Implementing the Rope data structure using binary search trees (splay trees)

Question

In a standard implementation of the Rope data structure using splay trees, the nodes would be ordered according to a rank statistic measuring the position of each one from the start of the string, so the keys normally found in binary search tree would be irrelevant, would they not?

I ask because the keys shown in the graphic below (thanks Wikipedia!) are letters, which would presumably become non-unique once the number of nodes exceeded the length of the chosen alphabet. Wouldn't it be better to use integers or avoid using keys altogether?

Separately, can anyone point me to a good implementation of the logic to recompute rank statistics after each operation?

Presumably, if the index for a split falls within the substring attached to a particular node, say, between "Hel" and "llo_" on the node E above, you would remove the substring from E, split it and reattach it as two children of E. Correct?

Finally, after a certain number of such operations, the tree could, I suppose, end up with as many leaves as letters. What would be the best way to keep track of that and prune the tree (by combining substrings) as necessary?

Thanks!

Answer 1

For what it's worth, you can implement a Rope using Splay Trees by attaching a substring to each node of the binary search tree (not just to the leaf nodes as shown above).

The rank of each node is its size plus the size of its left subtree. But when recomputing ranks during splay operations, you need to remember to walk down the node.left.right branch, too.

If each node records a reference to the substring it represents (cf. the actual substring itself), everything runs faster. That way when a split operation falls within an existing node, you just need to modify the node's attributes to reflect the right part of the substring you want to split, then add another node to represent the left part and merge it with the left subtree.

Done as above, each node records (in addition its left, right and parent attributes etc.) its rank, size (in characters) and the location of the first character it represents in the string you're trying to modify. That way, you never actually modify the initial string: you just do your operations on bits of the tree and reproduce the final string when you're ready by walking it in order.