High-order determinants: easier way?

Ok, so I understand the method of finding a determinant of any order by expansion of minors. I was recently challenged by my teacher to find the determinant of a 10th order determinant she gave me. I succeeded, and felt quite proud of myself, after working for 3 months and filling up 300 pages with the math. Recently, I have grown fond of programming, and challenged myself to write a program in C++ that will find any determinant of an order of 10 or less. Coding the basic algorithm for expansion of minors has become quite tiresome. So, I am wondering, is there a simpler way to find any determinant? I'm only concerned with 4th-10th order determinants, as 2nd and 3rd orders are relatively painless. The solution has to be universal.

I'm not worried about implementing the method, as I can figure that out on my own. I just want to know if there is a simpler way (simpler here meaning needing less than 250,460 minors, and minors of minors, and so on) to go about finding a determinant?