Java algorithm for finding the largest set of independent nodes in a binary tree

Question

By independent nodes, I mean that the returned set cannot contain nodes that are in a direct relationship, the parent and child cannot be included. I tried to use Google without success. I don’t think I have the right search words.

Link, any help would be greatly appreciated. Just started it now.

I need to return the actual set of independent nodes, not just the amount.

Answer 1

You can compute this recursive function using dynamic programming (memoization):

MaxSet(node) = 1 if "node" is a leaf
MaxSet(node) = Max(1 + Sum{ i=0..3: MaxSet(node.Grandchildren[i]) },  
                       Sum{ i=0..1: MaxSet(node.Children[i])      })

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Answer 2

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