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

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typesetting package for the text and Adobe FrameMaker® and Microsoft Visio® for the figures. Finally, we would like to warmly thank Isabel Cruz, Karen Goodrich, Giuseppe Di Battista, Franco Preparata, Ioannis Tollis, and our parents for providing advice, encouragement, and support at various stages of the preparation of this book. We also thank them for reminding us that there are things in life beyond writing books. Michael T. Goodrich Roberto Tamassia Chapter 1 Java Programming Basics Contents 1.1 12
Getting Started: Classes, Types, and Objects... 2 1.1.1 Base Types......................................................... .. 5 1.1.2 Objects....................................................... ....... 7 1.1.3 Enum Types......................................................... . 14 1.2 Methods....................................... 15 1.3 Expressions................................... 20 1.3.1 Literals...................................................... ...... 20 1.3.2 Operators..................................................... ...... 21 1.3.3 13
Page 1 and 2: Data Structures and Algorithms in J
Page 3 and 4: To Isabel -Roberto Tamassia Preface
Page 5 and 6: The Java code implementing fundamen
Page 7 and 8: PL6. Object-Oriented Programming Ch
Page 9 and 10: 14. Memory A. Useful Mathematical F
Page 11: Sun, Nikos Triandopoulos, Luca Vism
Page 15 and 16: 39 1.7 An Example Program..........
Page 17 and 18: The main "actors" in a Java program
Page 19 and 20: else interface switch boolean exten
Page 21 and 22: Class modifiers are optional keywor
Page 23 and 24: Comments Note the use of comments i
Page 25 and 26: Calling the new operator on a class
Page 27 and 28: n.longValue( ) float Float n = new
Page 29 and 30: The Dot Operator Every object refer
Page 31 and 32: object (assuming we are allowed acc
Page 33 and 34: Note the uses of instance variables
Page 35 and 36: 1.2 Methods Methods in Java are con
Page 37 and 38: Abstract methods may only appear wi
Page 39 and 40: is intended to be used to initializ
Page 41 and 42: } int i = 512; double e = 2.71828;
Page 43 and 44: % the modulo operator This last ope
Page 45 and 46: zeros >>> shift bits right, filling
Page 47 and 48: 3 add./subt. + − 4 shift > >>> 5
Page 49 and 50: double d1 = 3.2; double d2 = 3.9999
Page 51 and 52: String s = " " + 4.5; // correct, b
Page 53 and 54: System.out.println("This is tough."
Page 55 and 56: Defining a For Loop Here is the syn
Page 57 and 58: that input and inform the user that
Page 59 and 60: if (a[i][j] == 0) { foundFlag = tru
Page 61 and 62: the array, we will sometimes refer
Page 63 and 64:
The cells of this new array, "a," a
Page 65 and 66:
ways to reference such an object. W
Page 67 and 68:
float height = s.nextFloat(); Syste
Page 69 and 70:
We show the CreditCard class in Cod
Page 71 and 72:
Code Fragment 1.7: Output from the
Page 73 and 74:
a text editor class may wish to def
Page 75 and 76:
The process of writing a Java progr
Page 77 and 78:
low-level implementation details. A
Page 79 and 80:
variable declaration, or method def
Page 81 and 82:
• @exception exception-name descr
Page 83 and 84:
A careful testing plan is an essent
Page 85 and 86:
Modify the CreditCard class from Co
Page 87 and 88:
A common punishment for school chil
Page 89 and 90:
Object-Oriented Design Principles .
