Project Euler #9
So I decided to start looking into the Project Euler problems. A number of fellow SRT employees have been tackling these over the past few months and after recently reading Bill's solutions for problems #7 and #8 I decided to look at #9.
Find the only Pythagorean triplet, {a, b, c}, for which a + b + c = 1000.
I thought about this for quite a while. I was trying to see how I could utilize LINQ to make this easier. In the end, I decided to just use the brute force method of nested loops:
private static void Euler9()
{ for (int a = 0; a < 1000; a++)
{ for (int b = a + 1; b < 1000; b++)
{ for (int c = b + 1; c < 1000; c++)
{ if (a + b + c == 1000 && (Math.Pow(a, 2) + Math.Pow(b, 2) == Math.Pow(c, 2)))
{ Console.WriteLine("{0},{1},{2}", a, b, c); return;
}
}
}
}
}
I added a few optimizations in an effort to speed this up:
- Since a+b+c has to equal 1000, no single element (a or b or c) can be greater than 1000. Therefore my loops are pretty short.
- I took advantage of C#'s short-circuiting to do the simple "a + b + c == 1000" check before doing the squares.
It runs pretty quick (under a second). The first time I ran it I took out the "return" to make sure my logic only produced a single result. It did! :)