Data Structures and Algorithms in Java[1].pdf - Fulvio Frisone

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Code Fragment 5.5: Array-based Stack. (Cont<strong>in</strong>ued from Code Fragment 5.4.) 272
273
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Data Structures and Algorithms in J
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To Isabel -Roberto Tamassia Preface
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The Java code implementing fundamen
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PL6. Object-Oriented Programming Ch
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14. Memory A. Useful Mathematical F
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Sun, Nikos Triandopoulos, Luca Vism
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Getting Started: Classes, Types, an
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39 1.7 An Example Program..........
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The main "actors" in a Java program
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else interface switch boolean exten
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Class modifiers are optional keywor
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Comments Note the use of comments i
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Calling the new operator on a class
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n.longValue( ) float Float n = new
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The Dot Operator Every object refer
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object (assuming we are allowed acc
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Note the uses of instance variables
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1.2 Methods Methods in Java are con
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Abstract methods may only appear wi
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is intended to be used to initializ
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} int i = 512; double e = 2.71828;
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% the modulo operator This last ope
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zeros >>> shift bits right, filling
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3 add./subt. + − 4 shift > >>> 5
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double d1 = 3.2; double d2 = 3.9999
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String s = " " + 4.5; // correct, b
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System.out.println("This is tough."
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Defining a For Loop Here is the syn
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that input and inform the user that
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if (a[i][j] == 0) { foundFlag = tru
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the array, we will sometimes refer
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The cells of this new array, "a," a
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ways to reference such an object. W
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float height = s.nextFloat(); Syste
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We show the CreditCard class in Cod
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Code Fragment 1.7: Output from the
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a text editor class may wish to def
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The process of writing a Java progr
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low-level implementation details. A
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variable declaration, or method def
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• @exception exception-name descr
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A careful testing plan is an essent
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Modify the CreditCard class from Co
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A common punishment for school chil
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Object-Oriented Design Principles .
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java.datastructures.net 2.1 Goals,
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Abstraction The notion of abstracti
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2.1.3 Design Patterns One of the ad
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Example 2.1: Consider a class S tha
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S's a() method when asked for o.a()
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Sometimes, in a Java class, it is c
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103
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Code Fragment 2.3: Class for arithm
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A Fibonacci Progression Class As a
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Figure 2.5 : Inheritance diagram fo
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2.3 Exceptions Exceptions are unexp
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goShopping(); // I don't have to tr
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try problem… // This code might h
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instance, wish to identify some of
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The class BoxedItem shows another f
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comparability feature to a class (i
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• T and S are class types and S i
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We show in Code Fragment 2.13 a cla
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Starting with 5.0, Java includes a
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public void insert (P person, P oth
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• Class Goat extends Object and a
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((Place) usa).printMe(); } } class
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C-2.5 Write a program that consists
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Chapter 3 Arrays, Linked Lists, and
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3.4 Circularly Linked Lists and Lin
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A Class for High Scores Suppose we
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Note that we include a method, toSt
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Once we have identified the place i
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Object Removal Suppose some hot sho
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These methods for adding and removi
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This description is much closer to
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there is no swap needed, and return
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num = [10,12,19,28,33,38,41,46,48,5
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In Code Fragment 3.9, we give a sim
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Many computer games, be they strate
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We give a complete Java class for m
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Code Fragment 3.11: A simple, compl
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Like an array, a singly linked list
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Code Fragment 3.14: Inserting a new
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The reverse operation of inserting
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Header and Trailer Sentinels To sim
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Likewise, we can easily perform an
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Figure 3.17: Adding a new node afte
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Code Fragment 3.23: Java class DLis
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We make the following observations
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advance(): Advance the cursor to th
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Some Observations about the CircleL
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Some Sample Output 185
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We show in Code Fragment 3.27 thein
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The factorial function can be defin
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Each multiple of 1 inch also has a
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The trace for drawTicks is more com
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The simplest form of recursion is l
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nonrecursive part of each call. Mor
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3.5.2 Binary Recursion When an algo
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Unfortunately, in spite of the Fibo
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To solve such a puzzle, we need to
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3.6 Exercises For source code and h
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C-3.2 Let A be an array of size n
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Write a recursive Java program that
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Chapter Notes The fundamental data
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Primitive Operations . . . . . . .