Page 91 and 92:
java.datastructures.net 2.1 Goals,
Page 93 and 94:
Abstraction The notion of abstracti
Page 95 and 96:
2.1.3 Design Patterns One of the ad
Page 97 and 98:
Example 2.1: Consider a class S tha
Page 99 and 100:
S's a() method when asked for o.a()
Page 101 and 102:
Sometimes, in a Java class, it is c
Page 103 and 104:
103
Page 105 and 106:
Code Fragment 2.3: Class for arithm
Page 107 and 108:
A Fibonacci Progression Class As a
Page 109 and 110:
Figure 2.5 : Inheritance diagram fo
Page 111 and 112:
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
Page 117 and 118:
instance, wish to identify some of
Page 119 and 120:
The class BoxedItem shows another f
Page 121 and 122:
comparability feature to a class (i
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• T and S are class types and S i
Page 125 and 126:
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
Page 137 and 138:
Chapter 3 Arrays, Linked Lists, and
Page 139 and 140:
3.4 Circularly Linked Lists and Lin
Page 141 and 142:
A Class for High Scores Suppose we
Page 143 and 144:
Note that we include a method, toSt
Page 145 and 146:
Once we have identified the place i
Page 147 and 148:
Object Removal Suppose some hot sho
Page 149 and 150:
These methods for adding and removi
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This description is much closer to
Page 153 and 154:
there is no swap needed, and return
Page 155 and 156:
num = [10,12,19,28,33,38,41,46,48,5
Page 157 and 158:
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
Page 163 and 164:
Code Fragment 3.11: A simple, compl
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Like an array, a singly linked list
Page 167 and 168:
Code Fragment 3.14: Inserting a new
Page 169 and 170:
The reverse operation of inserting
Page 171 and 172:
Header and Trailer Sentinels To sim
Page 173 and 174:
Likewise, we can easily perform an
Page 175 and 176:
Figure 3.17: Adding a new node afte
Page 177 and 178:
Code Fragment 3.23: Java class DLis
Page 179 and 180:
We make the following observations
Page 181 and 182:
advance(): Advance the cursor to th
Page 183 and 184:
Some Observations about the CircleL
Page 185 and 186:
Some Sample Output 185
Page 187 and 188:
We show in Code Fragment 3.27 thein
Page 189 and 190:
The factorial function can be defin
Page 191 and 192:
Each multiple of 1 inch also has a
Page 193 and 194:
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
Page 199 and 200:
3.5.2 Binary Recursion When an algo
Page 201 and 202:
Unfortunately, in spite of the Fibo
Page 203 and 204:
To solve such a puzzle, we need to
Page 205 and 206:
3.6 Exercises For source code and h
Page 207 and 208:
C-3.2 Let A be an array of size n
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Write a recursive Java program that
Page 211 and 212:
Chapter Notes The fundamental data
Page 213 and 214:
Primitive Operations . . . . . . .
Page 215 and 216:
4.1.2 The Logarithm function One of
Page 217 and 218:
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:
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primarily as slopes. Even so, the e
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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
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is O(4n 2 + 6n log n), although thi
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256 16 4 16 64 256 4,096 65,536 32
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Running Maximum Problem Size (n) Ti
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should the constant factors they "h
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• There are two nested for loops,
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This definition leads immediately t
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Besides showing a use of the contra
Page 247 and 248:
We may sometimes feel overwhelmed b
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The number of operations executed b
Page 251 and 252:
R-4.22 Show that if d(n) is O(f(n))
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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.............................
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down on the stack to become the new
Page 263 and 264:
7 (5) top() 5 (5) pop() 5 () pop()
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In addition, we must define excepti
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5.1.2 A Simple Array-Based Stack Im
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we indicate that the stack no longe
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271
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273
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The array implementation of a stack
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of the list and return its element.
Page 279 and 280:
5.1.5 Matching Parentheses and HTML
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Matching Tags in an HTML Document A
Page 283 and 284:
Code Fragment 5.12: Java program fo
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Another fundamental data structure
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true ( ) enqueue(9) - (9) enqueue(7
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5.2.2 A Simple Array-Based Queue Im
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Using the Modulo Operator to Implem
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which gives the correct result both
Page 295 and 296:
Each of the methods of the singly l
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potato is equivalent to dequeuing a
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- (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:
Page 307 and 308:
Suppose Alice has picked three dist
Page 309 and 310:
Implement a program that can input
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223 6.1.3 A Simple Array-Based Impl
Page 313 and 314:
Sequences....................... 25
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- (7) add(0,4) - (4,7) get(1) 7 (4,
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get(size() −1) addFirst(e) add(0,
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have to be shifted forward. A simil
Page 321 and 322:
Moreover, the java.util.ArrayList c
Page 323 and 324:
An Amortized Analysis of Extendable
Page 325 and 326:
Proposition 6.2: Let S be an array
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linked list without revealing this
Page 329 and 330:
The node list ADT allows us to view
Page 331 and 332:
(8,3,5) set(p 3 ,7) 3 (8,7,5) addAf
Page 333 and 334:
Deque Method Realization with Node-
Page 335 and 336:
new node v to hold the element e, l
Page 337 and 338:
In conclusion, using a doubly linke
Page 339 and 340:
Code Fragment 6.11: Portions of the
Page 341 and 342:
An iterator is a software design pa
Page 343 and 344:
Since looping through the elements
Page 345 and 346:
Code Fragment 6.15: The iterator()
Page 347 and 348:
the last element. That is, it uses
Page 349 and 350:
isEmpty() isEmpty() O(1) time get(i
Page 351 and 352:
deletion is at cursor; A is O(n),L
Page 353 and 354:
where n is the number of elements i
Page 355 and 356:
Efficiency Trade-Offs with an Array
Page 357 and 358:
357
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The previous implementation of a fa
Page 361 and 362:
decreasing order and then pops up a
Page 363 and 364:
accesses several Web pages and then
Page 365 and 366:
Page 367 and 368:
R-6.16 Describe how to create an it
Page 369 and 370:
Think about how to extend the circu
Page 371 and 372:
C-6.24 Isabel has an interesting wa
Page 373 and 374:
Chapter 7 Trees Contents 7.1 Genera
Page 375 and 376:
