1 Lists 105/** Array-based l
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Sec. 4.1 Lists 107Insert 23:1312 20
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Sec. 4.1 Lists 109currtailheadFigur
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Sec. 4.1 Lists 111// Linked list im
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Sec. 4.1 Lists 113curr... 23 12 ...
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Sec. 4.1 Lists 115// Singly linked
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Sec. 4.1 Lists 117determined size.
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Sec. 4.1 Lists 119pointer to each e
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Sec. 4.1 Lists 121// Insert "it" at
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Sec. 4.1 Lists 123curr... 20curr23
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Sec. 4.2 Stacks 125/** Stack ADT */
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Sec. 4.2 Stacks 127// Linked stack
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Sec. 4.2 Stacks 129Currptr β 1Curr
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Sec. 4.2 Stacks 131Example 4.3 The
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Sec. 4.3 Queues 133/** Queue ADT */
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Sec. 4.3 Queues 135frontfront20 512
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Sec. 4.3 Queues 137// Array-based q
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Sec. 4.4 Dictionaries 139enqueue pl
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Sec. 4.4 Dictionaries 141Method cle
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Sec. 4.4 Dictionaries 143// Contain
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Sec. 4.4 Dictionaries 145/** Dictio
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Sec. 4.5 Further Reading 1474.5 Fur
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Sec. 4.6 Exercises 149(a) The data
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Sec. 4.7 Projects 1514.3 Use singly
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5Binary TreesThe list representatio
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Sec. 5.1 Definitions and Properties
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Sec. 5.1 Definitions and Properties
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Sec. 5.2 Binary Tree Traversals 159
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Sec. 5.2 Binary Tree Traversals 161
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Sec. 5.3 Binary Tree Node Implement
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Sec. 5.4 Binary Search Trees 171Thi
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Sec. 5.4 Binary Search Trees 173120
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Sec. 5.4 Binary Search Trees 175/**
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Sec. 5.4 Binary Search Trees 177min
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Sec. 5.4 Binary Search Trees 17937
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Sec. 5.5 Heaps and Priority Queues
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Sec. 5.6 Huffman Coding Trees 189Le
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Sec. 5.6 Huffman Coding Trees 191St
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Sec. 5.6 Huffman Coding Trees 193/*
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Sec. 5.6 Huffman Coding Trees 195//
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Sec. 5.6 Huffman Coding Trees 197A
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Sec. 5.8 Exercises 199Many techniqu
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Sec. 5.8 Exercises 2015.19 Write a
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Sec. 5.9 Projects 203(d) The record
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6Non-Binary TreesMany organizations
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Sec. 6.1 General Tree Definitions a
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Sec. 6.2 The Parent Pointer Impleme
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Sec. 6.3 General Tree Implementatio
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Sec. 6.3 General Tree Implementatio
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Sec. 6.4 K-ary Trees 221RRABABCDEFC
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Sec. 6.5 Sequential Tree Implementa
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Sec. 6.5 Sequential Tree Implementa
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Sec. 6.7 Exercises 2276.2 Write an
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Sec. 6.7 Exercises 229CAFBEHGDIFigu
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Sec. 6.8 Projects 231proved perform
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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 24559 20 17 13 2
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Sec. 7.4 Mergesort 24736 20 17 13 2
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Sec. 7.5 Quicksort 249static
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Sec. 7.5 Quicksort 251static
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Sec. 7.5 Quicksort 253InitialPass 1
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Sec. 7.5 Quicksort 255The initial c
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Sec. 7.6 Heapsort 257and fast. The
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Sec. 7.7 Binsort and Radix Sort 259
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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 271• A
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Sec. 7.11 Exercises 2737.7 Recall t
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Sec. 7.12 Projects 2757.16 (a) Devi
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Sec. 7.12 Projects 277classmates? W
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280 Chap. 8 File Processing and Ext
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318 Chap. 9 SearchingThis and the f
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320 Chap. 9 Searchingelement in L,
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322 Chap. 9 SearchingThis is equal
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324 Chap. 9 Searching9.2 Self-Organ
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326 Chap. 9 SearchingWhen a frequen
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328 Chap. 9 Searchingand the total
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330 Chap. 9 SearchingThe set differ
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332 Chap. 9 Searchingprobability th
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334 Chap. 9 SearchingExample 9.6 A
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336 Chap. 9 Searchingand the next f
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338 Chap. 9 Searching01HashTable100
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340 Chap. 9 Searching/** Insert rec
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342 Chap. 9 Searching09050090501100
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344 Chap. 9 SearchingExample 9.9 Co
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346 Chap. 9 Searchingproject at the
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348 Chap. 9 SearchingIf N and M are
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350 Chap. 9 SearchingDepending on t
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352 Chap. 9 SearchingBentley et al.