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4.1.2 The Logarithm function One of
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4.1.5 The Quadratic function Anothe
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which assigns to an input value n t
Page 221 and 222: For example, we have the following:
Page 223 and 224: primarily as slopes. Even so, the e
Page 225 and 226: and y-coordinate equal to the runni
Page 227 and 228: Counting Primitive Operations Speci
Page 229 and 230: Simplifying the Analysis Further In
Page 231 and 232: Proposition 4.7: The Algorithmarray
Page 233 and 234: is O(4n 2 + 6n log n), although thi
Page 235 and 236: 256 16 4 16 64 256 4,096 65,536 32
Page 237 and 238: Running Maximum Problem Size (n) Ti
Page 239 and 240: should the constant factors they "h
Page 241 and 242: • There are two nested for loops,
Page 243 and 244: This definition leads immediately t
Page 245 and 246: Besides showing a use of the contra
Page 247 and 248: We may sometimes feel overwhelmed b
Page 249 and 250: The number of operations executed b
Page 251 and 252: R-4.22 Show that if d(n) is O(f(n))
Page 253 and 254: R-4.29 Show that 2 n+1 is O(2 n ).
Page 255 and 256: Describe a method for finding both
Page 257 and 258: Describe, in pseudo-code a method f
Page 259 and 260: Stacks.............................
Page 261 and 262: down on the stack to become the new
Page 263 and 264: 7 (5) top() 5 (5) pop() 5 () pop()
Page 265 and 266: In addition, we must define excepti
Page 267 and 268: 5.1.2 A Simple Array-Based Stack Im
Page 269 and 270: we indicate that the stack no longe
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Page 275 and 276: The array implementation of a stack
Page 277 and 278: of the list and return its element.
Page 279 and 280: 5.1.5 Matching Parentheses and HTML
Page 281 and 282: Matching Tags in an HTML Document A
Page 283 and 284: Code Fragment 5.12: Java program fo
Page 285 and 286: Another fundamental data structure
Page 287 and 288: true ( ) enqueue(9) - (9) enqueue(7
Page 289 and 290: 5.2.2 A Simple Array-Based Queue Im
Page 291 and 292: Using the Modulo Operator to Implem
Page 293 and 294: which gives the correct result both
Page 295 and 296: Each of the methods of the singly l
Page 297 and 298: potato is equivalent to dequeuing a
Page 299 and 300: - (3) addFirst(5) - (5,3) removeFir
Page 301 and 302: Thus, a doubly linked list can be u
Page 303 and 304: Code Fragment 5.18: Class NodeDeque
Page 305 and 306: 5.4 Exercises For source code and h
Page 307 and 308: Suppose Alice has picked three dist
Page 309 and 310: Implement a program that can input
Page 311 and 312: 223 6.1.3 A Simple Array-Based Impl
Page 313 and 314: Sequences....................... 25
Page 315 and 316: - (7) add(0,4) - (4,7) get(1) 7 (4,
Page 317 and 318: get(size() −1) addFirst(e) add(0,
Page 319 and 320: have to be shifted forward. A simil
Page 321 and 322: Moreover, the java.util.ArrayList c
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An Amortized Analysis of Extendable
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Proposition 6.2: Let S be an array
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linked list without revealing this
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The node list ADT allows us to view
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(8,3,5) set(p 3 ,7) 3 (8,7,5) addAf
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Deque Method Realization with Node-
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new node v to hold the element e, l
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In conclusion, using a doubly linke
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Code Fragment 6.11: Portions of the
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An iterator is a software design pa
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Since looping through the elements
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Code Fragment 6.15: The iterator()
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the last element. That is, it uses
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isEmpty() isEmpty() O(1) time get(i
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deletion is at cursor; A is O(n),L
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where n is the number of elements i
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Efficiency Trade-Offs with an Array
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357
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The previous implementation of a fa
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decreasing order and then pops up a
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accesses several Web pages and then
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6.6 Exercises For source code and h
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R-6.16 Describe how to create an it
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Think about how to extend the circu
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C-6.24 Isabel has an interesting wa
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Chapter 7 Trees Contents 7.1 Genera
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7.3.3 Properties of Binary Trees ..
