I need a cheap (max 600$) server pc that is able to do quick c++ algorithms. Any recommendations?

You need a friend who is familiar with computer parts. You can buy a good desktop computer for 600 bux or less, but you need someone to show you how to put it together. Go to newegg.com or tigerdirect.com and discuss your needs with a customer service agent, although your needs don't need much discussion. You can just as well buy a kit with parts already chosen to work together.