Arrays

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Arrays

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Title: Arrays

1
Arrays

Chapter 8
Fall 2005
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 v 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)

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
Todays demotivators
14
Explicit initialization

Syntax

ElementType
id

exp
,
exp
,
...
exp

0
1
-1
n
15
Explicit initialization

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

16
Array members

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

17
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)

18
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)

19
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()

20
Making a deep copy
21
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)

22
How Java represents arrays

Consider
int a 1, 2, 3, 4, 5

a
23
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

-
24
Fan-supplied demotivators!
25
ArrayTools
26
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

27
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

28
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)

29
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

30
End of lecture on 7 Nov 2005
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

Demo.java

35
main (String args)
36
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 "'")

37
Program Demo

MainParameters.java
Via JCreator
Via the command line

38
Basic array searching
39
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
40
Searching for the minimum value

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

41
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)

42
Todays demotivators
43
Sorting
44
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

45
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

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 1
Swaps second smallest element with v1
This results in second 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 2
Swaps third smallest element with v2
This results in third 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 3
Swaps fourth smallest element with v3
This results in fourth 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 4
Swaps fifth smallest element with v4
This results in fifth smallest element being in
the correct place for a sorted result

50
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

51
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

52
Todays demotivators
53
Binary search
54
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

55
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))

56
Binary search use demo

BSDemo.java

57
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

58
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
59
Binary search

But what if the element is not in the list?

60
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
61
Binary search

A somewhat alternative view of what a binary
search does

62
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

63
Binary search vs. sequential search

Assume the array has n elements
Sequential search can take (in the worst-case) n
iterations to find the element
Binary search can take (in the worst case) 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

64
Demotivators
65
Multi-dimensional arrays
66
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

67
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
68
Example

Alternative
int m new int34
Produces

69
Multidimensional array visualization

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

or
70
End of lecture on 9 November 2005
71
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()

72
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
73
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()
For sake of simplicity, well always put the
column first in this course
Just like Excel

74
Example

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

75
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
76
Explicit Initialization

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

77
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

78
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

79
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

80
Homework J8

You will be creating a Grid (or Map, Dungeon,
etc.) class
It will contain a 2-D array
In each spot will be a Room object
The Room object from the current homework
The descriptions for the rooms will be from this
weeks lab
Can move between the rooms
Rooms may contain a monster, weapon, etc.

81
Todays demotivators
82
Vector class

This is also the review
for the third midterm

83
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
Well see why I chose that name later

84
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

85
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

86
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 Objectlengthfs
What does this mean?
Well see that a bit later
But briefly, it means the array can store any
object

87
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

88
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

89
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

90
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

91
Miscellaneous other methods

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

92
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

93
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)

94
Program Demo

VectorUsage.java

95
The real Vector class

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

96
Program Demo

VectorUsage.java
But using java.util.Vector

97
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

98
More on using the Vector class

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

99
New demotivators!!!
100
Wrapper classes
101
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!

102
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)
var y j.intValue()
Pretty annoying syntax well see how to get
around it in a bit

103
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

104
End of lecture on 14 November 2005

The slides on wrapper classes were copied to the
slide set for chapter 7

105
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?

106
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

107
More on auto-boxing