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

Question

By independent nodes, I mean that the returned set can not contain nodes that are in immediate relations, parent and child cannot both be included. I tried to use Google, wi

Answer 1

I would take-and-remove all leaves first while marking their parents as not-to-take, then remove all leaves that are marked until no such leaves are left, then recurse until the tree is empty. I don't have a proof that this always produces the largest possible set, but I believe it should.