You need to explain these problems better. It's not always clear what we are supposed to do. I guess that at Google Jam they've explained it better, but the link is currently broken. For instance if you give me two types and ask me to alternate between them I can create an infinite sequence...so why should we stop at some point?
I guess that this is the official description https://open.kattis.com/problems/closingtheloop (found it at a blog.) Please copy from there if that's the case. Basically, Each number represents a length of rope that we are tying in a loop, and each knot consumes 1 unit (1/2 unit from each different type). We must answer what the maximum length of rope is possible for this loop. For instance, if we have 1 unit of red rope (type 0) and tie it with one piece of blue rope (type 1), we end up with a loop of zero units (due to the two knots that should not be taken into account for the length).
you only need to substract 1 inside the sum ;-)
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