Ch5. Linear Lists – Array Representationocw.snu.ac.kr/sites/default/files/NOTE/481.pdf©copyright...

SNU

IDB Lab.

Ch5. Linear Lists –Array Representation

© copyright 2006 SNU IDB Lab.

2SNU

IDB Lab.Data Structures

Bird’s-Eye View

� Ch.5 ~ Ch.7: Linear List� Ch. 5 – array representation

� Ch. 6 – linked representation

� Ch. 7 – simulated pointer representation

※ In succeeding chapters - matrices, stacks, queues, dictionaries, priority queues

� Java’s linear list classes� java.util.ArrayList

� Java.util.Vector

� java.util.LinkedList

� In an array representation of linear list� Elements are stored in an array

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Table of Contents

� Data Objects and Structures

� The Linear List Data Structure

� Array Representation

� Vector Representation

� Multiple Lists in a Single Array

� Performance

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Data Objects

� Data Object: A set of instances of values� Boolean = {false, true}

� Integer = {0, +1, -1, +2, -2, +3, -3, …}

� daysOfWeek = {S, M, T, W, Th, F, Sa}

� Individual instances of a data object� Primitive (atomic)

� 3, 5, a, Z,

� Composed of instances of another data object� Element: the individual components of an instance of an object

� good: an instance of String class� g, o, o, d is four elements of good

� each element is an instance of the data object Letter

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Data Structures� Definition: Data structure

� Data object +� Relationships that exist among instances and elements

� Relationships among instances of integer� 369 < 370� 280 + 4 = 284

� Relationships among elements that comprise an instance 369� 3 is more significant than 6� 9 is immediately to the right of 6

� The relationships are usually specified by specifying operations on instances� add, subtract, predecessor, multiply

� Our primary concern: � the representation of data objects� the implementation of the operations of interest for the data objects

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Table of Contents






� Performance

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Linear List (Ordered List)

� An ordered collection of elements� Instances are of the form

� (e0, e1, e2, …, en-1)� Where ei denotes a list element� i : The index of ei� n : The list length or size, n (>= 0) is finite

� L = (e0, e1, e2, e3, …, en-1)

� Relationships� e0 is the zero’th (or front) element� en-1 is the last element� ei immediately precedes ei+1

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Linear List Examples

Students in COP3530 = (Jack, Jill, Abe, Henry, Mary, …, Judy)

Exams in COP3530 = (exam1, exam2, exam3)

Grades in COP3530 = (“Jack A+”, “Jill B-”, “Abe D”, … “Judy F”)

Days of Week = (S, M, T, W, Th, F, Sa)

Months = (Jan, Feb, Mar, Apr, …, Nov, Dec)

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LinearList operations

Suppose L = (a, b, c, d, e, f, g)

� size() : Determine list size

�L.size() = 7

� get(index) : Get element with given index�get(0) = a get(2) = c get(4) = e get(-1) = error get(9) = error

� indexOf(element) : Determine the index of an element�indexOf(d) = 2 indexOf(a) = 0 indexOf(z) = -1

� remove(index) : Remove and return element with given index.

� remove(2) returns c, L becomes (a,b,d,e,f,g), indices of d,e,f and g are decreased by 1

� remove(-1) � error remove(20) � error

� add(index, element) : Add an element so that the new element has a specified index.

�add(0,h) � L = (h,a,b,c,d,e,f,g) // indices of a,b,c,d,e,f, and g are increased by 1

�add(2,h) � L = (a,b,h,c,d,e,f,g) // indices of c,d,e,f, and g are increased by 1

�add(10,h) � error add(-6,h) � error

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Data Structure Specification

� Abstract Data Type (ADT)� Specification of

� The instances

� The operations to be performed

� Language independent

� All representation of the ADT must satisfy the specification

� A way to validate the representation

� Hiding the details of implementation

� Two ways of ADT specification in Java� Interface

� Abstract class

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Abstract Data Type LinearListAbstractDataType LinearList {

instancesordered finite collections of zero or more elements

operations

isEmpty(): return true iff the list is empty, false otherwisesize(): return the list size (i.e., number of elements in the list)

get(index): return the indexth element of the list

indexOf(x):return the index of the first occurrence of x in the list, return -1 if x is not in the list

remove(index): remove and return the indexth element,

elements with higher index have their index reduced by 1add(theIndex, x): insert x as the indexth element, elements

with theIndex >= index have their index increased by 1

output(): output the list elements from left to right}

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Interface in Java

� A named collection of method definitions � Does not provide any implementation (no nonabstract methods)

� A class implements an interface� A class that implements the interface agrees to implement all of the

methods defined in the interface

� Useful for� Capturing similarities between unrelated classes� Declaring methods that one or more classes are expected to implement � Revealing an object's programming interface without revealing its class

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Abstract class in Java

� Two types of classes in java� Abstract and Nonabstract

� Default type is Nonabstract

� Abstract class� Contains zero or more abstract methods

� Abstract method: implementation is not provided

� Can also contain nonabstract methods

� You cannot create an instance of an abstract class

� A class extends an abstract class (as usual classes)

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Abstract class vs. Interface� Abstract class or interface ?

