Arrays

1
Arrays

• Chapter 8
• Spring 2006
• CS 101
• Aaron Bloomfield

2
Introduction to arrays
3
Background

• Programmer often need the ability to represent a
  group of values as a list
• List may be one-dimensional or multidimensional
• Java provides arrays and the collection classes
• The Vector class is an example of a collection
  class
• Consider arrays first

4
Example

• Definitions
• char c
• int value new int10
• Causes
• Array object variable c is un-initialized
• Array object variable value references a new ten
  element list of integers
• Each of the integers is default initialized to 0

5
An array example
int v new int10 int i 7 int j 2 int
k 4 v0 1 vi 5 vj vi
3 vj1 vi v0 vvj
12 System.out.println(v2) vk
stdin.nextInt()
int v new int10 int i 7 int j 2 int
k 4 v0 1 vi 5 vj vi
3 vj1 vi v0 vvj
12 System.out.println(v2) vk
stdin.nextInt()
int v new int10 int i 7 int j 2 int
k 4 v0 1 vi 5 vj vi
3 vj1 vi v0 vvj
12 System.out.println(v2) vk
stdin.nextInt()
int v new int10 int i 7 int j 2 int
k 4 v0 1 vi 5 vj vi
3 vj1 vi v0 vvj
12 System.out.println(v2) vk
stdin.nextInt()
int v new int10 int i 7 int j 2 int
k 4 v0 1 vi 5 vj vi
3 vj1 vi v0 vvj
12 System.out.println(v2) vk
stdin.nextInt()
int v new int10 int i 7 int j 2 int
k 4 v0 1 vi 5 vj vi
3 vj1 vi v0 vvj
12 System.out.println(v2) vk
stdin.nextInt()
int v new int10 int i 7 int j 2 int
k 4 v0 1 vi 5 vj vi
3 vj1 vi v0 vvj
12 System.out.println(v2) vk
stdin.nextInt()
int v new int10 int i 7 int j 2 int
k 4 v0 1 vi 5 vj vi
3 vj1 vi v0 vvj
12 System.out.println(v2) vk
stdin.nextInt()
int v new int10 int i 7 int j 2 int
k 4 v0 1 vi 5 vj vi
3 vj1 vi v0 vvj
12 System.out.println(v2) vk
stdin.nextInt()
8 is displayed
Suppose 3 is extracted
6
Array variable definition styles

• Without initialization

int a int a
7
Array variable definition styles

• With initialization

8
Where weve seen arrays

• public static void main (String args)
• Thus, the main() method takes in a String array
  as the parameter
• Note that you can also define it as
• public static void main (String args)
• or
• public static void main (String foobar)

9
Basic terminology

• List is composed of elements
• Elements in a list have a common name
• Example a3 5
• The common name is a
• The list as a whole is referenced through the
  common name
• List elements are of the same type the base
  type
• Elements of a list are referenced by subscripting
  (indexing) the common name

10
Java array features

• Subscripts are denoted as expressions within
  brackets
• Base (element) type can be any type
• Size of array can be specified at run time
• This is different that pure C! (for the most
  part, at least)
• Index type is integer and the index range must be
  0 ... n-1
• Where n is the number of elements
• Just like Strings indexing!
• Automatic bounds checking
• Ensures any reference to an array element is
  valid
• Data field length specifies the number of
  elements in the list
• Array is an object
• Has features common to all other objects
• More on this later

11
Consider

• Segment
• int b new int100
• b-1 0
• b100 0
• Causes
• Array variable to reference a new list of 100
  integers
• Each element is initialized to 0
• Two exceptions to be thrown
• -1 is not a valid index too small
• 100 is not a valid index too large
• IndexOutOfBoundsException

12
Consider

• Point p new Point3
• p0 new Point(0, 0)
• p1 new Point(1, 1)
• p2 new Point(2, 2)
• p0.setX(1)
• p1.setY(p2.getY())
• Point vertex new Point(4,4)
• p1 p0
• p2 vertex

• Point p new Point3
• p0 new Point(0, 0)
• p1 new Point(1, 1)
• p2 new Point(2, 2)
• p0.setX(1)
• p1.setY(p2.getY())
• Point vertex new Point(4,4)
• p1 p0
• p2 vertex

