Structural Sharing in Scala Vector

Question

Structural sharing in Scala List is straightforward and easy to understand. But Scala Vector is a more complicated data structure than a list. How is structural sharing achieved in Scala Vector?

Answer 1

Vector is basically a tree (trie) with 32-wide branching at each level. If you have a Vector of, say, 3000 elements and you want to index element 2045, for example, which converts to 100000010101 in binary, it will decompose it into 5-bit blocks to use as indices into the tree: 10 (i.e. 2) in the first branch then 00000 (i.e. 0) in the next, and finally 10101 (i.e. 21) in the terminal branch, and then there's the data.

Given this structure, it's easy to see how to structurally share things: you can share any sub-trees that aren't changed. So if you make a new vector with a different element 2045, you have to change not all 3000 elements but recreate "only" three arrays of size 32: the terminal one is replaced by a copy with its element 21 updated; then its parent has to be replaced by a copy with this new child in index 0; then its parent has to be replaced with the correct subtree in index 2.

Now, this provides quite a lot of structural sharing as long as you have far more than 32 elements in your vector, but it's still a pretty big overhead. Because of this, additions to the end of the vector are special-cased so that you just add to the existing array. The old Vectors still point to that array, but they think the end is earlier (and that part is unchanged) so it works out okay.

There's a more complex but similar scheme to allow addition at the front of a vector in a similar fashion (basically, by leaving space at the front and keeping track of where to point via indices and offsets in addition to the indexing scheme).

The trick as implemented doesn't work to allow alternating addition to both front and back, though, so there you effectively rebuild the trees every addition. Making a version with even better structural sharing would be possible, but it would probably be a bit slower to access.