� An abstract class can define nonconstant data members and nonabstract methods

� If only constants and abstract methods are needed � interface will do

� A class can implement many interfaces but can extend at most one class

� Only single inheritance among classes

� Multiple inheritance is simulated using interfaces

� Data Structures in this Text� Use interfaces to specify ADTs throughout this lecture

� Exception is Graph in Chapter 17 (The abstract class Graph)

� Java specifies all of its data structures as interfaces� Ex) java.util.Map, java.util.Set

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The Java Interface: LinearListpublic interface LinearList{ public boolean isEmpty();

public int size();public Object get(int index);public int indexOf(Object elem);public Object remove(int index);public void add(int index, Object obj);public String toString();

}

public class ArrayLinearList implements LinearList{// code for all LinearList methods must be provided here by the user

}

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The Java Abstract Class: LinearListAsAbstractClass

public abstract class LinearListAsAbstractClass{ public abstract boolean isEmpty();public abstract int size();public abstract Object get(int index);public abstract int indexOf(Object theElement);public abstract Object remove(int index);public abstract void add(int index, Object theElement);public abstract String toString();

}

public class ArrayLinearList extends LinearListAsAbstractClass{// code for all abstract classes of LinearListAsAbstractClass must come here

}

� ArrayLinearList inherits “implemented nonabstract methods”

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Table of Contents






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The Array Representation

public class ArrayLinearList implements LinearList {protected Object[] element; // no array size declaration in Javaprotected int size; // no of elements in array// …element = new Object[initialCapacity]; // initialization

}

� Use a one-dimensional array element[]

� L = (a, b, c, d, e)

� Store element i of linear list into element[i]

� location(i) = i

0 1 2 3 4 5 6

a b c d e

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Various mapping strategies

� Right to Left mapping � location (i) = last - i

abcde

� Mapping that skips every other position

a b c d e

� Wrap around mapping � location (i) = (7 + i) % 15

a b cd e

� Put element i of list in element[i]

a b c d e

size = 5� Use a variable size to record current number of elements

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Add/Remove An Element

a b c d e

a g b c d e

add(1,g)

� Add

a g c d e

remove(3)

� Remove

size = 5

size = 6

size = 5

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Declaring Array in Java� Primitive Data Types

� int[] anArray; anArray = new int[10];

� int anArray[]; anArray = new int[10];

� Non-Primitive Data Types� Auto[] KoreanCar;

KoreanCar = new Auto[10];

� Auto KoreanCar[]; KoreanCar = new Auto[10];

� int[] anArray= new int[10];

� int anArray[] = new int[10];

� Auto[] KoreanCar = new Auto[10];

� Auto KoreanCar[] = new Auto[10];

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“element” array of type “Object”

� Syntax: Object[] element or Object element[]� element[] hold references to elements of any user-defined data type

� Data type of element is unknown

� Cannot put elements of primitive data types (int, float, double, char)� Instead, Use corresponding Class – Integer, Float, Double, Character, etc.

� Array Length� Don’ t know how many elements will be in list

� Must pick an initial length

� Dynamically increase the length as needed by the user

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Increasing Array Length

� Define an array of the new length

� Copy the n elements from old array to the new array � θ(n)

� Change the references to the new array

// create a new array of proper length and data type

Object[] newArray = new Object[newLength];

// copy all elements from old array “element” into new one “newArray”

System.arrayCopy(element, 0, newArray, 0, element.length);

// change the reference

element = newArray;

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Space Complexity (1)

� Increase the array size 1 by 1� element = new char [6]

� MaxListSize=6

� newArray = new char[7];� newLength=7

� Space needed during array copying� 2 * newLength – 1 = 2 * maxListSize + 1

a b c d e f

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Space complexity (2)

� The array length is normally doubled wherever the array becomes full.

a b c d e f

newArray = new char[12]; newLength = 12

a b c d e f

� maxListSize increased by *2 � newLength

� Space needed = 1.5 * newLength = 3 * maxListSize

element maxListSize = 6

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How Big Should The New Array Be? (1)

