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

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else if (second_boolean_exp) else second_true_statement false_statement If the first Boolean expression is false, the second Boolean expression will be tested, and so on. An if statement can have an arbitrary number of else if parts. For example, the following is a correct if statement. if (snowLevel < 2) { } goToClass(); comeHome(); else if (snowLevel < 5) { } else goSledding(); haveSnowballFight(); stayAtHome(); Switch Statements Java provides for multiple-value control flow using the switch statement, which is especially useful with enum types. The following is an indicative example (based on a variable d of the Day enum type of Section 1.1.3). switch (d) { case MON: 52
System.out.println("This is tough."); break; case TUE: System.out.println("This is getting better."); break; case WED: System.out.println("Half way there."); break; case THU: System.out.println("I can see the light."); break; case FRI: System.out.println("Now we are talking."); break; default: System.out.println("Day off ! "); break; } The switch statement evaluates an integer or enum expression and causes control flow to jump to the code location labeled with the value of this expression. If there is no matching label, then control flow jumps to the location labeled "default." This is the only explicit jump performed by the switch statement, however, so flow of control "falls through" to other cases if the code for each case is not ended with a break statement (which causes control flow to jump to the next line after the switch statement). 1.4.2 Loops 53
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 and 12: Sun, Nikos Triandopoulos, Luca Vism
Page 13 and 14: Getting Started: Classes, Types, an
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: String s = " " + 4.5; // correct, b
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
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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
Page 147 and 148:
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
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
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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
Page 179 and 180:
We make the following observations
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advance(): Advance the cursor to th
Page 183 and 184:
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
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
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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
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4.1.5 The Quadratic function Anothe
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which assigns to an input value n t
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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
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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
Page 245 and 246:
Besides showing a use of the contra
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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
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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
Page 289 and 290:
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
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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
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Implement a program that can input
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223 6.1.3 A Simple Array-Based Impl
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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
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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
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-
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new node v to hold the element e, l
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In conclusion, using a doubly linke
Page 339 and 340:
Code Fragment 6.11: Portions of the
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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()
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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
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
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decreasing order and then pops up a
Page 363 and 364:
accesses several Web pages and then
Page 365 and 366:
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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
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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
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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
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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
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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
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ExpressionTerm at each node. Class
Page 431 and 432:
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
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
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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
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
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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
Page 501 and 502:
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
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C-8.13 We can represent a path from
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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
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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
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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
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539
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9.2.7 Load Factors and Rehashing In
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example, when pundits study politic
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for the keys, and we provide additi
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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
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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
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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
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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 ★.
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10.1.1 Searching To perform operati
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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
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10.2 AVL Trees In the previous sect
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(10.3) > 2 i · n(h − 2i). That i
Page 603 and 604:
We restore the balance of the nodes
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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
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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
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When we perform a splaying, we pay
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≤ r ′(x)−r(x) ≤ 3(r ′(x)
Page 627 and 628:
Proposition 10.6: Consider a sequen
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629
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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
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A split operation affects a constan
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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
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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.
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constant amount of work (in a restr
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Performance of Red-Black Trees Tabl
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Thus, a red-black tree achieves log
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Methods insert (Code Fragment 10.10
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665
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Are the rotations in Figures 10.8 a
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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
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Projects P-10.1 N-body simulations
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early approaches to balancing trees
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11.5 Comparison of Sorting Algorith
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elements of S; that is, S 1 contain
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for a child invocation to return. (
Page 683 and 684:
Proposition 11.1: The merge-sort tr
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idea is to iteratively remove the s
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merge-sort, are implemented by eith
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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
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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
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algorithm to output the elements of
Page 711 and 712:
itself is a sequence (of entries wi
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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
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The worst case for the number of no
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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
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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
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not. The optimal performance of met
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came from to get to v, and repeat t
Page 811 and 812:
We can visualize a DFS traversal by
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• 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
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13.7.1 Kruskal's Algorithm The reas
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Figure 13.19: An example of an exec
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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
Page 899 and 900:
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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