This is the final version, or the version I ended on. I could not get it to work 100% on my machine. however, on my friends OSX machine, it worked fine. I am including a screen shot of his computer with the results displayed. There was also erro checking printf's involved, which is why the output in the screen shot is so long. There are two commands to run this. "make run" will run the same input as my friends computer did. "make time" will run different input with the timing included. On my machine, an error says time was not available. I think there may be discrepancies between the cygwin and unix shells. Please advise.