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Lowest Common Denominator

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Join Date: Dec 2005

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riscphree

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Lowest Common Denominator

Apr 27th, 2006

In case anyone has this book, I'll mention it. I'm trying to complete Exercise 8-2 from Oreilly's Practical C++ Programming. The problem is to total the resistance of n resistors in parallel. The forumla for this is 1/R = 1/R1 + 1/R2+ ... 1/Rn

For example, say you have one 400Ohm and one 200Ohm resistors: 1/R = 1/400 + 1/200 which, when you do the math, comes out to R = 400/3 = 133.33Ohms

The problem I am having with with the algorithm of determining how to get the lowest common denominator in order to be able to easily add the fractions. Below is a start of what I got, but I have no idea where to start with the math ...

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 C++ Syntax (Toggle Plain Text) 
int main(void)
{
 
   int num_of_resis; // number of resistors
   int values[256];  // holds values for resistors
   int i;            // specifys data range
   int index;        // index into data
   int div;
   int var1, var2, count;
 
   cout << "How many resistors: ";
   cin >> num_of_resis;
   for(i=0;i < num_of_resis;i++){ // stores resistor values
      cout << "What is the value of one resistor?: ";
      cin >> values[i]; // used for debug
      cout << "value is " << values[i] << endl;
   }
 
   /*********************************************
   * math: 1/R = 1/R1 + 1/R2 + 1/R3 ... + 1/Rn  *
   * ex: 1/R = 1/400 + 1/200                    *
   * 1/R = 3/400                                *
   * R = 400/3                                  *
   * R = 133.33 ohms                            *
   **********************************************/
 
   cout << " ---------- " << endl; // make output look somewhat better
 
   for(i=0;i<num_of_resis;i++){
      count = div = values[i];
      if(values[i] < 1){
         cout << "error\n";
         cout << "cannot be negative\n";
         break;
      }
      if(values[i] == 0){
         cout << "continuing\n";
         cout << "value cannot be 0";
         break;
      }else{
         var1 = values[i] / values[i++];
         cout << "values[i] is " << values[i] << endl;
         cout << var1 << endl;
         }
   }
 
return 0;
}
int main(void)
{

   int num_of_resis; // number of resistors
   int values[256];  // holds values for resistors
   int i;            // specifys data range
   int index;        // index into data
   int div;
   int var1, var2, count;
   
   cout << "How many resistors: ";
   cin >> num_of_resis;
   for(i=0;i < num_of_resis;i++){ // stores resistor values
      cout << "What is the value of one resistor?: ";
      cin >> values[i]; // used for debug
      cout << "value is " << values[i] << endl;
   }

   /*********************************************
   * math: 1/R = 1/R1 + 1/R2 + 1/R3 ... + 1/Rn  *
   * ex: 1/R = 1/400 + 1/200                    *
   * 1/R = 3/400                                *
   * R = 400/3                                  *
   * R = 133.33 ohms                            *
   **********************************************/

   cout << " ---------- " << endl; // make output look somewhat better

   for(i=0;i<num_of_resis;i++){
      count = div = values[i];
      if(values[i] < 1){
         cout << "error\n";
         cout << "cannot be negative\n";
         break;
      }
      if(values[i] == 0){
         cout << "continuing\n";
         cout << "value cannot be 0";
         break;
      }else{
         var1 = values[i] / values[i++];
         cout << "values[i] is " << values[i] << endl;
         cout << var1 << endl;
         }
   }

return 0;
}

Someone suggested using Euclid's algorithm, but I don't know exactly how that would work in this situation.

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Join Date: Jun 2005

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WolfPack

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Re: Lowest Common Denominator

Apr 27th, 2006

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Originally Posted by riscphree

The problem I am having with with the algorithm of determining how to get the lowest common denominator in order to be able to easily add the fractions.

Someone suggested using Euclid's algorithm, but I don't know exactly how that would work in this situation.

Why on earth do you want the lowest common denominator to add the fractions?? Can't you just add them just like any double value?

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Join Date: Dec 2005

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riscphree

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Re: Lowest Common Denominator

Apr 27th, 2006

Well, in order to add them, I need to get them to have the same denominator, correct?

If they have the same denominator, thats no problem.

Am I going in the wrong direction with this?

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WolfPack

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Re: Lowest Common Denominator

Apr 27th, 2006

Let's go with your example.

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/*********************************************
   * math: 1/R = 1/R1 + 1/R2 + 1/R3 ... + 1/Rn  *
   * ex: 1/R = 1/400 + 1/200                    *
   * 1/R = 3/400                                *
   * R = 400/3                                  *
   * R = 133.33 ohms                            *
   **********************************************/

Can't you add it and then get it's reciprocal like this?

 Help with Code Tags 
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1/R = 1/400 + 1/200
1/R = 0.0025 + 0.005
1/R = 0.0075
R    = 1 / 0.0075
R    = 133.33333333
1/R = 1/400 + 1/200
1/R = 0.0025 + 0.005
1/R = 0.0075
R    = 1 / 0.0075
R    = 133.33333333

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Rashakil Fol Rashakil Fol is offline

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Re: Lowest Common Denominator

Apr 27th, 2006

In C and C++, the 'double' datatype can be used to store approximations of the real numbers. For example, double x = 3.5;. Use doubles to store all your resistances, and then you can do approximate arithmetic on them. These approximations can store about fourteen decimal digits of precision. They're like numbers in a calculator (where if you multiply (1 / 3) * 3 you're liable to get 0.9999999999999).

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