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

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Example Output Below, we show the output from the above ArrayStack program. Note that, through the use of generic types, we are able to create an ArrayStack A for storing integers and another ArrayStack B that stores character strings. ------> new ArrayStack A, returns null result: size = 0, isEmpty = true, stack: [] ------> A.push(7), returns null result: size = 1, isEmpty = false, stack: [7] ------> A.pop(), returns 7 result: size = 0, isEmpty = true, stack: [] ------> A.push(9), returns null result: size = 1, isEmpty = false, stack: [9] ------> A.pop(), returns 9 result: size = 0, isEmpty = true, stack: [] ------> new ArrayStack B, returns null result: size = 0, isEmpty = true, stack: [] ------> B.push("Bob"), returns null result: size = 1, isEmpty = false, stack: [Bob] ------> B.push("Alice"), returns null result: size = 2, isEmpty = false, stack: [Bob, Alice] ------> B.pop(), returns Alice result: size = 1, isEmpty = false, stack: [Bob] ------> B.push("Eve"), returns null result: size = 2, isEmpty = false, stack: [Bob, Eve] A Drawback with the Array-Based Stack Implementation 274
The array implementation of a stack is simple and efficient. Nevertheless, this implementation has one negative aspect—it must assume a fixed upper bound, CAPACITY, on the ultimate size of the stack. In Code Fragment 5.4, we chose the capacity value 1,000 more or less arbitrarily. An application may actually need much less space than this, which would waste memory. Alternatively, an application may need more space than this, which would cause our stack implementation to generate an exception as soon as a client program tries to push its 1,001st object on the stack. Thus, even with its simplicity and efficiency, the array-based stack implementation is not necessarily ideal. Fortunately, there is another implementation, which we discuss next, that does not have a size limitation and use space proportional to the actual number of elements stored in the stack. Still, in cases where we have a good estimate on the number of items needing to go in the stack, the array-based implementation is hard to beat. Stacks serve a vital role in a number of computing applications, so it is helpful to have a fast stack ADT implementation such as the simple array-based implementation. 5.1.3 Implementing a Stack with a Generic Linked List In this section, we explore using a singly linked list to implement the stack ADT. In designing such an implementation, we need to decide if the top of the stack is at the head or at the tail of the list. There is clearly a best choice here, however, since we can insert and delete elements in constant time only at the head. Thus, it is more efficient to have the top of the stack at the head of our list. Also, in order to perform operation size in constant time, we keep track of the current number of elements in an instance variable. Rather than use a linked list that can only store objects of a certain type, as we showed in Section 3.2, we would like, in this case, to implement a generic stack using a generic linked list. Thus, we need to use a generic kind of node to implement this linked list. We show such a Node class in Code Fragment 5.6. Code Fragment 5.6: Class Node, which implements a generic node for a singly linked list. 275
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Data Structures and Algorithms in J
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To Isabel -Roberto Tamassia Preface
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The Java code implementing fundamen
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PL6. Object-Oriented Programming Ch
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14. Memory A. Useful Mathematical F
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Sun, Nikos Triandopoulos, Luca Vism
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Getting Started: Classes, Types, an
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39 1.7 An Example Program..........
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The main "actors" in a Java program
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else interface switch boolean exten
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Class modifiers are optional keywor
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Comments Note the use of comments i
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Calling the new operator on a class
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n.longValue( ) float Float n = new
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The Dot Operator Every object refer
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object (assuming we are allowed acc
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Note the uses of instance variables
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1.2 Methods Methods in Java are con
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Abstract methods may only appear wi
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is intended to be used to initializ
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} int i = 512; double e = 2.71828;
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% the modulo operator This last ope
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zeros >>> shift bits right, filling
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3 add./subt. + − 4 shift > >>> 5
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double d1 = 3.2; double d2 = 3.9999
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String s = " " + 4.5; // correct, b
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System.out.println("This is tough."