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Electronics R'Us. The children of t
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Edges and Paths in Trees An edge of
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There are also a number of generic
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Figure 7.5: The linked structure fo
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Code Fragment 7.3: Method depth wri
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Code Fragment 7.6: Algorithm height
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Example 7.6: The preorder traversal
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Code Fragment 7.10: Algorithm paren
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The postorder traversal method is u
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Although the preorder and postorder
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A Recursive Binary Tree Definition
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same depth d as the level dof T. In
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Figure 7.13: Operation that removes
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We use a Java interface BTPosition
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addition to the Binary Tree interfa
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Binary Tree interface. (Continues i
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• Methods size() and isEmpty() us
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The level numbering function p sugg
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Time size, isEmpty O(1) iterator, p
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As is the case for general trees, t
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The inorder traversal of a binary t
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The inorder traversal can also be a
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start an Euler tour by initializing
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• Calls auxiliary method visitRig
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ExpressionTerm at each node. Class
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Code Fragment 7.31: Class EvaluateE
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Let T be an n-node binary tree that
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c. Let T be a proper binary tree wi
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Creativity C-7.1 For each node v in
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C-7.10 Two ordered trees T ′ and
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postorderDraw is similar to preorde
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Describe a nonrecursive method for
Page 445 and 446:
P-7.8 Write a program that can play
Page 447 and 448:
Chapter 8 Priority Queues Contents
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The Heap Data Structure............
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As in the examples above from an ai
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package includes a similar Entry in
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Code Fragment 8.3: Class representi
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insert(5,A) e 1 [=(5,A)] {(5,A)} in
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size() size() isEmpty() isEmpty() i
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at the time the method is executed.
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Code Fragment 8.7: Java class Defau
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465
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Insertion-Sort If we implement the
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An efficient realization of a prior
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Proposition 8.5: A heap T storing n
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The Array List Representation of a
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java.util.ArrayList. (Continues in
Page 477 and 478:
Code Fragment 8.12: Class ArrayList
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8.3.3 Implementing a Priority Queue
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The upward movement of the newly in
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Analysis Table 8.3 shows the runnin
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We conclude that the heap data stru
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Code Fragment 8.15: Remaining auxil
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As we have previously observed, rea
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8.3.6 Bottom-Up Heap Construction
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Recursive Bottom-Up Heap Constructi
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Figure 8.11: Visual justification o
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insert(3,B) e 2 {(3,B), (5,A)} inse
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The performance of an adaptable pri
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Code Fragment 8.18: An adaptable pr
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503
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Illustrate the execution of the sel
Page 507 and 508:
A group of children want to play a
Page 509 and 510:
C-8.13 We can represent a path from
Page 511 and 512:
P-8.1 Give a Java implementation of
Page 513 and 514:
Chapter 9 Maps and Dictionaries Con
Page 515 and 516:
9.3.3 Ordered Search Tables and Bin
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In either case, we use a key as a u
Page 519 and 520:
null {(5,A), (7,B)} put(2,C) null {
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get(k) put(k,v) put(k,v) remove(k)
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time of map operations in an n-entr
Page 525 and 526:
Hash Codes in Java The generic Obje
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of the word lists provided in two v
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6 6 2 7 14 2 8 105 2 9 18 2 10 277
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however, for if there is a repeated
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only the one entry. We leave the de
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key k will skip over cells containi
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537
Page 539 and 540:
539
Page 541 and 542:
9.2.7 Load Factors and Rehashing In
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example, when pundits study politic
Page 545 and 546:
for the keys, and we provide additi
Page 547 and 548:
findAll(2) {(2,C), (2,E)} {(5,A), (
Page 549 and 550:
Analysis of a List-Based Dictionary
Page 551 and 552:
for entries with duplicate keys. As
Page 553 and 554:
Figure 9.7: Realization of a dictio
Page 555 and 556:
Considering the running time of bin
Page 557 and 558:
Method List Hash Table Search Table
Page 559 and 560:
An example of a skip list is shown
Page 561 and 562:
We give a pseudo-code description o
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the new entry are drawn with thick
Page 565 and 566:
can go into what is almost an infin
Page 567 and 568:
of entries in the dictionary at the
Page 569 and 570:
O(n) O(logn) (expected) 9.5.2 The O
Page 571 and 572:
lastKey() last().getValue() get(las
Page 573 and 574:
Formally, we say a price-performanc
Page 575 and 576:
What is the worst-case running time
Page 577 and 578:
Describe how to use a map to implem
Page 579 and 580:
in memory, describe a method runnin
Page 581 and 582:
please see the various research pap
Page 583 and 584:
Amortized Analysis of Splaying ★.
