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EXAMPLE 8.10 SORTING A LIST OF NUMBERS
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Here is a more comprehensive example, based upon the well-known problem of sorting a list of numbers into ascending (or descending) order. Let us generate ten random numbers (using the RND library function, as explained in Example 7.10) and store them in a single-precision array, x. We will then rearrange the array so that the elements are sorted from smallest to largest. The program will be written so that unnecessary storage is not required. Therefore, the program will contain only one array, and the rearrangement will be carried out one element at a time. The rearrangement will begin by scanning the first n elements of x for the smallest number. This value will then be interchanged with the first number in x, thus placing the smallest number at the top of the list. Next the remaining (n 1) numbers will be scanned for the smallest, which will be exchanged with the second number. Then the remaining (n 2) numbers will be scanned for the smallest, which will be interchanged with the third number, and so on, until the entire array has been rearranged. Note that a complete rearrangement will require a total of (n 1) passes through the array, though the length of each scan will become progressively smaller with each successive pass. In order to find the smallest number within each pass (i.e., within the ith pass), we sequentially compare the starting number x(i), with each successive number in the array, x(j), where j > i. If x(j) is smaller than x(i), we interchange
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the two numbers; otherwise, we leave the two numbers in their original positions. Once this procedure has been applied to the entire array, the ith number will be smaller than any of the subsequent numbers. This process is carried out (n 1) times, for i = 1, 2, . . . , n 1. The only remaining question is how the two numbers are actually interchanged. To carry out the interchange, we first assign the value of x(i) to a temporary variable, Temp, for future reference. Then we assign the current value of x(j) to x(i). Finally, we assign the original value of x(i), which is now assigned to Temp, to x(j). The interchange of the two numbers is now complete. The following programmer-defined sub procedure (Sort_Array) carries out this strategy for an n-element array x.
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Private Sub Sort_Array(x() As Single, n As Integer) Dim Temp As Single Dim i As Integer, j As Integer For i = 0 To n - 1 For j = i + 1 To n If (x(j) < x(i)) Then Temp = x(i) x(i) = x(j) x(j) = Temp End If Next j Next i End Sub
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To display the results, we create a form containing a label, two combo boxes, and three command buttons, as shown in Fig. 8.8. One combo box will be used to display the list of random numbers, in the order they were generated. The other will display the sorted list of numbers. The three command buttons will generate and sort the list, clear the list, and end the computation, respectively.
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Fig. 8.8
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We now consider the corresponding event procedures. In contrast to our customary practice, we will assign initial values to the control properties at run time, when the form is first loaded. Event procedure Form_Load contains the property assignments.
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Private Sub Form_Load() Form1.Caption = "Random Number Sort" Label1.Caption = "Sorting Random Numbers" Label1.FontSize = 12 Label1.Alignment = 2 'Center Command1.Caption = "Go" Command1.FontSize = 10 Command2.Caption = "Clear" Command2.FontSize = 10 Command3.Caption = "End" Command3.FontSize = 10 Combo1.FontSize = 10 Combo1.Visible = False Combo2.FontSize = 10 Combo2.Visible = False End Sub
Event procedure Command1_Click does most of the actual computation. In particular, this procedure initializes the random number generator, generates the random numbers, assigns them to the array elements and copies the array elements to Combo1, carries out the sort, and then copies the sorted array elements to Combo2. Command2_Click clears the combo boxes by assigning empty strings to the list elements, and Command3_Click ends the computation. Here are the remaining event procedures.
Private Sub Command1_Click() Dim x(10) As Single, Temp As Single Dim Index As Integer, SubIndex As Integer Randomize 'Generate the random array elements and copy into Combo1 For Index = 0 To 9 x(Index) = Rnd Combo1.List(Index) = Str(x(Index)) Next Index Combo1.Text = "Random List" 'Sort the array Call Sort_Array(x(), 9) 'Copy the sorted array elements into Combo2 For Index = 0 To 9 Combo2.List(Index) = Str(x(Index)) Next Index Combo2.Text = "Sorted List" Combo1.Visible = True Combo2.Visible = True End Sub
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