Lecture (12)Multidimensional Arrays

8142019 Lecture (12)Multidimensional Arrays

httpslidepdfcomreaderfulllecture-12multidimensional-arrays 114

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Lecture 13

Multidimensional Arrays

Mdm Ratnawati Ibrahim



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Multidimensional arrays

- These are often used to represent tables of values arranged

in rows and columnsbull To identify a particular table element two indexes must

be specified The first identifies the elementrsquos row and thesecond its columnEg an array may be declared

Dim grid(3 2) As Integer This is a 4 row x 3 column table called grid whoseelements are of type integer

bull The largest index value of an array can be found usingUbound

(the smallest index value using LBound)Eg Dim info(19 27) As Integer largestRowIndex AsInteger

largestRowIndex = Ubound(info 1)produces the value 19



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Multidimensional arrays ndash contrsquod

bull As in the case of one dimension arrays initialisation may

be performed when the array is declaredEg Dim table( ) As Integer = 1 0 10 1 0

ie values are entered as rows

or by assignment statements later

bull Once created an array has a fixed size that can only bechanged explicitly using the ReDim command Even then only the last dimension can be modified Theoptional word Preserve causes the values of the array tobe preserved when the size is changed

Eg ReDim Preserve info(19 37)



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Example ndash Magic Squares

Re wwwmarkfarrarcoukmsfmsq01htm

bull A numeric magic square must consist of a series of numbersarranged in a square in such a manner that the each row eachcolumn and both the corner diagonals sum to the same amountwhich is called the magic total

bull The magic total may be determined from the formula

where n is the number of cells on each side of the magic square

The aim of the program is to display magic squares for oddvalues of n from 3 to 9 (Even number magic squares are morechallenging)

)1(2

2+times n

n



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Example ndash contrsquod

Analysis

1 What is to be input n the number of cells on eachside of the square

2 How is problem to be solved ndash Construct analgorithm

(i) Place 1 in middle cell of top row

(ii) Move diagonally up to next cell (rows and columnswrap around - above top row becomes bottomrow outside right most column becomes leftmostcolumn)

(iii)If cell occupied move to cell directly belowotherwise enter next number

(iv)If not last number ( ) go back to step (ii)

3 What is to be output Grid of numbers and magictotal

2n



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Form designMagic Squares

Enter odd n lt 10 Find

Exit

Label lblTitle

Label lblPrompt Button cmdFind

Button cmdExit

PictureBox

picBox

Textbox

txtNumber

Magic total is

Label

lblMagicTotal

Run



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Algorithm design findOddSolution (grid( )n)

Start

i = 0

j =(n-1) 2

k = 1

k gt nn

grid(i j) = k

nextI = i ndash 1nextJ = j + 1

1 End

Yes

No

3

n ndash side of squarei ndash row position

j ndash column position

Set initial position

Top row centre

k - number to be placed in grid

Is number greater than max

possible

Store number

Determine next position



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Algorithm design - contrsquod

1

nextI lt 0

nextJ gt n - 1

nextI = n - 1

nextJ = 0

2

Yes

Yes

No

No

Is next position above top line

Move to bottom row

Is next position to right of

last column

Move to first (leftmost) column



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Example ndash contrsquod Algorithm design - contrsquod 2

grid(nextInextJ) gt 0

nextI gt n - 1

nextI = 0

i = nextI

j = nextJ

k = k +1

nextI = i + 1

nextJ = j

No

No

Yes

Yes

3

Is cell occupied

Move down one cell

Is next position below

bottom row

Move to top row

Confirm next position

Increase number by 1


nextI gt n - 1

nextI = 0

i = nextI

j = nextJ

k = k +1

nextI = i + 1

nextJ = j

No

No

Yes

Yes

Is cell occupied

Move down one cell


bottom row

Move to top row




httpslidepdfcomreaderfulllecture-12multidimensional-arrays 1014 FSB23103 10

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Method Implementation



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Input design

Need to 1 ensure entries of storage array grid are set to 0

2 clear display picture box

3 receive dimension of square performing any validationchecks

Output design

Once arrangement of numbers has been determined andstored in grid array we require code to format and outputsolution

