I've been playing with a RBT visualizer and don't understand how the following is considered height-balanced. The wikipedia article claims that if the RBT properties are satisfied, then the height of the farthest leaf is no greater than twice the height of height of the closest leaf. From my understanding, the below would violate this property, even if the RBT properties are satisfied (the depth of 1 is 1 and the depth of 6 is 3). Where is my logic flawed here?
How is this RBT considered balanced?
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From the Wikipedia article:
The diagram you've included in your question has omitted these
NILnodes, but they are relevant for the determination of balanced. Using the rule you describe ("the path from the root to the farthest leaf is no more than twice as long as the path from the root to the nearest leaf"), the path from the root to the nearest leaf has a distance of two (not one), and the path from the root to the farthest leaf has a distance of four (not three).Since four is not more than twice two, this tree complies with the "balanced" rule.