I've just built a self-balancing tree (red-black) in Java (language should be irrelevant for this question though), and I'm trying to come up with a good means of testing that it's properly balanced. I've tested all the basic tree operations, but I can't think of a way to test that it is indeed well and truly balanced. I've tried inserting a large dictionary of words, both pre-sorted and un-sorted. With a balanced tree, those should take roughly the same amount of time, but an unbalanced tree would take significantly longer on the already-sorted list. But I don't know how to go about testing for that in any reasonable, reproducible way. (I've tried doing millisecond tests on these, but there's no noticeable difference - probably because my source data is too small.) Is there a better way to be sure that the tree is really balanced? Say, by looking at the tree after it's created and seeing how deep it goes? (That is, without modifying the tree itself by adding a depth field to each node, which is just wasteful if you don't need it for anything other than testing.)