Page 585 and 586:
10.1.1 Searching To perform operati
Page 587 and 588:
We can also show that a variation o
Page 589 and 590:
The implementation of the remove(k)
Page 591 and 592:
O(h) time, where h is the height of
Page 593 and 594:
Class BinarySearchTree uses locatio
Page 595 and 596:
Code Fragment 10.4: Class BinarySea
Page 597 and 598:
Code Fragment 10.5: Class BinarySea
Page 599 and 600:
10.2 AVL Trees In the previous sect
Page 601 and 602:
(10.3) > 2 i · n(h − 2i). That i
Page 603 and 604:
We restore the balance of the nodes
Page 605 and 606:
Figure 10.9: Schematic illustration
Page 607 and 608:
find another, we perform a restruct
Page 609 and 610:
In Code Fragments 10.7 and 10.8, we
Page 611 and 612:
Code Fragment 10.8: Auxiliary metho
Page 613 and 614:
10.3 Splay Trees Another way we can
Page 615 and 616:
We perform a zig-zig or a zig-zag w
Page 617 and 618:
Figure 10.16: Example of splaying a
Page 619 and 620:
10.3.2 When to Splay The rules that
Page 621 and 622:
10.3.3 Amortized Analysis of Splayi
Page 623 and 624:
When we perform a splaying, we pay
Page 625 and 626:
≤ r ′(x)−r(x) ≤ 3(r ′(x)
Page 627 and 628:
Proposition 10.6: Consider a sequen
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629
Page 631 and 632:
The dictionary we store at each nod
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h≤log(n+1) (10.10) are true. To j
Page 635 and 636:
insertion of 5, which causes an ove
Page 637 and 638:
A split operation affects a constan
Page 639 and 640:
operation; (f) after the fusion ope
Page 641 and 642:
collection returned by findAll. The
Page 643 and 644:
Figure 10.27: Correspondence betwee
Page 645 and 646:
• Take node z, its parent v, and
Page 647 and 648:
Figures 10.30 and 10.31 show a sequ
Page 649 and 650:
The cases for insertion imply an in
Page 651 and 652:
and (b) and for node b in part (c)
Page 653 and 654:
Case 2: The Sibling y of r is Black
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Case 3: The Sibling y of r is Red.
Page 657 and 658:
constant amount of work (in a restr
Page 659 and 660:
Performance of Red-Black Trees Tabl
Page 661 and 662:
Thus, a red-black tree achieves log
Page 663 and 664:
Methods insert (Code Fragment 10.10
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665
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Are the rotations in Figures 10.8 a
Page 669 and 670:
T is a (2,4) tree. c. T is a red-bl
Page 671 and 672:
C-10.8 Let D be an ordered dictiona
Page 673 and 674:
Projects P-10.1 N-body simulations
Page 675 and 676:
early approaches to balancing trees
Page 677 and 678:
11.5 Comparison of Sorting Algorith
Page 679 and 680:
elements of S; that is, S 1 contain
Page 681 and 682:
for a child invocation to return. (
Page 683 and 684:
Proposition 11.1: The merge-sort tr
Page 685 and 686:
idea is to iteratively remove the s
Page 687 and 688:
merge-sort, are implemented by eith
Page 689 and 690:
Code Fragment 11.3: Methods mergeSo
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A Nonrecursive Array-Based Implemen
Page 693 and 694:
the case when n is a power of 2. (W
Page 695 and 696:
each node of the quick-sort tree. T
Page 697 and 698:
eturn). Note the divide steps perfo
Page 699 and 700:
Performing Quick-Sort on Arrays and
Page 701 and 702:
E has at least one element (the piv
Page 703 and 704:
the size of the input for this call
Page 705 and 706:
In-place quick-sort modifies the in
Page 707 and 708:
Unfortunately, the implementation a
Page 709 and 710:
algorithm to output the elements of
Page 711 and 712:
itself is a sequence (of entries wi
Page 713 and 714:
first component, we guarantee that
Page 715 and 716:
Bucket-Sort and Radix-Sort Finally,
Page 717 and 718:
generic merging takes time proporti
Page 719 and 720:
• In class Union Merge, merge cop
Page 721 and 722:
Performance of the Sequence Impleme
Page 723 and 724:
With this partition data structure,
Page 725 and 726:
The Log-Star and Inverse Ackermann
Page 727 and 728:
This may come as a small surprise,
Page 729 and 730:
is the same as the expected number
Page 731 and 732:
Show that the probability that any
Page 733 and 734:
Describe what additional informatio
Page 735 and 736:
Argue why the previous claim proves
Page 737 and 738:
threads of b. Describe and analyze
Page 739 and 740:
Design and implement a stable versi
Page 741 and 742:
Contents 12.1 String Operations ...
Page 743 and 744:
567 12.5 Text Similarity Testing ..