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Defining a For Loop Here is the syn
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that input and inform the user that
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if (a[i][j] == 0) { foundFlag = tru
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the array, we will sometimes refer
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The cells of this new array, "a," a
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ways to reference such an object. W
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float height = s.nextFloat(); Syste
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We show the CreditCard class in Cod
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Code Fragment 1.7: Output from the
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a text editor class may wish to def
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The process of writing a Java progr
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low-level implementation details. A
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variable declaration, or method def
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• @exception exception-name descr
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A careful testing plan is an essent
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Modify the CreditCard class from Co
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A common punishment for school chil
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Object-Oriented Design Principles .
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java.datastructures.net 2.1 Goals,
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Abstraction The notion of abstracti
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2.1.3 Design Patterns One of the ad
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Example 2.1: Consider a class S tha
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S's a() method when asked for o.a()
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Sometimes, in a Java class, it is c
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103
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Code Fragment 2.3: Class for arithm
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A Fibonacci Progression Class As a
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Figure 2.5 : Inheritance diagram fo
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2.3 Exceptions Exceptions are unexp
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goShopping(); // I don't have to tr
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try problem… // This code might h
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instance, wish to identify some of
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The class BoxedItem shows another f
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comparability feature to a class (i
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• T and S are class types and S i
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We show in Code Fragment 2.13 a cla
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Starting with 5.0, Java includes a
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public void insert (P person, P oth
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• Class Goat extends Object and a
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((Place) usa).printMe(); } } class
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C-2.5 Write a program that consists
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Chapter 3 Arrays, Linked Lists, and
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3.4 Circularly Linked Lists and Lin
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A Class for High Scores Suppose we
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Note that we include a method, toSt
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Once we have identified the place i
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Object Removal Suppose some hot sho
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These methods for adding and removi
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This description is much closer to
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there is no swap needed, and return
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num = [10,12,19,28,33,38,41,46,48,5
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In Code Fragment 3.9, we give a sim
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Many computer games, be they strate
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We give a complete Java class for m
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Code Fragment 3.11: A simple, compl
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Like an array, a singly linked list
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Code Fragment 3.14: Inserting a new
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The reverse operation of inserting
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Header and Trailer Sentinels To sim
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Likewise, we can easily perform an
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Figure 3.17: Adding a new node afte
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Code Fragment 3.23: Java class DLis
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We make the following observations
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advance(): Advance the cursor to th
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Some Observations about the CircleL
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Some Sample Output 185
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We show in Code Fragment 3.27 thein
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The factorial function can be defin
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Each multiple of 1 inch also has a
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The trace for drawTicks is more com
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The simplest form of recursion is l
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nonrecursive part of each call. Mor
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3.5.2 Binary Recursion When an algo
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Unfortunately, in spite of the Fibo
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To solve such a puzzle, we need to
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3.6 Exercises For source code and h
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C-3.2 Let A be an array of size n
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Write a recursive Java program that
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Chapter Notes The fundamental data
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Primitive Operations . . . . . . .
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4.1.2 The Logarithm function One of
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4.1.5 The Quadratic function Anothe
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which assigns to an input value n t
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For example, we have the following:
Page 223 and 224: primarily as slopes. Even so, the e
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Page 227 and 228: Counting Primitive Operations Speci
Page 229 and 230: Simplifying the Analysis Further In
Page 231 and 232: Proposition 4.7: The Algorithmarray
Page 233 and 234: is O(4n 2 + 6n log n), although thi
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Page 237 and 238: Running Maximum Problem Size (n) Ti
Page 239 and 240: should the constant factors they "h
Page 241 and 242: • There are two nested for loops,
Page 243 and 244: This definition leads immediately t
Page 245 and 246: Besides showing a use of the contra
Page 247 and 248: We may sometimes feel overwhelmed b
Page 249 and 250: The number of operations executed b
Page 251 and 252: R-4.22 Show that if d(n) is O(f(n))
Page 253 and 254: R-4.29 Show that 2 n+1 is O(2 n ).
Page 255 and 256: Describe a method for finding both
Page 257 and 258: Describe, in pseudo-code a method f
Page 259 and 260: Stacks.............................
Page 261 and 262: down on the stack to become the new
Page 263 and 264: 7 (5) top() 5 (5) pop() 5 () pop()
Page 265 and 266: In addition, we must define excepti
Page 267 and 268: 5.1.2 A Simple Array-Based Stack Im
Page 269 and 270: we indicate that the stack no longe
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Page 277 and 278: of the list and return its element.
