Example Application: Algebra

In the study of statistics, a factorial is a technique of finding different ways to arrange a series of objects (or values). For example, imagine you have five colors as red, green, blue, white, and black. In how many arrangements can you produce a list of those four objects? You can get the answer by calculating the factorial of the number of objects. The formula to calculate the factorial is:

F = n!

Imagine you have a set of five objects in different colors as red, green, blue, white, and black. Imagine you want to arrange the objects in different sequences but you want each sequence to start with two specific objects, for example you may want to arrange the objects so that you always start with any combination of black and white followed by any combination of the other objects. This type of arrangement is called a permutation. The formula to calculate a permutation is:

Imagine you have five objects and you want to arrange the objects in different sequences but you want each sequence to start with certain two objects. This type of arrangement is called a combination. To calculate it, you can use the following formula:

1. Start Microsoft Visual C# and create a Windows Application named Algebra2
2. On the main menu, click Project -> Add Class...
3. In the middle list, make sure Class is selected.
   Change the Name to Algebra and click Add
4. Change the file as follows:
   

   using System;
   using System.Collections.Generic;
   using System.Linq;
   using System.Text;
   
   namespace Algebra2
   {
       public class Algebra
       {
           public static long Factorial(long x)
           {
               if (x <= 1)
                   return 1;
               else
                   return x * Factorial(x - 1);
           }
   
           public static long Permutation(long n, long r)
           {
               if (r == 0)
                   return 0;
               if (n == 0)
                   return 0;
               if ((r >= 0) && (r <= n))
                   return Factorial(n) / Factorial(n - r);
               else
                   return 0;
           }
   
           public static long Combination(long a, long b)
           {
               if (a <= 1)
                   return 1;
   
               return Factorial(a) / (Factorial(b) * Factorial(a - b));
           }
       }
   }

5. In the Solution Explorer, right-click Form1.cs and click Rename
6. Type Exercise.cs and press Enter twice (to save and to open the form)
7. Click the body of the form to make sure it is selected.
   In the Properties window, change the following characteristics
   FormBorderStyle: FixedDialog
   Text: Factorial, Permutation, and Combination
   Size: 304, 208
   StartPosition: CenterScreen
   MaximizeBox: False
   MinimizeBox: False
8. In the Containers section of the Toolbox, click TabControl and click the form
9. On the form, right-click the right side of tabPage2 and click Add Page
10. Design the form as follows:
     

    Control Text Name Additional Properties TabControl   tclAlgebra HotTrack: True Location: 12, 12 Size: 304, 235 TabPage   Factorial tabFactorial   Label Number:   Location: 22, 21 Button Calculate btnCalcFactorial   TextBox   txtNumber TextAlign: Right Location: 88, 18 Size: 50, 20 Label Result:   Location: 22, 56 TextBox   txtFactorial TextAlign: Right Location: 88, 54 Size: 140, 20 Button Close btnClose

    Control Text Name Location Size TabPage   Permutation tabPermutation     Label n:   22, 21   TextBox   txtPermutationN 88, 18 50, 20 Label r:   22, 56   Button Calculate btnCalcPermutation     TextBox   txtPermutationR 88, 54 50, 20 Label P(n, r):   22, 92   TextBox   txtPermutation 88, 90 140, 20

    Control Text Name Location Size TabPage   Combination tabCombination     Label n:   22, 21   TextBox   txtCombinationN 88, 18 50, 20 Label r:   22, 56   Button Calculate btnCalcCombination     TextBox   txtCombinationR 88, 54 50, 20 Label C(n, r):   22, 92   TextBox   txtCombination 88, 90 140, 20

11. Access the Factorial tab page and double-click its Calculate button
12. Implement the event as follows:
    

    private void btnCalcFactorial_Click(object sender, EventArgs e)
    {
            long number = 0;
            long result;
    
            try
            {
                    number = long.Parse(txtFactNumber.Text);
                    result = Algebra.Factorial(number);
                    txtFactorial.Text = result.ToString();
            }
            catch (FormatException)
            {
                    MessageBox.Show("Invalid Number");
            }
    }

13. Return to the form
14. Access the Permutation tab page and double-click its Calculate button
15. Implement the event as follows:
    

    private void btnCalcPermutation_Click(object sender, EventArgs e)
    {
            long n = 0, r = 0;
            long result;
    
            try
            {
                    n = long.Parse(txtPermutationN.Text);
            }
            catch (FormatException)
            {
                    MessageBox.Show("Invalid Number");
            }
    
            try
            {
                    r = long.Parse(txtPermutationR.Text);
                    result = Algebra.Permutation(n, r);
                    txtPermutation.Text = result.ToString();
            }
            catch (FormatException)
            {
                    MessageBox.Show("Invalid Number");
            }
    }

16. Return to the form
17. Access the Combination tab page and double-click its Calculate button
18. Implement the event as follows:
    

    private void btnCalcCombination_Click(object sender, EventArgs e)
    {
            long n = 0, r = 0;
            long result;
    
            try
            {
                    n = long.Parse(txtCombinationN.Text);
            }
            catch (FormatException)
            {
                    MessageBox.Show("Invalid Number");
            }
    
            try
            {
                    r = long.Parse(txtCombinationR.Text);
                    result = Algebra.Combination(n, r);
                    txtCombination.Text = result.ToString();
            }
            catch (FormatException)
            {
                    MessageBox.Show("Invalid Number");
            }
    }

19. Return to the form and double-click the Close button
20. Implement the event as follows:
    

    private void btnClose_Click(object sender, EventArgs e)
    {
                Close();
    }

21. Execute the application to test the calculations
     
22. Close the form and return to your programming environment