7.3.3 Properties of Binary Trees ..
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Electronics R'Us. The children of t
Page 379 and 380:
Edges and Paths in Trees An edge of
Page 381 and 382:
There are also a number of generic
Page 383 and 384:
Figure 7.5: The linked structure fo
Page 385 and 386:
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
Page 391 and 392:
Code Fragment 7.10: Algorithm paren
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The postorder traversal method is u
Page 395 and 396:
Although the preorder and postorder
Page 397 and 398:
A Recursive Binary Tree Definition
Page 399 and 400:
same depth d as the level dof T. In
Page 401 and 402:
Figure 7.13: Operation that removes
Page 403 and 404:
We use a Java interface BTPosition
Page 405 and 406:
addition to the Binary Tree interfa
Page 407 and 408:
Page 409 and 410:
Page 411 and 412:
Binary Tree interface. (Continues i
Page 413 and 414:
• Methods size() and isEmpty() us
Page 415 and 416:
The level numbering function p sugg
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Time size, isEmpty O(1) iterator, p
Page 419 and 420:
As is the case for general trees, t
Page 421 and 422:
The inorder traversal of a binary t
Page 423 and 424:
The inorder traversal can also be a
Page 425 and 426:
start an Euler tour by initializing
Page 427 and 428:
• Calls auxiliary method visitRig
Page 429 and 430:
ExpressionTerm at each node. Class
Page 431 and 432:
Code Fragment 7.31: Class EvaluateE
Page 433 and 434:
Let T be an n-node binary tree that
Page 435 and 436:
c. Let T be a proper binary tree wi
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Creativity C-7.1 For each node v in
Page 439 and 440:
C-7.10 Two ordered trees T ′ and
Page 441 and 442:
postorderDraw is similar to preorde
Page 443 and 444:
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
Page 453 and 454:
package includes a similar Entry in
Page 455 and 456:
Code Fragment 8.3: Class representi
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insert(5,A) e 1 [=(5,A)] {(5,A)} in
Page 459 and 460:
size() size() isEmpty() isEmpty() i
Page 461 and 462:
at the time the method is executed.
Page 463 and 464:
Code Fragment 8.7: Java class Defau
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465
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Insertion-Sort If we implement the
Page 469 and 470:
An efficient realization of a prior
Page 471 and 472:
Proposition 8.5: A heap T storing n
Page 473 and 474:
The Array List Representation of a
Page 475 and 476:
java.util.ArrayList. (Continues in
Page 477 and 478:
Code Fragment 8.12: Class ArrayList
Page 479 and 480:
8.3.3 Implementing a Priority Queue
Page 481 and 482:
The upward movement of the newly in
Page 483 and 484:
Analysis Table 8.3 shows the runnin
Page 485 and 486:
We conclude that the heap data stru
Page 487 and 488:
Code Fragment 8.15: Remaining auxil
Page 489 and 490:
As we have previously observed, rea
Page 491 and 492:
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
Page 501 and 502:
Code Fragment 8.18: An adaptable pr
Page 503 and 504:
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
Page 517 and 518:
In either case, we use a key as a u
Page 519 and 520:
null {(5,A), (7,B)} put(2,C) null {
Page 521 and 522:
get(k) put(k,v) put(k,v) remove(k)
Page 523 and 524:
time of map operations in an n-entr
Page 525 and 526:
Hash Codes in Java The generic Obje
Page 527 and 528:
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
Page 533 and 534:
only the one entry. We leave the de
Page 535 and 536:
key k will skip over cells containi
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537
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539
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9.2.7 Load Factors and Rehashing In
Page 543 and 544:
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
Page 563 and 564:
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
Page 629 and 630:
629
Page 631 and 632:
The dictionary we store at each nod
Page 633 and 634:
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
Page 655 and 656:
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
Page 691 and 692:
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
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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
Page 841 and 842:
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.
Page 851 and 852:
The main computation of Dijkstra's
Page 853 and 854:
13.7 Minimum Spanning Trees Suppose
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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. (
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Analyzing the Prim-Jarn ık Algorit
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13.8 Exercises For source code and
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LA22: (none) • LA31: LA15 • LA3
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The graph has 10,000 vertices and 2
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265 175 215 180 185 155 3- - - - 26
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_ _ _ _ Find which bridges to build
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determine if it is constructed corr
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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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