13
New 2005 demotivatiors!
14
End of lecture on 5 April 2006
15
Explicit initialization

• Syntax

ElementType
id

exp
,
exp
,
...
exp










0
1
-1
n
16
Explicit initialization

• Example
• String puppy pika, mila, arlo,
  nikki
• int unit 1
• Equivalent to
• String puppy new String4
• puppy0 pika" puppy1 mila"
• puppy2 arlo" puppy3 nikki"
• int unit new int1
• unit0 1

17
Array members

• Member length
• Size of the array
• for (int i 0 i lt puppy.length i)
• System.out.println(puppyi)

18
Array members

• Member clone()
• Produces a shallow copy
• Point u new Point(0, 0), new Point(1, 1)
• Point v u.clone()
• v1 new Point(4, 30)

• Point u new Point(0, 0), new Point(1, 1)
• Point v u.clone()
• v1 new Point(4, 30)

19
Array members

• Member clone()
• Produces a shallow copy
• Point u new Point(0, 0), new Point(1, 1)
• Point v u.clone()
• v1.setX(10)

• Point u new Point(0, 0), new Point(1, 1)
• Point v u.clone()
• v1.setX(10)

20
Making a deep copy

• We want to copy the array and all the objects
  each element of the array references
• This is called a deep copy
• Example
• Point w new Pointu.length
• for (int i 0 i lt u.length i)
• wi (Point) ui.clone()

21
Making a deep copy
22
Review of arrays

• Creating an array
• int foo new int10
• Accessing an array
• foo3 7
• System.out.print (foo1)
• Creating an array
• String bar new String10
• Accessing an array
• bar3 qux
• System.out.println (bar1)

23
How Java represents arrays

• Consider
• int a 1, 2, 3, 4, 5

a
24
More about how Java represents Arrays

• Consider
• int a
• int b null
• int c new int5
• int d 1, 2, 3, 4, 5
• a c
• d c

• int a
• int b null
• int c new int5
• int d 1, 2, 3, 4, 5
• a c
• d c

-
25
What do these pictures mean?

• Light beer
• Dandy lions
• Assaulted peanut
• Eggplant
• Dr. Pepper
• Pool table
• Tap dancers
• Card shark
• King of pop
• I Pod
• Gator aide
• Knight mare
• Hole milk

26
ArrayTools
27
ArrayTools.java

• We want to create a series of general utility
  methods to be used for arrays
• We will put these into an ArrayTools class

28
ArrayTools.java outline

• public class ArrayTools
• // class constant
• private static final int MAX_LIST_SIZE 1000
• // sequentialSearch() examine unsorted list
  for key
• public static int sequentialSearch(int
  data, int key) ...
• // putList () prints list to screen
• public static void putList(int data) ...
• // getList() extract and return up to
  MAX_LIST_SIZE values
• public static int getList() ...
• // reverse() reverses the order of the element
  values
• public static void reverse(int list) ...
• // binarySearch() examine sorted list for a
  key

29
ArrayTools.java method putList()

• To print the array
• public static void putList(int data)
• for (int i 0 i lt data.length i)
• System.out.println(datai)
• Consider
• int score 6, 9, 82, 11, 29, 85, 11, 28, 91
  
• putList(score)

30
ArrayTools.java method getList()

• public static int getList()
• Scanner stdin new Scanner (System.in)
• int buffer new intMAX_LIST_SIZE
• int listSize 0
• for (int i 0 (i lt MAX_LIST_SIZE)
• stdin.hasNext() i)
• bufferi stdin.nextInt()
• listSize
• int data new intlistSize
• for (int i 0 i lt listSize i)
• datai bufferi
• return data

31
ArrayTools.java method reverse()

• public static void reverse(int data)
• int clone data.clone()
• for ( int i 0 i lt clone.length i )
• datai cloneclone.length-1-i
• Consider
• int foo 1, 2, 3, 4, 5
• reverse (foo)
• putList (foo)

