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Petr For the TopCoder problem, mentioned, I'm unable to prove this part:
However, we still have the freedom of choosing which pair of green and red ends we use for reducing the problem to size n-1. If b>0, then we will choose which green end is one of the red ends of the first green-red string paired with.
If we delay merging green-green strings with red-red strings until the end, how do we prove that the answer doesn't change? Playing around with the DP recurrence didn't help.
Thanks for your help!