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since we are only interested in the water at cup i, you can just go back up by tracing the parents instead of tracing the kids. algorithmically it should be < O(n) but i dont know how to prove that. ie
- sharathgeorge September 15, 2011water(cup i ) = water (cup (1stparent(i)) + water (cup(2ndparent(i))
That way you only calculate water for the tree that is responsible for pouring water into cup i.