Page 279 and 280: 5.1.5 Matching Parentheses and HTML
Page 281 and 282: Matching Tags in an HTML Document A
Page 283 and 284: Code Fragment 5.12: Java program fo
Page 285 and 286: Another fundamental data structure
Page 287 and 288: true ( ) enqueue(9) - (9) enqueue(7
Page 289 and 290: 5.2.2 A Simple Array-Based Queue Im
Page 291 and 292: Using the Modulo Operator to Implem
Page 293 and 294: which gives the correct result both
Page 295 and 296: Each of the methods of the singly l
Page 297 and 298: potato is equivalent to dequeuing a
Page 299 and 300: - (3) addFirst(5) - (5,3) removeFir
Page 301 and 302: Thus, a doubly linked list can be u
Page 303 and 304: Code Fragment 5.18: Class NodeDeque
Page 305 and 306: 5.4 Exercises For source code and h
Page 307 and 308: Suppose Alice has picked three dist
Page 309 and 310: Implement a program that can input
Page 311 and 312: 223 6.1.3 A Simple Array-Based Impl
Page 313 and 314: Sequences....................... 25
Page 315 and 316: - (7) add(0,4) - (4,7) get(1) 7 (4,
Page 317 and 318: get(size() −1) addFirst(e) add(0,
Page 319 and 320: have to be shifted forward. A simil
Page 321 and 322: Moreover, the java.util.ArrayList c
Page 323 and 324: An Amortized Analysis of Extendable
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Proposition 6.2: Let S be an array
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linked list without revealing this
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The node list ADT allows us to view
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(8,3,5) set(p 3 ,7) 3 (8,7,5) addAf
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Deque Method Realization with Node-
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new node v to hold the element e, l
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In conclusion, using a doubly linke
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Code Fragment 6.11: Portions of the
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An iterator is a software design pa
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Since looping through the elements
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Code Fragment 6.15: The iterator()
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the last element. That is, it uses
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isEmpty() isEmpty() O(1) time get(i
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deletion is at cursor; A is O(n),L
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where n is the number of elements i
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Efficiency Trade-Offs with an Array
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357
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The previous implementation of a fa
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decreasing order and then pops up a
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accesses several Web pages and then
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6.6 Exercises For source code and h
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R-6.16 Describe how to create an it
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Think about how to extend the circu
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C-6.24 Isabel has an interesting wa
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Chapter 7 Trees Contents 7.1 Genera
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7.3.3 Properties of Binary Trees ..
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Electronics R'Us. The children of t
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Edges and Paths in Trees An edge of
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There are also a number of generic
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Figure 7.5: The linked structure fo
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Code Fragment 7.3: Method depth wri
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Code Fragment 7.6: Algorithm height
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Example 7.6: The preorder traversal
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Code Fragment 7.10: Algorithm paren
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The postorder traversal method is u
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Although the preorder and postorder
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A Recursive Binary Tree Definition
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same depth d as the level dof T. In
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Figure 7.13: Operation that removes
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We use a Java interface BTPosition
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addition to the Binary Tree interfa
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Binary Tree interface. (Continues i
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• Methods size() and isEmpty() us
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The level numbering function p sugg
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Time size, isEmpty O(1) iterator, p
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As is the case for general trees, t
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The inorder traversal of a binary t
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The inorder traversal can also be a
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start an Euler tour by initializing
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• Calls auxiliary method visitRig
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ExpressionTerm at each node. Class
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Code Fragment 7.31: Class EvaluateE
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Let T be an n-node binary tree that
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c. Let T be a proper binary tree wi
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Creativity C-7.1 For each node v in
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C-7.10 Two ordered trees T ′ and
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postorderDraw is similar to preorde
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Describe a nonrecursive method for
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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. (
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
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the size of the input for this call
Page 705 and 706:
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
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
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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
Page 741 and 742:
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
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
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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
Page 837 and 838:
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
Page 899 and 900:
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
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
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[69] B. Liskov and J. Guttag, Abstr
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