32
Demo.java

• public class Demo
• // main() application entry point
• public static void main(String args)
• System.out.println ("")
• System.out.println ("Enter list of integers")
• int numbers ArrayTools.getList ()
• System.out.println ("")
• System.out.println ("Your list")
• ArrayTools.putList (numbers)
• ArrayTools.reverse (numbers)
• System.out.println ("")
• System.out.println ("Your list in reverse")
• ArrayTools.putList (numbers)
• System.out.println ()

33
(No Transcript)
34
ArrayTools demo

• ArrayDemo.java

35
End of lecture on 10 April 2006

• Also went over HW J7 in detail

36
main (String args)
37
Consider that main() method again

• public static void main (String args)
• How does one pass in a parameter to the main
  method?
• public class MainParameters
• public static void main (String args)
• System.out.println ("Number of paramters to
  "main() " args.length)
• if ( args.length gt 0 )
• for ( int i 0 i lt args.length i )
• System.out.println ("parameter "
• i " '" argsi "'")

38
Program Demo

• MainParameters.java
• Via JCreator
• Via the command line

39
Basic array searching
40
Searching for a value

• System.out.println("Enter search value (number)
  ")
• int key stdin.nextInt()
• int i
• for (i 0 i lt data.length i)
• if (key datai)
• break
• if (i ! data.length)
• System.out.println(key " is the " i "-th
  element")
• else
• System.out.println(key " is not in the list")

i
System.out.println("Enter search value (number)
") int key stdin.nextInt() int i if (key
datai) break if (i ! data.length)
System.out.println(key " is the " i
"-th element")
i lt data.length
i 0
41
Searching for the minimum value

• Segment
• int minimumSoFar sample0
• for (int i 1 i lt sample.length i)
• if (samplei lt minimumSoFar)
• minimumSoFar samplei

42
ArrayTools.java method sequentialSearch()

• public static int sequentialSearch(int data,
  int key)
• for (int i 0 i lt data.length i)
• if (datai key)
• return i
• return -1
• Consider
• int score 6, 9, 82, 11, 29, 85, 11, 28, 91
  
• int i1 sequentialSearch(score, 11)
• int i2 sequentialSearch(score, 30)

43
Todays demotivators
44
Sorting
45
Sorting

• Problem
• Arranging elements so that they are ordered
  according to some desired scheme
• Standard is non-decreasing order
• Why don't we say increasing order?
• Major tasks
• Comparisons of elements
• Updates or element movement

46
Selection sorting

• Algorithm basis
• On iteration i, a selection sorting method
• Finds the element containing the ith smallest
  value of its list v and exchanges that element
  with vi
• Example iteration 0
• Swaps smallest element with v0
• This results in smallest element being in the
  correct place for a sorted result

47
Selection sorting

• Algorithm basis
• On iteration i, a selection sorting method
• Finds the element containing the ith smallest
  value of its list v and exchanges that element
  with vi
• Example iteration 1
• Swaps second smallest element with v1
• This results in second smallest element being in
  the correct place for a sorted result

48
Selection sorting

• Algorithm basis
• On iteration i, a selection sorting method
• Finds the element containing the ith smallest
  value of its list v and exchanges that element
  with vi
• Example iteration 2
• Swaps third smallest element with v2
• This results in third smallest element being in
  the correct place for a sorted result

49
Selection sorting

• Algorithm basis
• On iteration i, a selection sorting method
• Finds the element containing the ith smallest
  value of its list v and exchanges that element
  with vi
• Example iteration 3
• Swaps fourth smallest element with v3
• This results in fourth smallest element being in
  the correct place for a sorted result

50
Selection sorting

• Algorithm basis
• On iteration i, a selection sorting method
• Finds the element containing the ith smallest
  value of its list v and exchanges that element
  with vi
• Example iteration 4
• Swaps fifth smallest element with v4
• This results in fifth smallest element being in
  the correct place for a sorted result

51
ArrayTools.java selection sorting

• public static void selectionSort(int v)
• for (int i 0 i lt v.length-1 i)
• // find the location of the ith smallest
  element
• int spot i
• for (int j i1 j lt v.length j)
• if (vj lt vspot) // is current location
  ok?
• // update spot to index of smaller
  element
• spot j
• // spot is now correct, so swap elements
• int rmbr vi
• vi vspot
• vspot rmbr

