COP1000 1

Processing Arrays

Lesson 8

McManus

COP1000 2

Overview• One-Dimensional Arrays

– Entering Data into an Array– Printing an Array– Accumulating the elements of an Array

• Two-Dimensional Arrays– Loading a Two-Dimensional Array– Printing a Two-Dimensional Array– Accumulating the Rows and Columns of a Two-

Dimensional Array

McManus

COP1000 3

Overview cont. • Multidimensional Arrays• Table Look-Up Technique

– Sequential Search– Binary Search

• The Pointer Technique– Frequency Distribution– Cross Tabulation

McManus

COP1000 4

Arrays• A consecutive group of memory locations

that all have the same name and the same data type.

• Are the simplest structured type.– Component access is by a position number (an

index) that indicates the component’s position within the collection.

• Examples MyArray(3)MyArray(n)

McManus

COP1000 5

Simple Arrays• Are declared at compile time.

– Compiler reserves the appropriate amount of contiguous memory to hold the array.

• Occupy storage in memory– System must have enough memory– Memory may be reserved for more than one

array in one statement, but not recommended.– Examples:

• Dim (99) As Integer in VB declares an array of 100 Integer elements

• Dim s(14) As String in VB declares an array of 15 String elements

• Int age[12]; in C++ declares an array of 12 Integer elementsMcManus

COP1000 6

Array Initialization

McManus

Private Sub cmdPrint_Click()Dim anarray(9) As Integer ‘10 ElementsDim x As Integer ‘Used as Loop CounterlblDisplay.Text = "Index" & Space(3) & _

"Value" ‘HeadingFor x = 0 To anarray.GetUpperbound(0) _

Step 1 anarray(x) = 5

lblDisplay.Text = x & Space(7)& anarray(x)Next x

End Sub

VB Code

What will it display?

COP1000 7

A Different Method of Initialization

McManus

Private Sub cmdPrint_Click()Dim anarray(9) As Integer ‘10 ElementsDim x As Integer ‘Used as Loop CounterlblDisplay.Text = "Index" & Space(3) & _

"Value" ‘HeadingFor x = 0 To anarray.GetUpperbound(0) _

Step 1 anarray(x) = x

lblDisplay.Text = x & Space(7)& anarray(x)Next x

End Sub

VB Code

What will it display?

COP1000 8

Array Initialization– In VB, by default, the first array index is

initialized to 0 and VB won’t allow you to change the default.

– However, other languages, like Pascal, will allow the programmer to initialize the array to something other than zero, but you have to do it...• Note…not all languages have this facility…• In other languages, you have to initialize the

array.McManus

COP1000 9

1 2 3 4 5 6 7a b c c d e f

Array Type Declarationtype

CharArray = array [1..7] of Char;Allocate storage for the array

varLetterArray : CharArray;

LetterArray

LetterArray[3] = ‘c’

the element in Position 3 is "c"McManus

Pascal Code

Index

Element

COP1000 10

Accessing Array ElementsTo access the array called numbers, call

the array by name and include in () the index (or location) of the value to be accessed.

numbers(2) 23; numbers(4) 32Note: the second element in the array

is not 23.Source of off-by-one errors

Print numbers(2) + numbers(3) will print 51

McManus

10 15 23 28 32 45 47

0 1 2 3 4 5 6An array calledNumbers

Index

COP1000 11

Some ExamplesNumbers( 2 ) + Numbers( 3 )

5 + 7 = 12 Numbers( 2 + 3 ) value stored in 5 is

6Numbers( 2 ) + 3 valued stored in 2 is

5 5 + 3 = 8Numbers( 5 - 3 + 2 ) value stored in 4 is

3Numbers( 2 * 3 ) value stored in 6 is

4Numbers( 9 + 2 ) generates a syntax

errorMcManus

Index 0 1 2 3 4 5 6 7 8 9 10Value 10 2 5 7 3 6 4 1 3 9 1

COP1000 12

How Random Access Works

• The computer calculates the addresses of an array for you.

McManus

Index_Location = Base + (Index * Element_Length)Index_Location = 1000 + ( 3 * 2 )

Index_Location(3) = 1006 which is the Address for the element stored at

Index 3.

