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  • "Depth first" means that the parents will have to know their children - seems that is what the OP is trying to avoid. And your second approach needs to have a method for finding the common ancestor of any two nodes, but you did not write anything how to do this programmatically, so IMHO it does not give an answer to the original question. Commented Feb 3, 2012 at 13:56
  • @JanHudec and DocBrown, Regardless, this answer gave me a lot to think about and set me off in the right direction. I found a some quick and dirty Tree and Node classes online that take order branches with a comparator. I am currently playing with that so I can build a tree and then just walk it to find out how far any one object is from another in my higher order comparator. The only drawback is that everytime I insert a new object into the unordered list, I need to rebuild the tree. Such is life, premature optimization is the root of all evils. Commented Feb 3, 2012 at 14:58
  • @maple_shaft: Well, you don't have to rebuild the tree when an item is added, you only need to insert the new item into it. Commented Feb 6, 2012 at 7:45