52
Iteration i

• // find the location of the ith smallest element
• int spot i
• for (int j i1 j lt v.length j)
• if (vj lt vspot) // is spot ok?
• // update spot with index of smaller element
• spot j
• // spot is now correct, swap elements vspot and
  vi

53
From Dubai
54
Binary search
55
Binary search

• Given a list, find a specific element in the list
• List MUST be sorted!
• Each time it iterates through, it cuts the search
  space in half
• A binary search is MUCH faster than a sequential
  search

56
Binary search use

• The BS in BSDemo is for Binary Search, mind you
• public class BSDemo
• public static void main(String args)
• int numbers 9, 3, 1, 8, 4, 6, 10, 2
• System.out.println ("The original list of
  numbers")
• ArrayTools.putList(numbers)
• System.out.println()
• ArrayTools.selectionSort(numbers)
• System.out.println ("The sorted list of
  numbers")
• ArrayTools.putList(numbers)
• System.out.println()
• System.out.println ("Searching for 0 "
  ArrayTools.binarySearch(numbers, 0))
• System.out.println ("Searching for 1 "
  ArrayTools.binarySearch(numbers, 1))
• System.out.println ("Searching for 4 "
  ArrayTools.binarySearch(numbers, 4))
• System.out.println ("Searching for 5 "
  ArrayTools.binarySearch(numbers, 5))

57
Binary search use demo

• BSDemo.java

58
Chapter 2 Computer bugs
59
Binary search

• public static int binarySearch (int data, int
  key)
• int i 0 // left endpoint of
  search interval
• int j data.length-1 // right endpoint of
  search interval
• while ( i lt j )
• int m (ij)/2
• if ( key gt datam )
• i m1
• else
• j m
• if ( key datai )
• return i
• else
• return -1

60
Binary search, take 1
public static int binarySearch (int data, int
key)
if ( key datai ) return i else
return -1
if ( key datai ) return i else
return -1
int i 0 int j data.length-1
int i 0 int j data.length-1
while ( i lt j ) int m (ij)/2 if ( key gt
datam ) i m1 else j m
while ( i lt j ) int m (ij)/2 if ( key gt
datam ) i m1 else j m
a0 a1 a2 a3 a4 a5 a6 a7 a8 a9
2 4 6 8 10 12 14 16 18 20
data
0
9
4
5
7
7
6
6
5
6
61
Binary search

• But what if the element is not in the list?

62
Binary search, take 2
public static int binarySearch (int data, int
key)
if ( key datai ) return i else
return -1
if ( key datai ) return i else
return -1
int i 0 int j data.length-1
int i 0 int j data.length-1
while ( i lt j ) int m (ij)/2 if ( key gt
datam ) i m1 else j m
while ( i lt j ) int m (ij)/2 if ( key gt
datam ) i m1 else j m
a0 a1 a2 a3 a4 a5 a6 a7 a8 a9
2 4 6 8 10 12 14 16 18 20
data
0
9
4
5
7
7
6
7
63
Binary search

• A somewhat alternative view of what a binary
  search does

64
How long does a binary search take?

• Given a array of 64 elements
• 1st iteration cuts the array to 32
• 2nd iteration cuts the array to 16
• 3rd to 8
• 4th to 4
• 5th to 2
• 6th to 1
• Given a array of 1024 elements
• 1st iteration cuts the array to 512
• ...
• 10th iteration cuts the list to 1 element
• Thus, the binary search takes log2 n iterations!
• Where n is the size of the array

65
Binary search vs. sequential search

• Assume the array has n elements
• Sequential search takes n iterations to find the
  element
• Binary search takes log2 n iterations to find the
  element
• Consider a list of 1 million elements
• Binary search takes about 20 iterations
• Sequential search takes 1,000,000 iterations
• Consider a list of 1 trillion elements
• Binary search takes about 40 iterations
• Sequential search takes 1,000,000,000,000
  iterations

66
End of lecture on 12 April 2006
67
Multi-dimensional arrays
68
Multidimensional arrays

• Many problems require information be organized as
  a two-dimensional or multidimensional list
• Examples
• Matrices
• Graphical animation
• Economic forecast models
• Map representation
• Time studies of population change
• Microprocessor design