Page 745 and 746:
finite, we usually assume that the
Page 747 and 748:
Return and update S to be the strin
Page 749 and 750:
Performance The brute-force pattern
Page 751 and 752:
We will formalize these heuristics
Page 753 and 754:
In Figure 12.3, we illustrate the e
Page 755 and 756:
A Java implementation of the BM pat
Page 757 and 758:
using an alternative shift heuristi
Page 759 and 760:
In Figure 12.5, we illustrate the e
Page 761 and 762:
A Java implementation of the KMP pa
Page 763 and 764:
12.3 Tries The pattern matching alg
Page 765 and 766:
The worst case for the number of no
Page 767 and 768:
A compressed trie is similar to a s
Page 769 and 770:
trie. In the next section, we prese
Page 771 and 772:
if such a path can be traced. The d
Page 773 and 774:
Let m be the size of pattern P and
Page 775 and 776:
transmit our text. Likewise, text c
Page 777 and 778:
12.4.2 The Greedy Method Huffman's
Page 779 and 780:
There are few algorithmic technique
Page 781 and 782:
Turning this definition of L[i, j]
Page 783 and 784:
Reinforcement R-12.1 List the prefi
Page 785 and 786:
C-12.5 Say that a pattern P of leng
Page 787 and 788:
suffix of length j in y. Design an
Page 789 and 790:
pattern matching. The reader intere
Page 791 and 792:
Depth-First Search Traversing a Dig
Page 793 and 794:
Example 13.2: We can associate with
Page 795 and 796:
In the propositions that follow, we
Page 797 and 798:
are communication connections betwe
Page 799 and 800:
vertices and m edges, an edge list
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The main feature of the edge list s
Page 803 and 804:
• The edge object for an edge e w
Page 805 and 806:
insertVertex, insertEdge, removeEdg
Page 807 and 808:
not. The optimal performance of met
Page 809 and 810:
came from to get to v, and repeat t
Page 811 and 812:
We can visualize a DFS traversal by
Page 813 and 814:
• Computing a cycle in G, or repo
Page 815 and 816:
depend on the implementation of the
Page 817 and 818:
Code Fragment 13.5: The main templa
Page 819 and 820:
Using the Template Method Pattern f
Page 821 and 822:
Class FindCycleDFS (Code Fragment 1
Page 823 and 824:
levels. BFS can also be thought of
Page 825 and 826:
825
Page 827 and 828:
• Given a start vertex s of G, co
Page 829 and 830:
Interesting problems that deal with
Page 831 and 832:
A DFS on a digraph partitions the e
Page 833 and 834:
Directed Breadth-First Search As wi
Page 835 and 836:
edges (vi,vk) and (vk,vj) with dash
Page 837 and 838:
ordering such that any directed pat
Page 839 and 840:
Justification: The initial computat
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computers. In this case, it is prob
Page 843 and 844:
their distances from v. Thus, in ea
Page 845 and 846:
edge for pulling in u with a solid
Page 847 and 848:
Proposition 13.23: In Dijkstra's al
Page 849 and 850:
Referring back to Code Fragment 13.
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The main computation of Dijkstra's
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13.7 Minimum Spanning Trees Suppose
Page 855 and 856:
13.7.1 Kruskal's Algorithm The reas
Page 857 and 858:
Figure 13.19: An example of an exec
Page 859 and 860:
execution of Kruskal's algorithm. (
Page 861 and 862:
Analyzing the Prim-Jarn ık Algorit
Page 863 and 864:
13.8 Exercises For source code and
Page 865 and 866:
LA22: (none) • LA31: LA15 • LA3
Page 867 and 868:
The graph has 10,000 vertices and 2
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265 175 215 180 185 155 3- - - - 26
Page 871 and 872:
_ _ _ _ Find which bridges to build
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determine if it is constructed corr
Page 875 and 876:
An Euler tour of a directed graph t
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C-13.21 Computer networks should av
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c. Now suppose that is weighted and
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P-13.9 Design an experimental compa
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Chapter 14 Memory Contents 14.1 Mem
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Multi-way Merging..................
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Keeping Track of the Program Counte
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In Section 7.3.6 we described how t
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Memory Allocation Algorithms The Ja
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identify and mark each live object.
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Caches and Disks Specifically, the
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are addressed. Virtual memory does
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The Random strategy is one of the e
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each would require to perform the s
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describe this structure, however, l
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are too large to fit entirely into
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Reinforcement R-14.1 Describe, in d
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Describe how to use a B-tree to imp
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Appendix A Useful Mathematical Fact
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The factorial function is defined a
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for any real number 0 < a ≠ 1. Pr
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E(X + Y) = E(X) + E(Y) and E(cX) =
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Bibliography [1] G. M. Adelson-Vels
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[28] S. A. Demurjian, Sr., Software
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[69] B. Liskov and J. Guttag, Abstr
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