By doubling the array, the complexity (num of copy) is θθθθ(n)

� T(n) = 1 + 2 + 4 + 8 + … + 2k = θ(2k+1 – 1) = θ(2n – 3) = θ(n)

2kn-1 (= 2k)2k → 2k+1

n (= 2k+1)

…

8

7

6

5

4

3

2

1

# of adds

……

8■■■■■■■■ →■■■■■■■■□□□□□□□□

0■■■■■■■□

0■■■■■■□□

0■■■■■□□□

4■■■■ → ■■■■□□□□

0

0■■■□

2■■ → ■■□□

1■ → ■□

CostProcess

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How Big Should The New Array Be? (2)

� By increasing the length by 1, the complexity of becoming

an array with size n is θ(n2)

� After n-1 adds, the array size is now n

� T(n) = 1 + 2 + 3 + … + (n – 1) = θ((n2 – n) / 2) = θ(n2)

n – 1n – 1 → n

......

2■■ → ■■□

1■ → ■□

Cost (No of Copy)Process

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Insert theElement with array doubling

Public void add(int index, Object theElement) {if (index < 0 || index > size) //invalid index

throw new IndexOoutOfBoundsException (…);

if (size == element.length) { // no space � double capacityObject[] newArray = new Object[2*size];System.arraycopy(element, 0, newArray, 0, size);element = newArray;

}

for (int i = size-1; i >=index; i--) element[i+1] = element[i]; // move up the remaining elements

element[index] = theElement;Size++;}

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Java’s Linear List Classes

size():intelementAt(index:int):ObjectaddElement(o:Object):voidremoveElement(o:Object):boolean

Vector

utilutil

javajava

size():intget(index:int):Objectadd(o:Object):booleanremove(o:Object):boolean

ArrayList

size():intget(index:int):Objectadd(o:Object):booleanremove(o:Object):boolean

LinkedList

� 연산속도는 ArrayList가조금 빠름

� Vector는 size에 신경쓸필요가 없음

� 내부구현:

� Vector � vector

� ArrayList � array

� LinkedList � reference

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The Class ArrayLinearList (ALL): program 5.4 — 5.8

public class ArrayLinearList implements LinearList{protected Object[] element;protected int size;...public boolean isEmpty() { return (size == 0); }public int size() { return size; }public Object get(int index) { return element[index]; }public int indexOf(Object theElement) { …..}public Object remove(int index) {Object removedElement = element[index];for (int i = index + 1; i < size; i++) element[i-1] = element[i];element[--size] = null;return removedElement; }

public void add(int index, Object theElement) { …….}}* FastArrayLinearList (FALL) : System.arraycopy() instead of for loop in

remove() and add()

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Implementing ArrayLinearList (1)

� Constructor� With initial capacity

� With default capacity (say, 10 elements)

� Removing an Element� Ascertain that the list contains an indexed element (if not, exception)

� Shift index+1,…, size-1 elements down (left) one position� Complexity = O(size – index)

� Reduce the value of size by 1

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Implementing ArrayLinearList (2)

� Inserting an Element� Move index ~ size-1 elements one position up (right)

� Complexity = O(size – index + 1)

� Insert the new element in position index

� Increment size by 1

� Decreasing the Length of element� To enable the linear list to free some of the array space when

the list size becomes small

� slight modification of the method remove

� Iterator� Navigate elements of linear list

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Iterator: Basic Concepts

� Specifies a unified mechanism to examine the elements in an object one at a time

� Related methods are in the interface java.util.Iterator

※※※※With iterator methods we can easily examine With iterator methods we can easily examine With iterator methods we can easily examine With iterator methods we can easily examine ArrayLinearList’’’’ssss all all all all elementselementselementselements

� Iterator ix = x.iterator();� Constructs and initializes an iterator to examine the elements of x

� constructed iterator is assigned to ix

� You must define & implement the method iterator() in the class for x

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Iterator: Methods

� 2 Main Methods� ix.hasNext()

� Returns true iff x has a next element

� ix.next()� Throws NoSuchElementException if there is no next element

� Returns next element otherwise

� Optional Method� ix.remove()

� Removes last element returned by ix.next()

� Throws UnsupportedMethodException if method not implemented

� Throws IllegalStateException if ix.next() not yet called or did not return an element

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Example using an Iterator� By iterator (more general)

Iterator ix = x.iterator();

while (ix.hasNext())

examine(ix.next());

vs

� By index (only for indexed data structure)

for (int i=0; i<x.size(); i++)

examine(get(i));

