The solution in Google+ needs to take the logarithm, and that is O(n) in many 
implementation including the Google+ solution.

I'm highly inspired by the rest of the argument though.

Anyway, my addition: if you allow "0" as a an element of the tree, then you 
always have a complete binary tree, e.g.

4 -> 2, 1 -> 1, 0, 0, 0

There is a nice property also: "sum of numbers in a level + cardinality of 
level" is a constant, including the terminal level. i.e.

4 + 1 = (2+1) + 2 = (1+0+0+0) + 4

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