69
Example

• Segment
• int m new int3
• m0 new int4
• m1 new int4
• m2 new int4
• Produces

When an array is created, each value is
initialized!
m
70
Example

• Alternative
• int m new int34
• Produces

71
Multidimensional array visualization

• A multi-dimensional array declaration (either
  one)
• int m new int34
• How we visualize it

or
72
Example

• Segment
• for (int c 0 c lt m.length c)
• for (int r 0 r lt mc.length r)
• System.out.print("Enter a value ")
• mcr stdin.nextInt()

73
Rows by columns or columns by rows?

• Consider int m new int34
• Is that 3 rows by 4 columns or 3 columns by 4
  rows?
• The answer is that it can be either
• As long as you are consistent with your
  column/row placement

or
74
Rows by columns or columns by rows?

• This makes it 3 columns by 4 rows
• for (int c 0 c lt m.length c)
• for (int r 0 r lt mc.length r)
• System.out.print("Enter a value ")
• mcr stdin.nextInt()
• This makes it 3 rows by 4 columns
• for (int c 0 c lt m.length c)
• for (int r 0 r lt mc.length r)
• System.out.print("Enter a value ")
• mrc stdin.nextInt()

75
Example

• Segment
• String s new String4
• s0 new String2
• s1 new String2
• s2 new String4
• s3 new String3
• Produces

76
Multidimensional array visualization

• Segment
• String s new String4
• s0 new String2
• s1 new String2
• s2 new String4
• s3 new String3
• Produces
• Called a ragged array

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
or
0
0
0
0
0
0
77
Explicit Initialization

• Segment
• int c 1, 2, 3, 4, 5, 6, 7, 8, 9
• Produces

78
Matrices

• A two-dimensional array is sometimes known as a
  matrix because it resembles that mathematical
  concept
• A matrix a with m rows and n columns is
  represented mathematically in the following
  manner

79
Matrix addition

• Definition C A B
• cij aij bij
• cij is sum of the elements in the same row and
  column of A and B

80
Matrix addition

• public static double add(double a,
  double b)
• // determine number of rows in solution
• int m a.length
• // determine number of columns in solution
• int n a0.length
• // create the array to hold the sum
• double c new doublemn
• // compute the matrix sum row by row
• for (int i 0 i lt m i)
• // produce the current row
• for (int j 0 j lt n j)
• cij aij bij

81
Homework J8

• You will be creating a Universe class
• The Universe class contains a 2-D array
• In each spot will be a Location object
• (from a previous HW)
• Lab 10 is going to be a Map class
• Will print out the 2-D Universe via text

82
Alien Song

• AlienSong.mpg

83
Vector class

• This is also the review
• for the third midterm

84
Limitations of arrays

• You cant change their size once created
• This can be a big problem!
• So we will create a new class that will operate
  like an array
• We can store and get elements by index number
• It will automatically increase in size as needed
• And other fancy features
• Lets call the class Vector
• As we are basically writing the java.util.Vector
  class

85
Properties of our Vector class

• It needs to have an array to hold the values
• As our internal array will often be bigger than
  the number of elements in the Vector, we need a
  size as well
• More on what this means in a slide or two
• Not much else

86
Methods in our Vector class

• Insert and remove elements into the Vector
• Get an element from the Vector
• Find the length
• Print it out to the screen
• What happens when the array field is full, and we
  want to add an element?
• We will need to increase the size of the array
• So we need a method to do that as well

87
Our first take on our Vector class

• public class Vector
• private Object array
• private int size 0
• Vector()
• array new Object100
• Vector(int length)
• array new Objectlength
• What does this mean?
• Well see that a bit later
• But briefly, it means the array can store any
  object

88
Adding an element to our Vector

• public void add (Object o)
• arraysize o
• Pretty easy!
• But what if the array is full?
• We need a way to increase the capacity of the
  array

89
Increasing the Vectors arrays capacity

• private void increaseCapacity()
• int oldSize array.length
• Object newArray new Object2oldSize
• for ( int i 0 i lt oldSize i )
• newArrayi arrayi
• array newArray
• And our new add() method
• public void add (Object o)
• if ( size array.length )
• increaseCapacity()
• arraysize o