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An Iterator for ArrayLinearList (1/3)

� By using a top-level class � Implemented as a separate class from “Iterator” interface

� Iterator class must access ArrayLinearList class data member

class ArrayLinearListIterator implements Iterator {private ArrayLinearList list;private int nextIndex;public ArrayLinearListIterator(ArrayLinearList theList) {

list = theList; nextIndex = 0;

}public boolean hasNext() { return nextIndex < list.size; } // access list’s data member directly

// …}

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public class ArrayLinearListWithIterator implements LinearList {public Iterator iterator()

{return new ArrayLinearListIterator();}private class ArrayLinearListIterator implements Iterator {

public boolean hasNext() { return nextIndex < size; }

// …}// … all ArrayLinearList members and operations

}

� By using a member class

� Implemented as a member class (nested class) of list class

� Can access private data members of enclosing class

� Can define the iterator in the same file


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� Using a member class is better than using a top-level class because list and iterator implementation can be separated

isEmpty():booleansize():intget(index:int):Objectremove(index:int):Objectiterator():Iterator...

ArrayLinearListWithIterator

hasNext():booleannext():Objectremove():void

ArrayLinearListIterator

uses

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Merits of an Iterator

� It is often possible to implement the method next() so that its complexity is less than that of get()

� Public Object get(int Index)

{ checkIndex(index); return element[Index]}

� Public Object next()

{ if (nextIndex < list.size) return list.element[nextIndex++];

else throw new NoSuchElementException(“No next element”)}

� TP page 45

� Iterators provide a uniform way to sequence through the elements of a data structure regardless of the data structure

� Iterators provide left-to-right access vs Get() gives bidirection

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Table of Contents






� Performance

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java.util.Vector

� One of most widely used data structure class in java

� Can think as array with variable length!

� Have many operations similar to that of LinearList

� Operations� boolean add(Object o)

� boolean add(int index, Object o)

� Object remove(int index)

� boolean remove(Object o)

� int size()

� boolean isEmpty()

� int indexOf(Object o)

� void removeAllElements()

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Remember “LinearList” interface

public interface LinearList{ public void add(int index, Object obj);public Object remove(int index);public boolean isEmpty();public int size();public Object get(int index);public int indexOf(Object elem);public String toString();

}

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Array vs. Vector in Java

� Object[] oa = new Object[3]; //using array� oa[0] = “A”;� oa[1] = “B”;� oa[2] = “C”;� oa[3] = “D”; // size increasing must be done manually

� Vector v = new Vector(3); //using vector� v.add(“A”)� v.add(“B”)� v.add(“C”)� v.add(“D”) // size is increased automatically (new size is now 6)

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Linear List using Vector

� LLAVS

Public class LinearListAsVectorSubclass extends Vector

implements LinearList

{ // Program 5.13}

� LLAV

Public class LinearListAsVector

{// Program 5.14: element = new Vector(initialSize)}

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Table of Contents






� Performance

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Multiple Lists in a Single Array

� Map all of lists into a single array element whose length is the maximum possible

� May need shift left or right sub-array when inserting an element in list I

� Utilize the allocated array space

1 2 3 4 8 97… …

front[1] last[1] front[2] front[3] last[3]last[2]

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Table of Contents






� Performance

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Performance Measurement

11.8s5.8s22.4ms11.8s5.8s48.2ms18.6msLinearListAsVectorSubclass

11.8s5.8s18.4ms11.8s5.8s51.2ms20.8msLinearListAsVector

11.7s5.7s8.6ms11.8s5.8s31.2ms5.6msFastArrayLinearList

worst-caseaveragebest-

caseworst-caseaveragebest-

case

142s71s6.9ms140s70s26.2ms5.6msArrayLinearList

removeinsertget

operation

class

(List is constructed with the default initial capacity of 10)

� Implement and measure the 4 classes in the textbook

� ALL in page 162-173

� FALL in page 167

� LLAV in page 179-180

� LLAVS in page 177

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Summary� Ch.5 ~ Ch.7: Linear List

� Ch. 5 – array representation� ADT LinearList, Java’s Interface & Abstract Class

� Array representation: Increasing array size, Iterator

� Vector representation

� Ch. 6 – linked representation

� Ch. 7 – simulated pointer representation

※ In succeeding chapters - matrices, stacks, queues, dictionaries, priority queues

� Java’s linear list classes� java.util.ArrayList, java.util.Vector, java.util.LinkedList

Ch5. Linear Lists – Array Representationocw.snu.ac.kr/sites/default/files/NOTE/481.pdf©copyright...

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