1. Arrays

2. What is an Array? Similar to a Matrix. Collection of data that needs similar processing. Example: Transpose of a matrix

3. 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

4. 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 Row # 1 Row # 2 Row # 3 Column # 1Column # 2Column # 3

5. Why an Array? For Row = 1 To 3 Input #10, A(Row,1),A(Row,2),A(Row,3) Next Row For Colm = 1 To 3 Write #20, A(1,Colm),A(2,Colm),A(3,Colm) Next Colm

6. 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) …

7. Using Arrays For Row = 1 To 3 For Column = 1 To 3 Input #10, A(Row,Column) Next Column Next Row For Row = 1 To 3 For Column = 1 To 3 Write #20, A(Column,Row) Next Column Next Row Order of Loops is same

8. Using Arrays For Row = 1 To 3 For Column = 1 To 3 Input #10, A(Row,Column) Next Column Next Row For Column = 1 To 3 For Row = 1 To 3 Write #20, A(Row,Column) Next Column Next Row Order of Loops is reversed

9. 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

10. 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

11. 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 column Next row

12. Matrix Multiplication # Columns of A = # Rows of B For j=1 To 3 P(1, j) = P(1, j)+A(1,1)*B(1, j)+A(1, 2)*B(2, j) Next j

13. Matrix Multiplication For j=1 To 3 P(1, j) = P(1, j) + A(1,1)*B(1, j) + A(1, 2)*B(2, j) Next j For j=1 To 3 P(2, j) = P(2, j) + A(2,1)*B(1, j) + A(2, 2)*B(2, j) Next j For j=1 To 3 P(3, j) = P(3, j) + A(3,1)*B(1, j) + A(3, 2)*B(2, j) Next j

14. Matrix Multiplication 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 j Next 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 j Next i

15. Matrix Multiplication Assume that A is mxn matrix and B is nxp matrix  P is mxp matrix For i = 1 To m For j = 1 To p For k = 1 To n P(i,j) = P(i,j) + A(i,k)*B(k,j) Next k Next j Next i

16. 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

17. 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

18. 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.

19. Bubble Sort For step = 1 To N-1 For index = 1 To N-run If x(index) > x(index+1) Then Temp = x(index) x(index) = x(index+1) x(index+1) = Temp End If Next index Next step

20. Bubble Sort Private Sub Command1_Click() Dim X(1 To 1000) As Integer Dim Count As Integer, UserData As String Dim N As Integer, Temp As Integer Picture1.Cls Picture2.Cls For 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

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

22. 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 k Next step

23. Bubble Sort Picture2.Cls For j = 1 To N Picture2.Print X(j) Next j End Sub