Arrays

What is an Array?

• Similar to a Matrix.

• Collection of data that needs similar processing.

• Example: Transpose of a matrix

1 3 4

7 2 9

6 8 5

1 7 6

3 2 8

4 9 5

Why an Array?

• Read a matrix from a file and write its transpose in another file

1,-3,4

-7,2,9

6,8,5

• Need to declare nine variables

• Write 3 Input & 3 Output statements

• Lot of complication in re-arrangement

• Program will fail for 4x4 matrix

Why an Array?

• An array allows us to use the same name for the data, but distinguish its elements by indices

Dim A(1 To 3, 1 To 3) As Integer

(1,1) (1,2) (1,3)

(2,1) (2,2) (2,3)

(3,1) (3,2) (3,3)

A A A

A A A

A A A

Row # 1

Row # 2

Row # 3

Column # 1 Column # 2 Column # 3

Why an Array?

For Row = 1 To 3Input #10, A(Row,1),A(Row,2),A(Row,3)

Next Row

For Colm = 1 To 3Write #20, A(1,Colm),A(2,Colm),A(3,Colm)

Next Colm

Array Storage

A(1,1) A(1,2) A(1,3)

A(2,1) A(2,2) A(2,3)

A(3,1) A(3,2) A(3,3)

A(1,1)A(1,2)A(1,3)A(2,1)A(2,2)A(2,3)A(3,1)A(3,2)A(3,3)A(1,1)

A(2,1)A(3,1)A(1,2)A(2,2)A(3,2)

…

Using Arrays

For Row = 1 To 3For Column = 1 To 3

Input #10, A(Row,Column)Next Column

Next RowFor Row = 1 To 3For Column = 1 To 3

Write #20, A(Column,Row)Next Column

Next Row

Order of Loops is same

Using Arrays

For Row = 1 To 3For Column = 1 To 3

Input #10, A(Row,Column)Next Column

Next RowFor Column = 1 To 3For Row = 1 To 3

Write #20, A(Row,Column)Next Column

Next Row

Order of Loops is reversed

Arrays

• Arrays can have multiple dimensions• Matrix is a 2-diemnsional array• One dimensional arrays

» Row Vector» Column Vector

• Three-dimensional Arrays• Multi-dimensional arrays

» 60 dimensions possible ????????

• Storage requirements» A(10,10,10,10,10) uses 100,000 x 2 bytes for integer

type data

Array Declaration

Dim ArrayOne(1 To 3, 1 To 7)– Two dimensional array of size 3 x 7

• Lower bound = 1, Upper bound = 3 and 7

Dim ArrayTwo(10,10)– Two dimensional array of size 11 x 11

• Lower bound = 0, Upper bound = 10

Option Base 1

Dim Array3(10,10)• 10 x 10 Array

Matrix Addition

• C = A + B– C, A, and B are the same size matrices (mxn)

For row = 1 To m For column = 1 To n C(row,column) = A(row,column) + B(row,column) Next columnNext row

Matrix Multiplication(1,1) (1,2) (1,3) (1,1) (1,2)

(1,1) (1,2) (1,3)(2,1) (2,2) (2,3) (2,1) (2,2)

(2,1) (2,2) (2,3)(3,1) (3,2) (3,3) (3,1) (3,2)

P P P A AB B B

P P P A AB B B

P P P A A

(1,1) (1,1)* (1,1) (1,2)* (2,1)P A B A B

# Columns of A = # Rows of B

(1,2) (1,1)* (1,2) (1,2)* (2,2)P A B A B (1,3) (1,1)* (1,3) (1,2)* (2,3)P A B A B

For j=1 To 3P(1 , j) = P(1 , j)+A(1,1)*B(1 , j)+A(1 , 2)*B(2 , j)

Next j

Matrix Multiplication(1,1) (1,2) (1,3) (1,1) (1,2)

(1,1) (1,2) (1,3)(2,1) (2,2) (2,3) (2,1) (2,2)

(2,1) (2,2) (2,3)(3,1) (3,2) (3,3) (3,1) (3,2)

P P P A AB B B

P P P A AB B B

P P P A A

For j=1 To 3P(1 , j) = P(1 , j) + A(1 ,1)*B(1 , j) + A(1 , 2)*B(2 , j)