Index

Elements1000Base2 bytes 2 bytes 2 bytes 2 bytes 2 bytes 2 bytes 2 bytes

0 1 2 3 4 5 610 15 23 28 32 45 47

Not On the Test!

COP1000 13

Storing Data in an Array• Must be read into an array one

element at a time.• Must be displayed one element at a

time.for Index := 1 to MaxItems do

Read (DataArray[Index]);

for Index := 1 to MaxItems doWriteLn (Index :4, DataArray[Index] :8:1);

McManus

Pascal Code

COP1000 14

One-Dimensional Arrays• The simplest Array Structure

Ex. Array - Age Variable Name

AGE (1) = 32AGE (2) = 54AGE (3) = 25AGE (4) = 36AGE (5) = 45AGE (6) = 20AGE (7) = 28AGE (8) = 50

McManus

The Number in the Parentheses refers to theBox number in the Array, the Element Number

Index

1 2 3 4 5 6 7 832 54 25 36 45 20 28 50

Elements

COP1000 15

Accessing Arrays• Individual array elements and entire arrays

can be passed as parameters.• Arrays can also be copied from one array

to another.const MaxSize = 100;type IndexRange = 1..MaxSize; TestArray = array [IndexRange] of Real;var XArray, YArray : TestArray; {declares both as arrays}

XArray := YArray {the code: copies YArray to XArray}

McManus

Both arrays must beof the same data type.

Pascal Code

COP1000 16

Entering Data into an Array

• To Load an Array, use a Loop– If you know the number of elements,

then use the automatic-counter loop (For loop)

– If you don’t know the number of elements, then use an indicator code with the Repeat/Until or the While/While-end loop

McManus

COP1000 17

Automatic-Counter Loop

McManus

Algorithm For Index = 1 To N Step 1  AnArray(Index) = X Next Index

Index = CounterN = Number of elements in AnArrayAnArray(Index) = Element Index in ArrayX = data entered into AnArray(Index)

AnArray(Index) = X

Index <= N

Index = Index + 1

Index = 1

False

True

FlowchartPseudocode

COP1000 18

Repeat/Until LoopUsing Definite Looping

McManus

AlgorithmIndex = 0Repeat

Index = Index + 1AnArray(Index) = X

Until Index > 10

X = data entered into AnArray(Index)

Index = 0

Index = Index + 1

AnArray(Index) = X

UntilIndex > 10

True

False

Pseudocode

Flowchart

COP1000 19

While/While-End LoopUsing Indefinite Looping

McManus

AlgorithmIndex = 1AnArray(Index) = ReadvalueWhile AnArray(Index) <>

SentinelAnArray(Index) = Readvalue

End While

Sentinel = end test valueReadvalue = value being read in

from user

Index= 1

AnArray(Index) = Readvalue

True

False

AnArray(Index) = Readvalue

AnArray(Index) <>

Sentinel

FlowchartPseudocode

COP1000 20

Printing an Array

McManus

AlgorithmFor Index= 1 To N Step 1

Print AnArray(Index)Next Index

N = Total number of elements

AnArray(Index) = ith element of Array

Print AnArray(Index)

Index <= N

Index = Index + 1

Index = 1

False

True

implicit

Implicit Step

Note: Not all languages begin with 1 as the default first element.Some, like VB, begin with 0

FlowchartPseudocode

COP1000 21

Two-Dimensional Arrays• A two-dimensional array is a block of

memory locations associated with a single memory variable name and designated by row and column numbers

• Each element is written as A (Row#,Column#) – The row number is always first, and the column

number second– Note: This is different than in Excel

McManus

COP1000 22

Two-Dimensional Arrays• For a two-dimensional array,

information is stored in rows and columns.– Requires two indexes:

• The first, by convention, represents the row• The second represents the column.• Cannot use the same index for both.

