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

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consistent with one of the checks performed in the checkPosition convenience function. 6.3 Iterators A typical computation on an array list, list, or sequence is to march through its elements in order, one at a time, for example, to look for a specific element. 6.3.1 The Iterator and Iterable Abstract Data Types 340
An iterator is a software design pattern that abstracts the process of scanning through a collection of elements one element at a time. An iterator consists of a sequence S, a current element in S, and a way of stepping to the next element in S and making it the current element. Thus, an iterator extends the concept of the position ADT we introduced in Section 6.2. In fact, a position can be thought of as an iterator that doesn't go anywhere. An iterator encapsulates the concepts of "place" and "next" in a collection of objects. We define the iterator ADT as supporting the following two methods: hasNext(): Test whether there are elements left in the iterator. next(): Return the next element in the iterator. Note that the iterator ADT has the notion of the "current" element in a traversal of a sequence. The first element in an iterator is returned by the first call to the method next, assuming of course that the iterator contains at least one element. An iterator provides a unified scheme to access all the elements of a collection of objects in a way that is independent from the specific organization of the collection. An iterator for an array list, list, or sequence should return the elements according to their linear ordering. Simple Iterators in Java Java provides an iterator through its java.util.Iterator interface. We note that the java.util.Scanner class (Section 1.6) implements this interface. This interface supports an additional (optional) method to remove the previously returned element from the collection. This functionality (removing elements through an iterator) is somewhat controversial from an object-oriented viewpoint, however, and it is not surprising that its implementation by classes is optional. Incidentally, Java also provides the java.util.Enumeration interface, which is historically older than the iterator interface and uses names hasMoreElements() and nextElement(). The Iterable Abstract Data Type In order to provide a unified generic mechanism for scanning through a data structure, ADTs storing collections of objects should support the following method: iterator(): Return an iterator of the elements in the collection. This method is supported by the java.util.ArrayList class. In fact, this method is so important, that there is a whole interface, 341
Page 1 and 2:
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
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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
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Counting Primitive Operations Speci
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Simplifying the Analysis Further In
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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
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We may sometimes feel overwhelmed b
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The number of operations executed b
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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 ).
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Describe a method for finding both
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Describe, in pseudo-code a method f
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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.
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5.1.5 Matching Parentheses and HTML
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Matching Tags in an HTML Document A
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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
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
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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
Page 323 and 324: An Amortized Analysis of Extendable
Page 325 and 326: Proposition 6.2: Let S be an array
Page 327 and 328: 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: Code Fragment 6.11: Portions of the
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
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Page 359 and 360: 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: 6.6 Exercises For source code and h
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 ..
Page 377 and 378: 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
Page 387 and 388: Code Fragment 7.6: Algorithm height
Page 389 and 390: 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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Code Fragment 7.17: Portions of the
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Code Fragment 7.18: Portions of the
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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
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P-7.8 Write a program that can play
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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
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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
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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
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Chapter 9 Maps and Dictionaries Con
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9.3.3 Ordered Search Tables and Bin
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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), (
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Analysis of a List-Based Dictionary
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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
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Method List Hash Table Search Table
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An example of a skip list is shown
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We give a pseudo-code description o
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the new entry are drawn with thick
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can go into what is almost an infin
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of entries in the dictionary at the
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O(n) O(logn) (expected) 9.5.2 The O
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lastKey() last().getValue() get(las
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Formally, we say a price-performanc
Page 575 and 576:
What is the worst-case running time
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Describe how to use a map to implem
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in memory, describe a method runnin
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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
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The implementation of the remove(k)
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O(h) time, where h is the height of
Page 593 and 594:
Class BinarySearchTree uses locatio
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Code Fragment 10.4: Class BinarySea
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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
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We restore the balance of the nodes
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Figure 10.9: Schematic illustration
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find another, we perform a restruct
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In Code Fragments 10.7 and 10.8, we
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Code Fragment 10.8: Auxiliary metho
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10.3 Splay Trees Another way we can
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We perform a zig-zig or a zig-zag w
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Figure 10.16: Example of splaying a
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10.3.2 When to Splay The rules that
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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)
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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
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insertion of 5, which causes an ove
Page 637 and 638:
A split operation affects a constan
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operation; (f) after the fusion ope
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collection returned by findAll. The
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Figure 10.27: Correspondence betwee
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• Take node z, its parent v, and
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Figures 10.30 and 10.31 show a sequ
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The cases for insertion imply an in
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and (b) and for node b in part (c)
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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
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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
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the case when n is a power of 2. (W
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each node of the quick-sort tree. T
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eturn). Note the divide steps perfo
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Performing Quick-Sort on Arrays and
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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,
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generic merging takes time proporti
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• 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
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This may come as a small surprise,
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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
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threads of b. Describe and analyze
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Design and implement a stable versi
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Contents 12.1 String Operations ...
Page 743 and 744:
567 12.5 Text Similarity Testing ..
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finite, we usually assume that the
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Return and update S to be the strin
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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
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A Java implementation of the BM pat
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using an alternative shift heuristi
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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
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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
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There are few algorithmic technique
Page 781 and 782:
Turning this definition of L[i, j]
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Reinforcement R-12.1 List the prefi
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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
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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
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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
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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
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Class FindCycleDFS (Code Fragment 1
Page 823 and 824:
levels. BFS can also be thought of
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825
Page 827 and 828:
• Given a start vertex s of G, co
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Interesting problems that deal with
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A DFS on a digraph partitions the e
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Directed Breadth-First Search As wi
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edges (vi,vk) and (vk,vj) with dash
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ordering such that any directed pat
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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
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edge for pulling in u with a solid
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Proposition 13.23: In Dijkstra's al
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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
Page 859 and 860:
execution of Kruskal's algorithm. (
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Analyzing the Prim-Jarn ık Algorit
Page 863 and 864:
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
Page 875 and 876:
An Euler tour of a directed graph t
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C-13.21 Computer networks should av
Page 879 and 880:
c. Now suppose that is weighted and
Page 881 and 882:
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
Page 893 and 894:
identify and mark each live object.
Page 895 and 896:
Caches and Disks Specifically, the
Page 897 and 898:
are addressed. Virtual memory does
Page 899 and 900:
The Random strategy is one of the e
Page 901 and 902:
each would require to perform the s
Page 903 and 904:
describe this structure, however, l
Page 905 and 906:
are too large to fit entirely into
Page 907 and 908:
Reinforcement R-14.1 Describe, in d
Page 909 and 910:
Describe how to use a B-tree to imp
Page 911 and 912:
Appendix A Useful Mathematical Fact
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The factorial function is defined a
Page 915 and 916:
for any real number 0 < a ≠ 1. Pr
Page 917 and 918:
E(X + Y) = E(X) + E(Y) and E(cX) =
Page 919 and 920:
Bibliography [1] G. M. Adelson-Vels
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[28] S. A. Demurjian, Sr., Software
Page 923 and 924:
[69] B. Liskov and J. Guttag, Abstr
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