Next jFor j=1 To 3

P(2 , j) = P(2 , j) + A(2 ,1)*B(1 , j) + A(2 , 2)*B(2 , j)Next jFor j=1 To 3

P(3 , j) = P(3 , j) + A(3 ,1)*B(1 , j) + A(3 , 2)*B(2 , j)Next j

Matrix Multiplication(1,1) (1,2) (1,3) (1,1) (1,2)

(1,1) (1,2) (1,3)(2,1) (2,2) (2,3) (2,1) (2,2)

(2,1) (2,2) (2,3)(3,1) (3,2) (3,3) (3,1) (3,2)

P P P A AB B B

P P P A AB B B

P P P A A

For i = 1 To 3 For j = 1 To 3

P(i , j) = P(i , j) + A(i ,1)*B(1 , j) + A(i , 2)*B(2 , j) Next jNext i

For i = 1 To 3 For j=1 To 3 For k=1 To 2

P(i , j) = P(i , j) + A(i ,k)*B(k , j) Next k Next jNext i

Matrix Multiplication

• Assume that A is mxn matrix and B is nxp matrix P is mxp matrix

For i = 1 To mFor j = 1 To p

For k = 1 To nP(i,j) = P(i,j) + A(i,k)*B(k,j)

Next kNext j

Next i

Sorting: Bubble Sort

Sort the elements of an array A shown below in ascending order. Use the bubble sort method. A=[7 3 2 4 10 9 0]

Solution• Step 1:

– Compare A(1)=7 and A(2)=3. Swap the numbers as they are not in ascending order. A=[3 7 2 4 10 9 0].

– Now compare A(2)=7 and A(3)=2 and swap A=[3 2 7 4 10 9 0].– Compare A(3)=7 and A(4)=4 A=[3 2 4 7 10 9 0]. – A(4)=7 and A(5)=10 No swapping.– Compare A(5)=10 and A(6)=9 A=[3 2 4 7 9 10 0]. – Compare A(6)=10 and A(7)=0 A=[3 2 4 7 9 0 10]. – Overall 6 comparisons were needed. 10 in correct place

Sorting: Bubble Sort

• Step 2: – The highest number in the list is already in its correct place.

• Exclude this number from any comparison

– Repeat step 1 but avoid any comparison with the last entry. This would result in A=[2 3 4 7 0 9 10]. 9 in correct place

– We needed 5 comparisons.

• Step 3: – Repeating 1 on the initial 5 numbers of the array gives

A=[2 3 4 0 7 9 10]. 7 in correct place – 4 comparisons were needed

Sorting: Bubble Sort

• Step 4: – A=[2 3 0 4 7 9 10]. 4 in correct place. – 3 comparisons

• Step 5: – A=[2 0 3 4 7 9 10]. 3 in correct place. – 2 comparisons.

• Step 6: – A=[0 2 3 4 7 9 10]. 2 and 0 in correct place. – 1 comparison.

Bubble Sort

For step = 1 To N-1For index = 1 To N-run

If x(index) > x(index+1) ThenTemp = x(index)x(index) = x(index+1)x(index+1) = Temp

End IfNext index

Next step

Bubble Sort

Private Sub Command1_Click()Dim X(1 To 1000) As IntegerDim Count As Integer, UserData As StringDim N As Integer, Temp As IntegerPicture1.ClsPicture2.ClsFor Index = 1 To 1000 UserData = InputBox("Number or End: ") If Left(UCase(UserData), 1) = "E" Then Exit For End If X(Index) = Val(UserData)Next Index

Bubble Sort

N = Index - 1For i = 1 To N Picture1.Print X(i)Next i

Bubble Sort

For step = 1 To N - 1 For Index = 1 To N - step If X(Index) > X(Index + 1) Then Temp = X(Index) X(Index) = X(Index + 1) X(Index + 1) = Temp End If Next Index Do While UCase(Left(InputBox("Enter Next for next step"), 1)) <> "N" Picture2.Print "Enter Next" Loop Picture2.Cls For k = 1 To N Picture2.Print X(k) Next kNext step

Bubble Sort

Picture2.ClsFor j = 1 To N Picture2.Print X(j)Next j

End Sub