Question

I’ve written a program that must find the solution to a EulerProblem. I want to train my program skills that’s why I’ve signed up on euler.

This is the problem:

A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
a^2 + b^2 = c^2

For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.

There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc.

and this is my code, but it runs soo slow, it take hours to give me the right abc.

static int findTriplet(int getal)
{
    boolean test = false;
    for(int a = 1; !test; a++)
        for(int b = a+1; !test; b++)
            for(int c = b+1; !test; c++)
            {
                if( a*a + b*b == c*c)
                {
                    if(a+b+c == getal)
                    {
                        return (a*b*c);
                    }
                }

            }
    return 0;
}

Is it possible to make the code much faster or is it normal that it takes hours?

Kind regards,

EDIT:

Thanks for helping. The !test boolean was useless sorry for that, This works :

static int findTriplet(int getal)
{
    for(int a = 1; a < 1000; a++)
        for(int b = a+1; b < 1000; b++)
            for(int c = b+1; c < 1000; c++)
            {
                if( a*a + b*b == c*c)
                {
                    if(a+b+c == getal)
                    {
                        return (a*b*c);
                    }
                }

            }
    return 0;
}

I’ve also wrote a haskell variation that also does the trick.

Think this was easier in Haskell and more efficient.

Thaks for the tips.

Answer 1

In order to optimize this naive algorithm, you have first to understand that :

1. Your actual source code does not stop at all. It will run as long as test is false. You also take the risk to encounter an overflow of c.
2. Trying every possible combination of a, b and c would result in trying 1000*999*988= 997 002 000 times (!).
3. Key points in this algorithms are :
   • stop conditions in loops
   • ways to find next one to try
   • ways to reduce loops if possible

Now, you know that you need to :

1. find ways to avoid the third loop, using conditions of your problems
2. find ways to increment a and b more smartly, using conditions of your problems
3. find ways to stop loops earlier, using conditions of your problems

Here are some hints for easy optimisations :

• As amit & sirko said, you can guess c if you already know a and b.
• You don’t need to recompute a*a each time you’re checking a new b
• You don’t need to check until a < 1000 and b < 999, there is far less possible combinations

And some hints for harder optimisations :

• You don’t need to recompute b*b each time too
• You don’t to need browse every possible combinations