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354 Chap. 9 Searching(c) How many s
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356 Chap. 9 Searching9.5 Implement
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358 Chap. 10 Indexingfile is create
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360 Chap. 10 Indexing1 2003 5894 10
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362 Chap. 10 IndexingSecondaryKeyJo
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364 Chap. 10 Indexingkey value for
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366 Chap. 10 IndexingFigure 10.7 Br
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368 Chap. 10 Indexing/** 2-3 tree n
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370 Chap. 10 Indexing18331223 30 48
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372 Chap. 10 Indexingprivate TTNode
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382 Chap. 10 IndexingAs mentioned e
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384 Chap. 10 Indexing(b) Show the i
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PART IVAdvanced Data Structures387
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390 Chap. 11 Graphs04123147123(a)(b
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392 Chap. 11 Graphs0 1 2 3 40201 11
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394 Chap. 11 GraphsThe adjacency ma
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396 Chap. 11 Graphsedge list. Funct
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398 Chap. 11 Graphspublic int weigh
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400 Chap. 11 Graphs}// Store edge w
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402 Chap. 11 GraphsABABCCDDFFEE(a)(
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404 Chap. 11 Graphs// Breadth first
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406 Chap. 11 GraphsAInitial call to
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408 Chap. 11 Graphsstatic void tops
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410 Chap. 11 Graphs// Compute short
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412 Chap. 11 Graphs// Dijkstra’s
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414 Chap. 11 Graphs// Compute a min
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416 Chap. 11 GraphsMarkedVertices v
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418 Chap. 11 GraphsInitialA B C D E
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420 Chap. 11 Graphs2 511032041032 6
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422 Chap. 11 Graphstriangular matri
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424 Chap. 12 Lists and Arrays Revis
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448 Chap. 13 Advanced Tree Structur
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Page 526 and 527: 15Lower BoundsHow do I know if I ha
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Page 530 and 531: Sec. 15.2 Lower Bounds on Searching
Page 532 and 533: Sec. 15.3 Finding the Maximum Value
Page 534 and 535: Sec. 15.4 Adversarial Lower Bounds
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Page 538 and 539: Sec. 15.5 State Space Lower Bounds
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Sec. 16.3 Numerical Algorithms 5511
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Sec. 16.3 Numerical Algorithms 555b
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Sec. 16.6 Projects 55716.8 What is
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560 Chap. 17 Limits to Computations
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562 Chap. 17 Limits to Computationf
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592 Chap. 17 Limits to Computationt
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594 BIBLIOGRAPHY[BG00] Sara Baase a
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596 BIBLIOGRAPHY[LLKS85] E.L. Lawle
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598 BIBLIOGRAPHY[WMB99][Zei07]I.H.
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600 INDEXbest fit, see memory manag
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602 INDEXrelation, 27, 50estimating
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604 INDEXinteger representation, 5,
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606 INDEXpath compression, 215-216,
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608 INDEXterminology, 236-237spatia
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A Practical Introduction to Data Structures and Algorithm Analysis

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