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

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A Generic NodeStack Class A Java implementation of a stack, by means of a generic singly linked list, is given in Code Fragment 5.7. All the methods of the Stack interface are executed in constant time. In addition to being time efficient, this linked list implementation has a space requirement that is O(n), where n is the current number of elements in the stack. Thus, this implementation does not require that a new exception be created to handle size overflow problems. We use an instance variable top to refer to the head of the list (which points to the null object if the list is empty). When we push a new element e on the stack, we simply create a new node v for e, reference e from v, and insert v at the head of the list. Likewise, when we pop an element from the stack, we simply remove the node at the head 276
of the list and return its element. Thus, we perform all insertions and removals of elements at the head of the list. Code Fragment 5.7: Class NodeStack, which implements the Stack interface using a singly linked list, whose nodes are objects of class Node from Code Fragment 5.6. 5.1.4 Reversing an Array Using a Stack We can use a stack to reverse the elements in an array, thereby producing a nonrecursive algorithm for the array-reversal problem introduced in Section 3.5.1. The basic idea is simply to push all the elements of the array in order into a stack 277
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
Page 225 and 226: and y-coordinate equal to the runni
Page 227 and 228: Counting Primitive Operations Speci
Page 229 and 230: Simplifying the Analysis Further In
Page 231 and 232: Proposition 4.7: The Algorithmarray
Page 233 and 234: is O(4n 2 + 6n log n), although thi
Page 235 and 236: 256 16 4 16 64 256 4,096 65,536 32
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
Page 271 and 272: 271
Page 273 and 274: 273
Page 275: The array implementation of a stack
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
Page 325 and 326: 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
Page 445 and 446:
P-7.8 Write a program that can play
Page 447 and 448:
Chapter 8 Priority Queues Contents
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The Heap Data Structure............
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As in the examples above from an ai
Page 453 and 454:
package includes a similar Entry in
Page 455 and 456:
Code Fragment 8.3: Class representi
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insert(5,A) e 1 [=(5,A)] {(5,A)} in
Page 459 and 460:
size() size() isEmpty() isEmpty() i
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at the time the method is executed.
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Code Fragment 8.7: Java class Defau
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465
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Insertion-Sort If we implement the
Page 469 and 470:
An efficient realization of a prior
Page 471 and 472:
Proposition 8.5: A heap T storing n
Page 473 and 474:
The Array List Representation of a
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java.util.ArrayList. (Continues in
Page 477 and 478:
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
Page 513 and 514:
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
Page 519 and 520:
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
Page 545 and 546:
for the keys, and we provide additi
Page 547 and 548:
findAll(2) {(2,C), (2,E)} {(5,A), (
Page 549 and 550:
Analysis of a List-Based Dictionary
Page 551 and 552:
for entries with duplicate keys. As
Page 553 and 554:
Figure 9.7: Realization of a dictio
Page 555 and 556:
Considering the running time of bin
Page 557 and 558:
Method List Hash Table Search Table
Page 559 and 560:
An example of a skip list is shown
Page 561 and 562:
We give a pseudo-code description o
Page 563 and 564:
the new entry are drawn with thick
Page 565 and 566:
can go into what is almost an infin
Page 567 and 568:
of entries in the dictionary at the
Page 569 and 570:
O(n) O(logn) (expected) 9.5.2 The O
Page 571 and 572:
lastKey() last().getValue() get(las
Page 573 and 574:
Formally, we say a price-performanc
Page 575 and 576:
What is the worst-case running time
Page 577 and 578:
Describe how to use a map to implem
Page 579 and 580:
in memory, describe a method runnin
Page 581 and 582:
please see the various research pap
Page 583 and 584:
Amortized Analysis of Splaying ★.