Suggest this might be a chequered board with numberscontrasting with the colour of their cell Accordingly werequire lsquoSquarersquo object and routine to output black and whitesquares with appropriate numbers



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Function implementation magicNumber(n)

Form1 code



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Form1 code - contrsquod


httpslidepdfcomreaderfulllecture-12multidimensional-arrays 1414FSB23103 14

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Multidimensional arrays

- These are often used to represent tables of values arranged

in rows and columnsbull To identify a particular table element two indexes must

be specified The first identifies the elementrsquos row and thesecond its columnEg an array may be declared

Dim grid(3 2) As Integer This is a 4 row x 3 column table called grid whoseelements are of type integer

bull The largest index value of an array can be found usingUbound

(the smallest index value using LBound)Eg Dim info(19 27) As Integer largestRowIndex AsInteger

largestRowIndex = Ubound(info 1)produces the value 19



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)1(2

2+times n

n



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Analysis








2n



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Exit

Label lblTitle


Button cmdExit

PictureBox

picBox

Textbox

txtNumber

Magic total is

Label

lblMagicTotal

Run



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Start

i = 0

j =(n-1) 2

k = 1

k gt nn

grid(i j) = k


1 End

Yes

No

3




Top row centre



possible

Store number




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1

nextI lt 0

nextJ gt n - 1

nextI = n - 1

nextJ = 0

2

Yes

Yes

No

No


Move to bottom row


last column




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nextI gt n - 1

nextI = 0

i = nextI

j = nextJ

k = k +1

nextI = i + 1

nextJ = j

No

No

Yes

Yes

3

Is cell occupied

Move down one cell


bottom row

Move to top row




nextI gt n - 1

nextI = 0

i = nextI

j = nextJ

k = k +1

nextI = i + 1

nextJ = j

No

No

Yes

Yes

Is cell occupied

Move down one cell


bottom row

Move to top row





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Input design




Output design





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Form1 code



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)1(2

2+times n

n



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Analysis








2n



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Exit

Label lblTitle


Button cmdExit

PictureBox

picBox

Textbox

txtNumber

Magic total is

Label

lblMagicTotal

Run



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Start

i = 0

j =(n-1) 2

k = 1

k gt nn

grid(i j) = k


1 End

Yes

No

3




Top row centre



possible

Store number




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1

nextI lt 0

nextJ gt n - 1

nextI = n - 1

nextJ = 0

2

Yes

Yes

No

No


Move to bottom row


last column




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nextI gt n - 1

nextI = 0

i = nextI

j = nextJ

k = k +1

nextI = i + 1

nextJ = j

No

No

Yes

Yes

3

Is cell occupied

Move down one cell


bottom row

Move to top row




nextI gt n - 1

nextI = 0

i = nextI

j = nextJ

k = k +1

nextI = i + 1

nextJ = j

No

No

Yes

Yes

Is cell occupied

Move down one cell


bottom row

Move to top row





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Input design




Output design





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Form1 code



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)1(2

2+times n

n



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Analysis








2n



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Exit

Label lblTitle


Button cmdExit

PictureBox

picBox

Textbox

txtNumber

Magic total is

Label

lblMagicTotal

Run



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Start

i = 0

j =(n-1) 2

k = 1

k gt nn

grid(i j) = k


1 End

Yes

No

3




Top row centre



possible

Store number




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1

nextI lt 0

nextJ gt n - 1

nextI = n - 1

nextJ = 0

2

Yes

Yes

No

No


Move to bottom row


last column




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nextI gt n - 1

nextI = 0

i = nextI

j = nextJ

k = k +1

nextI = i + 1

nextJ = j

No

No

Yes

Yes

3

Is cell occupied

Move down one cell


bottom row

Move to top row




nextI gt n - 1

nextI = 0

i = nextI

j = nextJ

k = k +1

nextI = i + 1

nextJ = j

No

No

Yes

Yes

Is cell occupied

Move down one cell


bottom row

Move to top row





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Input design




Output design





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Form1 code



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Analysis








2n



