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AVL tree

For a long time, self-balancing trees had seemed like magic to me. Earlier this year I put my mind to figuring them out, and on my own came up with the idea of a weight-balanced tree. With a bit of peeking, I then moved on to a height-balanced tree, pretty much an AVL tree. Then I started coding one in pure C, for Real Programmer (TM) cred.

Stage one, achieved some months ago, fulfilled the basic criterion: you could feed it an increasing sequence of keys, and get a beautifully balanced tree back out. Woo! It had problems, though. Most obviously, I concentrated on the balancing part first, so got heights on the fly via a function rather than from cached values. Not exactly computationally efficient. Less obviously, I had a clever-seeming tree-rotation function I'd come up with: "to rotate right: insert root value to the right, copy rightmost left value into root, delete same value from the left tree." Elegant, but O(log(N)), when there are actually O(1) rotations available.

I went back to the project this evening, and got the faster rotations working. It took longer than I expected, because when you do rotations that way, there's complexity: 1->2->3 can be rotated left, but 1->3->2 needs a rotation right (on 3->2) then left, to come out balanced. Turns out that my slower rotation did the correct thing in both cases, so simply replacing my rotate functions wasn't working until I added more logic. Grumble grumble.

I still don't have heights cached, and the whole thing feels like an unholy mess of pointer manipulations (especially with parent points in the tree.) But, progress!

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Damien Sullivan

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September 2017


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