Page 585 and 586:
10.1.1 Searching To perform operati
Page 587 and 588:
We can also show that a variation o
Page 589 and 590:
The implementation of the remove(k)
Page 591 and 592:
O(h) time, where h is the height of
Page 593 and 594:
Class BinarySearchTree uses locatio
Page 595 and 596:
Code Fragment 10.4: Class BinarySea
Page 597 and 598:
Code Fragment 10.5: Class BinarySea
Page 599 and 600:
10.2 AVL Trees In the previous sect
Page 601 and 602:
(10.3) > 2 i · n(h − 2i). That i
Page 603 and 604:
We restore the balance of the nodes
Page 605 and 606:
Figure 10.9: Schematic illustration
Page 607 and 608:
find another, we perform a restruct
Page 609 and 610:
In Code Fragments 10.7 and 10.8, we
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Code Fragment 10.8: Auxiliary metho
Page 613 and 614:
10.3 Splay Trees Another way we can
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We perform a zig-zig or a zig-zag w
Page 617 and 618:
Figure 10.16: Example of splaying a
Page 619 and 620:
10.3.2 When to Splay The rules that
Page 621 and 622:
10.3.3 Amortized Analysis of Splayi
Page 623 and 624:
When we perform a splaying, we pay
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≤ r ′(x)−r(x) ≤ 3(r ′(x)
Page 627 and 628:
Proposition 10.6: Consider a sequen
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629
Page 631 and 632:
The dictionary we store at each nod
Page 633 and 634:
h≤log(n+1) (10.10) are true. To j
Page 635 and 636:
insertion of 5, which causes an ove
Page 637 and 638:
A split operation affects a constan
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operation; (f) after the fusion ope
Page 641 and 642:
collection returned by findAll. The
Page 643 and 644:
Figure 10.27: Correspondence betwee
Page 645 and 646:
• Take node z, its parent v, and
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Figures 10.30 and 10.31 show a sequ
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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
Page 659 and 660:
Performance of Red-Black Trees Tabl
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Thus, a red-black tree achieves log
Page 663 and 664:
Methods insert (Code Fragment 10.10
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665
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Are the rotations in Figures 10.8 a
Page 669 and 670:
T is a (2,4) tree. c. T is a red-bl
Page 671 and 672:
C-10.8 Let D be an ordered dictiona
Page 673 and 674:
Projects P-10.1 N-body simulations
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early approaches to balancing trees
Page 677 and 678:
11.5 Comparison of Sorting Algorith
Page 679 and 680:
elements of S; that is, S 1 contain
Page 681 and 682:
for a child invocation to return. (
Page 683 and 684:
Proposition 11.1: The merge-sort tr
Page 685 and 686:
idea is to iteratively remove the s
Page 687 and 688:
merge-sort, are implemented by eith
Page 689 and 690:
Code Fragment 11.3: Methods mergeSo
Page 691 and 692:
A Nonrecursive Array-Based Implemen
Page 693 and 694:
the case when n is a power of 2. (W
Page 695 and 696:
each node of the quick-sort tree. T
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eturn). Note the divide steps perfo
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Performing Quick-Sort on Arrays and
Page 701 and 702:
E has at least one element (the piv
Page 703 and 704:
the size of the input for this call
Page 705 and 706:
In-place quick-sort modifies the in
Page 707 and 708:
Unfortunately, the implementation a
Page 709 and 710:
algorithm to output the elements of
Page 711 and 712:
itself is a sequence (of entries wi
Page 713 and 714:
first component, we guarantee that
Page 715 and 716:
Bucket-Sort and Radix-Sort Finally,
Page 717 and 718:
generic merging takes time proporti
Page 719 and 720:
• In class Union Merge, merge cop
Page 721 and 722:
Performance of the Sequence Impleme
Page 723 and 724:
With this partition data structure,
Page 725 and 726:
The Log-Star and Inverse Ackermann
Page 727 and 728:
This may come as a small surprise,
Page 729 and 730:
is the same as the expected number
Page 731 and 732:
Show that the probability that any
Page 733 and 734:
Describe what additional informatio
Page 735 and 736:
Argue why the previous claim proves
Page 737 and 738:
threads of b. Describe and analyze
Page 739 and 740:
Design and implement a stable versi
Page 741 and 742:
Contents 12.1 String Operations ...
Page 743 and 744:
567 12.5 Text Similarity Testing ..