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Exit

Label lblTitle


Button cmdExit

PictureBox

picBox

Textbox

txtNumber

Magic total is

Label

lblMagicTotal

Run



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Start

i = 0

j =(n-1) 2

k = 1

k gt nn

grid(i j) = k


1 End

Yes

No

3




Top row centre



possible

Store number




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1

nextI lt 0

nextJ gt n - 1

nextI = n - 1

nextJ = 0

2

Yes

Yes

No

No


Move to bottom row


last column




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nextI gt n - 1

nextI = 0

i = nextI

j = nextJ

k = k +1

nextI = i + 1

nextJ = j

No

No

Yes

Yes

3

Is cell occupied

Move down one cell


bottom row

Move to top row




nextI gt n - 1

nextI = 0

i = nextI

j = nextJ

k = k +1

nextI = i + 1

nextJ = j

No

No

Yes

Yes

Is cell occupied

Move down one cell


bottom row

Move to top row





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Input design




Output design





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Form1 code



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Exit

Label lblTitle


Button cmdExit

PictureBox

picBox

Textbox

txtNumber

Magic total is

Label

lblMagicTotal

Run



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Start

i = 0

j =(n-1) 2

k = 1

k gt nn

grid(i j) = k


1 End

Yes

No

3




Top row centre



possible

Store number




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1

nextI lt 0

nextJ gt n - 1

nextI = n - 1

nextJ = 0

2

Yes

Yes

No

No


Move to bottom row


last column




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nextI gt n - 1

nextI = 0

i = nextI

j = nextJ

k = k +1

nextI = i + 1

nextJ = j

No

No

Yes

Yes

3

Is cell occupied

Move down one cell


bottom row

Move to top row




nextI gt n - 1

nextI = 0

i = nextI

j = nextJ

k = k +1

nextI = i + 1

nextJ = j

No

No

Yes

Yes

Is cell occupied

Move down one cell


bottom row

Move to top row





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Input design




Output design





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Form1 code



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Start

i = 0

j =(n-1) 2

k = 1

k gt nn

grid(i j) = k


1 End

Yes

No

3




Top row centre



possible

Store number




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1

nextI lt 0

nextJ gt n - 1

nextI = n - 1

nextJ = 0

2

Yes

Yes

No

No


Move to bottom row


last column




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nextI gt n - 1

nextI = 0

i = nextI

j = nextJ

k = k +1

nextI = i + 1

nextJ = j

No

No

Yes

Yes

3

Is cell occupied

Move down one cell


bottom row

Move to top row




nextI gt n - 1

nextI = 0

i = nextI

j = nextJ

k = k +1

nextI = i + 1

nextJ = j

No

No

Yes

Yes

Is cell occupied

Move down one cell


bottom row

Move to top row





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Input design




Output design





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Form1 code



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1

nextI lt 0

nextJ gt n - 1

nextI = n - 1

nextJ = 0

2

Yes

Yes

No

No


Move to bottom row


last column




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nextI gt n - 1

nextI = 0

i = nextI

j = nextJ

k = k +1

nextI = i + 1

nextJ = j

No

No

Yes

Yes

3

Is cell occupied

Move down one cell


bottom row

Move to top row




nextI gt n - 1

nextI = 0

i = nextI

j = nextJ

k = k +1

nextI = i + 1

nextJ = j

No

No

Yes

Yes

Is cell occupied

Move down one cell


bottom row

Move to top row





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Input design




Output design





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Form1 code



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nextI gt n - 1

nextI = 0

i = nextI

j = nextJ

k = k +1

nextI = i + 1

nextJ = j

No

No

Yes

Yes

3

Is cell occupied

Move down one cell


bottom row

Move to top row




nextI gt n - 1

nextI = 0

i = nextI

j = nextJ

k = k +1

nextI = i + 1

nextJ = j

No

No

Yes

Yes

Is cell occupied

Move down one cell


bottom row

Move to top row





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Input design




Output design





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Form1 code



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Input design




Output design





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Form1 code



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Input design




Output design





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Form1 code



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NIVERS

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A

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U

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Documents

Lecture (12)Multidimensional Arrays