Problem #33

Nothing too special...heres what I did to solve it:

#include <iostream>
#include <string>

using namespace std;

struct fraction
{
    int numerator;
    int denominator;
};

fraction factor (fraction);
int missingWhatNumber (int, int);

int main()
{
    fraction fract, fract2, total;

    // Because the fraction 49/98 -> 4/8 -> 1/2, and the program would not detect that, because it 
    // only looks at the 1/2, not that middle step. So I am using that as an initial value, since
    // I already know that (it was given in the problem).
    total.numerator = 4;
    total.denominator = 8;

    for (unsigned int i = 10; i < 100; i++)
        for (unsigned int j = i + 1; j < 100; j++)
        {
            fract.numerator = i;
            fract.denominator = j;
            
            fract2 = factor (fract);

            if (fract2.numerator != fract.numerator || fract2.denominator != fract.denominator)
                if (missingWhatNumber (fract.numerator, fract2.numerator) == missingWhatNumber (fract.denominator, fract2.denominator) && missingWhatNumber (fract.numerator, fract2.numerator) != 0)
                {
                    total.numerator *= fract2.numerator;
                    total.denominator *= fract2.denominator;
                }
        }

    total = factor (total);

    cout << total.denominator << endl;

    system ("pause");
    return 0;
}

fraction factor (fraction fract)
{
    fraction newFract;
    unsigned int goTo = 0;
    unsigned int gcf = 0;

    if (fract.numerator > fract.denominator)
        goTo = fract.denominator;
    else
        goTo = fract.numerator;

    if (fract.denominator == 0 || fract.numerator == 0)
    {
        // Nothing...
    }
    else
    {
        for (unsigned int i = 1; i <= goTo; i++)
            if (fract.numerator % i == 0 && fract.denominator %i == 0)
                gcf = i;

        newFract.numerator = fract.numerator / gcf;
        newFract.denominator = fract.denominator / gcf;
    }

    return newFract;
}

int missingWhatNumber (int a, int b)
{
    string str1, str2;
    char cString1[4], cString2[4];

    sprintf (cString1, "%i", a);
    sprintf (cString2, "%i", b);

    str1 = cString1;
    str2 = cString2;

    // Ok, to make it easy on myself, I will assume that str1 contains
    // 2 charactesr, and str2 contains 1 character. Bad coding practice to
    // just assume something like that, but I will make sure thats all that is passed
    // to it wherever it is used. If you plan to change anything in this
    // program that might pass other stuff to it, then you may want to add in
    // some error checking.

    if (str2[0] == str1[0])
        return (str1[1] - '0');
    else if (str2[0] == str1[1])
        return (str1[0] - '0');
    else
        return 0;
}