Page 745 and 746:
finite, we usually assume that the
Page 747 and 748:
Return and update S to be the strin
Page 749 and 750:
Performance The brute-force pattern
Page 751 and 752:
We will formalize these heuristics
Page 753 and 754:
In Figure 12.3, we illustrate the e
Page 755 and 756:
A Java implementation of the BM pat
Page 757 and 758:
using an alternative shift heuristi
Page 759 and 760:
In Figure 12.5, we illustrate the e
Page 761 and 762:
A Java implementation of the KMP pa
Page 763 and 764:
12.3 Tries The pattern matching alg
Page 765 and 766:
The worst case for the number of no
Page 767 and 768:
A compressed trie is similar to a s
Page 769 and 770:
trie. In the next section, we prese
Page 771 and 772:
if such a path can be traced. The d
Page 773 and 774:
Let m be the size of pattern P and
Page 775 and 776:
transmit our text. Likewise, text c
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12.4.2 The Greedy Method Huffman's
Page 779 and 780:
There are few algorithmic technique
Page 781 and 782:
Turning this definition of L[i, j]
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Reinforcement R-12.1 List the prefi
Page 785 and 786:
C-12.5 Say that a pattern P of leng
Page 787 and 788:
suffix of length j in y. Design an
Page 789 and 790:
pattern matching. The reader intere
Page 791 and 792:
Depth-First Search Traversing a Dig
Page 793 and 794:
Example 13.2: We can associate with
Page 795 and 796:
In the propositions that follow, we
Page 797 and 798:
are communication connections betwe
Page 799 and 800:
vertices and m edges, an edge list
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The main feature of the edge list s
Page 803 and 804:
• The edge object for an edge e w
Page 805 and 806:
insertVertex, insertEdge, removeEdg
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not. The optimal performance of met
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came from to get to v, and repeat t
Page 811 and 812:
We can visualize a DFS traversal by
Page 813 and 814:
• Computing a cycle in G, or repo
Page 815 and 816:
depend on the implementation of the
Page 817 and 818:
Code Fragment 13.5: The main templa
Page 819 and 820:
Using the Template Method Pattern f
Page 821 and 822:
Class FindCycleDFS (Code Fragment 1
Page 823 and 824:
levels. BFS can also be thought of
Page 825 and 826:
825
Page 827 and 828:
• Given a start vertex s of G, co
Page 829 and 830:
Interesting problems that deal with
Page 831 and 832:
A DFS on a digraph partitions the e
Page 833 and 834:
Directed Breadth-First Search As wi
Page 835 and 836:
edges (vi,vk) and (vk,vj) with dash
Page 837 and 838:
ordering such that any directed pat
Page 839 and 840:
Justification: The initial computat
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computers. In this case, it is prob
Page 843 and 844:
their distances from v. Thus, in ea
Page 845 and 846:
edge for pulling in u with a solid
Page 847 and 848:
Proposition 13.23: In Dijkstra's al
Page 849 and 850:
Referring back to Code Fragment 13.
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The main computation of Dijkstra's
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13.7 Minimum Spanning Trees Suppose
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13.7.1 Kruskal's Algorithm The reas
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Figure 13.19: An example of an exec
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execution of Kruskal's algorithm. (
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Analyzing the Prim-Jarn ık Algorit
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13.8 Exercises For source code and
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LA22: (none) • LA31: LA15 • LA3
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The graph has 10,000 vertices and 2
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265 175 215 180 185 155 3- - - - 26
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_ _ _ _ Find which bridges to build
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determine if it is constructed corr
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An Euler tour of a directed graph t
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C-13.21 Computer networks should av
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c. Now suppose that is weighted and
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P-13.9 Design an experimental compa
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Chapter 14 Memory Contents 14.1 Mem
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Multi-way Merging..................
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Keeping Track of the Program Counte
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In Section 7.3.6 we described how t
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Memory Allocation Algorithms The Ja
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identify and mark each live object.
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Caches and Disks Specifically, the
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are addressed. Virtual memory does
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The Random strategy is one of the e
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each would require to perform the s
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describe this structure, however, l
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are too large to fit entirely into
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Reinforcement R-14.1 Describe, in d
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Describe how to use a B-tree to imp
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Appendix A Useful Mathematical Fact
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The factorial function is defined a
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for any real number 0 < a ≠ 1. Pr
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E(X + Y) = E(X) + E(Y) and E(cX) =
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Bibliography [1] G. M. Adelson-Vels
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[28] S. A. Demurjian, Sr., Software
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[69] B. Liskov and J. Guttag, Abstr
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