90
Methods can be private as well

• Notice that the increaseCapacity() method is
  called only by the add() method when necessary
• Its not ever going to be called by whomever is
  using our Vector
• Thus, we will make it private
• That means that only other Vector methods can
  call it

91
Removing an element from a Vector

• public Object remove (int which)
• Object ret arraywhich
• for ( int i which i lt array.length-1 i )
• arrayi arrayi1
• arrayarray.length-1 null
• size--
• return ret

92
Miscellaneous other methods

• public int size()
• return size
• public Object get (int which)
• return arraywhich

93
Our toString() method

• public String toString()
• String ret ""
• for ( int i 0 i lt size i )
• ret arrayi
• if ( i ! size-1 )
• ret ", "
• ret ""
• return ret

94
Using our Vector

• This code is in a separate class called
  VectorUsage
• public static void main (String args)
• Vector v new Vector()
• for ( int i 12 i lt 30 i )
• v.add (String.valueOf(i))
• System.out.println (v)
• System.out.println (v.size())
• String s (String) v.get(5)
• System.out.println (s)
• v.remove (5)
• System.out.println (v)
• v.remove (5)
• System.out.println (v)

95
Program Demo

• VectorUsage.java

96
The real Vector class

• Java provides a Vector class
• In java.util
• It contains all of the methods shown

97
Program Demo

• VectorUsage.java
• But using java.util.Vector

98
What about those errors?

• When compiled with java.util.Vector, we see
• Note C\...\VectorUsage.java uses unchecked or
  unsafe operations.
• Note Recompile with -Xlintunchecked for
  details.
• You can ignore these
• They deal with generics, which you will see in
  future courses
• The program was still compiled

99
More on using the Vector class

• To add a Location object l to the end of a Vector
  v
• v.add(l)
• To get the Location object at the end of the
  Vector v
• Location l (Location) v.get(v.size()-1)
• To remove a Location object from the end of a
  Vector v
• Location l (Location) v.remove(v.size()-1)
• This both removes the object from the Vector and
  stores the removed value into l

100
Very unofficial demotivators
101
End of lecture on 17 Apr 2006
102
Wrapper classes
103
But what about adding variables?

• The add method takes an Object as a parameter
• public void add (Object o)
• Although we havent seen it yet, this means you
  can add any object you want to the vector
• Primitive types (i.e. variables) are not objects
• How can they be added?
• The solution wrapper classes!

104
The Integer wrapper class

• This is how you add an int variable to a Vector
• int x 5
• Integer i new Integer(x)
• vector.add (i)
• //
• Integer j (Integer) v.get(0)
• int y j.intValue()
• Pretty annoying syntax well see how to get
  around it in a bit

105
More on wrapper classes

• All the primitive types have wrapper classes
• Usually, the names are just the capitalized
  version of the type
• I.e. Double for double, Byte for byte, etc.
• Two exceptions int and char
• int has Integer
• char has Character

106
More on wrapper classes

• Consider this code
• int x 5
• vector.add (x)
• //
• int y vector.get(0)
• Does this code work?
• It shouldnt
• As we are adding a variable (not an object) to a
  vector
• But it does work!
• Why?

107
Auto-boxing

• Java 1.5 will automatically wrap a primitive
  value into its wrapper class when needed
• And automatically unwrap a wrapper object into
  the primitive value
• So Java translates the previous code into the
  following
• int x 5
• vector.add (new Integer(x))
• //
• int y ((Integer)vector.get(0)).intValue()
• This is called autoboxing
• And auto-unboxing (unauto-boxing?)
• This does not work in Java 1.4 or before

108
More on auto-boxing

• Consider the following code
• Double d 7.5
• Double e 6.5
• Double f d e
• System.println (f)
• This is doing a lot of auto-boxing (and
  auto-unboxing)
• Double d new Double(7.5)
• Double e new Double(6.5)
• Double f newDouble(d.doubleValue()
  e.doubleValue())
• System.println (f)

109
A solution to commenting your code

• The commentator http//www.cenqua.com/commentator
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