– Ex. mArray (x, y) or mArray(row, col) In

VBint TwoDimArray[r],[c] In C+

+McManus

COP1000 23

Two-Dimensional Array

McManus

Rows

Columns1st

Element

Subscripts (indexes)

0,3

1,1 1,3

0,1 0,2

1,21,0

0,0

1843959315612

78

COP1000 24

Loading a Two-Dimensional Array

• You load a Two-dimensional Array with nested loops—one loop for each dimension– When the data is loaded row by row, the

outer loop represents the row, and the inner loop represents the column

– This order of the loops allows the row number to stay constant while the column number varies

McManus

COP1000 25

Loading a Two-Dimensional Array

AlgorithmFor R = 0 To 4 Step 1 Sum = Sum + Sales(R,C) For C = 0 To 4 Step 1 Total = Total + Sales(R,C) Next CNext R

McManus

FlowchartEnter

Exit

C = 0 to 4

Sum = Sum + Sales(R,C)

Total = Total + Sales(R,C)C

R = 0 to 4

R

0,3

1,1 1,3

0,1 0,2

1,21,0

0,0876

43219

2,3

3,1 3,3

2,1 2,2

3,23,0

2,0181716

1413121119

4,1 4,34,24,0 232221 24

0,4

1,4

510

2,4

3,4

1520

4,425

rows

columns

An array called Sales

Pseudocode

COP1000 26

Multidimensional Arrays• Arrays with 3 or more dimensions

– can facilitate an understanding of the data,

– improve the readability of algorithms, and

– facilitate processing since the data can be processed through the use of three or more nested loops.

McManus

COP1000 27

Multidimensional Arrays• The recommended variable names

for the indexes for a 3-dimensional array would be – R for Row– C for Column – D for Depth– V for Volume

• These arrays are processed much like 2-dimensional arrays

McManus

For each additional dimension, an additional loop is used to manipulate the dimension

COP1000 28

Arrays and Lists

How do they differ?

McManus

COP1000 29

Arrays vs. ListsArrays• Arrays use Random

Access• Arrays use Indices

to access elements• Arrays are declared

at Compile Time• Array elements are

stored in contiguous memory

Lists• Lists use Sequential

Access• Lists use Pointers• Lists are declared at

Run Time• List elements are

stored in any available location

McManus

Know This!

COP1000 30

Attempt the end, and never stand to doubt; Nothing’s so hard, but search will find it out.

Robert Herrick

McManus

COP1000 31

Table Look-up Technique• A common application for arrays is

using a value to look up another value in a table

• Two (of many) methods for looking up values in an array or table – The Sequential search method– The Binary search method

McManus

COP1000 32

Sequential Search • This method is used when you don’t know

the element number, but you do know the value of the element

• The methodology is simple. – Given the search value of the element you

want to find, element one is tested to see if it matches the search variable. • If it does, the flow of the program drops out of the

loop. • If it doesn’t, the element number is incremented and

loops back to test again

McManus

COP1000 33

Binary Search• This is a High speed search• This search technique involves comparing

the mid-element of all or part of the array. – If it compares then it drops you out of the loop.– If it does not, the program checks to see if the

value is lower or higher than the middle value.

McManus

[First] [Middle] [Last]

Item

F M-1 M M+1 L

COP1000 34

Binary Search cont.– The boundaries are then reset to select a new

section of the array. – The program continues to divide the array in

half until the desired element is found• A 1,000 element array would take

less than 10 comparisons

McManus

COP1000 35

The Pointer Technique• Method using arrays to specify the

value of an element in one array as the element number in another array– The value of the element in the first

array points to element in the second array

• Techniques– Frequency Distribution and – Cross-Tabulation

McManus

COP1000 36

Frequency Distribution • A tally of one type of value in an

array– Example: how many students in a

school are in each class or how many of a company’s customers live in each zip code area

• The result of a frequency distribution is a one dimensional array that contains the value for each element number

McManus

COP1000 37

Frequency Distribution Example

McManus

Index Values(Age Groups)

1 1-20

2 21-30

3 31-40

4 41-50

5 51-60

Index Frequency(# in each

Group)1 3

2 5

3 4

4 2

5 1

COP1000 38

Cross-Tabulation• This uses the pointer technique for

calculating statistics from a questionnaire– Example: How many students are in each

major and each class• The result of this cross-tabulation is a two-

dimensional array containing the tally for the combination of the majors and classes– The majors would be the rows and the classes

would be the columns

McManus

COP1000 39

Cross Tabulation Example

Yes(1)

No(2)

Females(1) 32 25

Males(2) 51 42

McManus

COP1000 40

Next?

McManus