Algorithm to simplify fractions

Hello that, today I bring you another function required to perform for newbies in programming, which is the Fractions Simplification. The structure is developed in VB.NET with framework 4.5.

It is much simpler than my previous solution of complex numbers, but it behaves almost in the same way; that is, I added:

-> Normal and character string constructors.

-> Conversion ToString () custom.

-> Overload of operators so that our rational numbers are handled directly in the line of code.

Rapid calculation of the MCD

In addition to adding, subtracting, multiplying, dividing and presenting the fractions, add the famous Euclid's algorithm for its simplification, but in its version of reduction by remains, which I show below:

Public Shared Function mcdFast(eN As Integer, eD As Integer) As Integer
   Dim DD, DS, R As Integer

   'Buscamos cual es mayor divisor, para asignarlo 
   'a nuestra comprobacion de restos
   DD = If(eN > eD, eN, eD)
   DS = If(eN <= eD, eN, eD)

   R = DD Mod DS 'Primer tanteo
   While R > 0
     'Dividimos e intercambiamos
     'con el resto generado y volvemos a comprobar
      DD = DS : DS = R
      R = DD Mod DS
   End While
   Return DS
 End Function

The simplified Euclid's algorithm above reads in modern language something like this:

To calculate the greatest common divisor between two positive integers a and b we divide the largest, say a, between the smallest, say b. This division will provide us with a quotient, "c1", and a remainder, "r1".

If "r1" = 0, then the gcd (between a and b) = b. If it is not zero, we divide the divisor, "c1", among the rest, "r1", obtaining another quotient, "c2", and another remainder, "r2". If "r2" = 0, then mcd (between a and b) = "r2". If it is not zero, we divide the divisor between the rest. And so on (we have the iteration loop).

Do not use recursion, because I really do not like it very much because the debugging process is a REAL HEADACHE. But I also included the recursive function that is quite widespread on the internet.

Is the next:

    Public Shared Function mcd(eN As Integer, eD As Integer) As Integer
        If eN Mod eD = 0 Then
            Return eD
        Else
            Return mcd(eD, eN Mod eD)
        End If
    End Function

For the inexperienced eye, it will immediately assume that the initial function is slower than the recursive one, since it has more code, but it is not. As you can see, the one that implements without recursividad puts the name of mcdFast, and is that in fact it is almost 50% faster than the original recursive. So not always the recursion is the best option; ).

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Use of the NumeroRacional structure

Creating a rational number in code line is defined as:

We create two fractions 1/2 and 1/3:

        Dim NR1 = New Rutional Number(1, 2)
        Dim NR2 = New Rutional Number("1/3")

As it is seen before, the constructor can construct the rational number with independent parameters or in presentation of chain of characters. Something important to add is that the fraction is always reduced at the end of the construction.

Once our rational numbers are created we can simply add them in the following way:

        Dim Resultado As Rutional Number

        Resultado = NR1 + NR2

We can then remove it by console screen:

Console.WriteLine("Resultado {0}", Resultado)

We will see in console screen the following:

Resultado 5/6

Below I leave the download link of the NumeroRacional structure program.

Here the video of the explanation

Written by:

Elimar D.

10/04/2018

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