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

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works exactly like this when acting on two strings. Thus, it is legal (and even useful) in Java to write an assignment statement like Strings = "kilo" + "meters"; This statement defines a variable s that references objects of the String class, and assigns it the string "kilometers". (We will discuss assignment statements and expressions such as that above in more detail later in this chapter.) Every object in Java is assumed to have a built-in method toString() that returns a string associated with the object. This description of the String class should be sufficient for most uses. We discuss the String class and its "relative" the StringBuffer class in more detail in Section 12.1. Object References As mentioned above, creating a new object involves the use of the new operator to allocate the object's memory space and use the object's constructor to initialize this space. The location, or address, of this space is then typically assigned to a reference variable. Therefore, a reference variable can be viewed as a "pointer" to some object. It is as if the variable is a holder for a remote control that can be used to control the newly created object (the device). That is, the variable has a way of pointing at the object and asking it to do things or give us access to its data. We illustrate this concept in Figure 1.4. Figure 1.4: Illustrating the relationship between objects and object reference variables. When we assign an object reference (that is, memory address) to a reference variable, it is as if we are storing that object's remote control at that variable. 28
The Dot Operator Every object reference variable must refer to some object, unless it is null, in which case it points to nothing. Using the remote control analogy, a null reference is a remote control holder that is empty. Initially, unless we assign an object variable to point to something, it is null. There can, in fact, be many references to the same object, and each reference to a specific object can be used to call methods on that object. Such a situation would correspond to our having many remote controls that all work on the same device. Any of the remotes can be used to make a change to the device (like changing a channel on a television). Note that if one remote control is used to change the device, then the (single) object pointed to by all the remotes changes. Likewise, if we use one object reference variable to change the state of the object, then its state changes for all the references to it. This behavior comes from the fact that there are many references, but they all point to the same object. One of the primary uses of an object reference variable is to access the members of the class for this object, an instance of its class. That is, an object reference variable is useful for accessing the methods and instance variables associated with an object. This access is performed with the dot (".") operator. We call a method associated with an object by using the reference variable name, following that by the dot operator and then the method name and its parameters. This calls the method with the specified name for the object referred to by this object reference. It can optionally be passed multiple parameters. If there are several methods with this same name defined for this object, then the Java runtime system uses the one that matches the number of parameters and most closely matches their respective types. A method's name combined with the number and types of its parameters is called a method's signature, for it takes all 29
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: n.longValue( ) float Float n = new
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
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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
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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
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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
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Code Fragment 5.18: Class NodeDeque
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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
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The node list ADT allows us to view
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(8,3,5) set(p 3 ,7) 3 (8,7,5) addAf
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Deque Method Realization with Node-
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new node v to hold the element e, l
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In conclusion, using a doubly linke
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Code Fragment 6.11: Portions of the
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An iterator is a software design pa
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Since looping through the elements
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Code Fragment 6.15: The iterator()
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the last element. That is, it uses
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isEmpty() isEmpty() O(1) time get(i
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deletion is at cursor; A is O(n),L
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where n is the number of elements i
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Efficiency Trade-Offs with an Array
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357
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The previous implementation of a fa
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decreasing order and then pops up a
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accesses several Web pages and then
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R-6.16 Describe how to create an it
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Think about how to extend the circu
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C-6.24 Isabel has an interesting wa
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Chapter 7 Trees Contents 7.1 Genera
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7.3.3 Properties of Binary Trees ..
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Electronics R'Us. The children of t
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Edges and Paths in Trees An edge of
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There are also a number of generic
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Figure 7.5: The linked structure fo
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Code Fragment 7.3: Method depth wri
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Code Fragment 7.6: Algorithm height
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Example 7.6: The preorder traversal
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Code Fragment 7.10: Algorithm paren
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The postorder traversal method is u
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Although the preorder and postorder
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A Recursive Binary Tree Definition
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same depth d as the level dof T. In
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Figure 7.13: Operation that removes
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We use a Java interface BTPosition
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addition to the Binary Tree interfa
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Binary Tree interface. (Continues i
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• Methods size() and isEmpty() us
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The level numbering function p sugg
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Time size, isEmpty O(1) iterator, p
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As is the case for general trees, t
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The inorder traversal of a binary t
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The inorder traversal can also be a
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start an Euler tour by initializing
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• Calls auxiliary method visitRig
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ExpressionTerm at each node. Class
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Code Fragment 7.31: Class EvaluateE
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Let T be an n-node binary tree that
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c. Let T be a proper binary tree wi
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Creativity C-7.1 For each node v in
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C-7.10 Two ordered trees T ′ and
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postorderDraw is similar to preorde
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Describe a nonrecursive method for
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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
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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
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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
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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
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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
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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. (
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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
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the size of the input for this call
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In-place quick-sort modifies the in
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Unfortunately, the implementation a
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algorithm to output the elements of
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itself is a sequence (of entries wi
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first component, we guarantee that
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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
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Performance of the Sequence Impleme
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With this partition data structure,
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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
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Show that the probability that any
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Describe what additional informatio
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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 ...
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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
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We will formalize these heuristics
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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
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A Java implementation of the KMP pa
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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
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trie. In the next section, we prese
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if such a path can be traced. The d
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Let m be the size of pattern P and
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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
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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
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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
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Example 13.2: We can associate with
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In the propositions that follow, we
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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
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• The edge object for an edge e w
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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
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We can visualize a DFS traversal by
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• Computing a cycle in G, or repo
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depend on the implementation of the
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Code Fragment 13.5: The main templa
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Using the Template Method Pattern f
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Class FindCycleDFS (Code Fragment 1
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levels. BFS can also be thought of
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825
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• 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
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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
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The Random strategy is one of the e
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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
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Reinforcement R-14.1 Describe, in d
Page 909 and 910:
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) =
Page 919 and 920:
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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