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Store the last node's-worth of elements separately from the tree itself to allow constant time access and update near the end of the vector. Clojure does this. Nicolas Stucki's version includes a generalized notion of a tail called a 'focus' or 'display', that moves the constant-time accessible portion to most recently accessed. So operations near the same portion of the tree that has been touched most recently will be fast. Do we want this? Maybe.

• method take(n :: Int) :: Tree
• method drop(n :: Int) :: Tree
• method splitAt(idx :: Int) :: Tree

per Matthew's feedback

At the point where you worry about performance, the leaf function may
need to be converted into a macro that constructs a vector more
directly. Right now, leaf will build up a list to receive its
arguments, and then have to apply the vec function to that list.
And then the vec function will also receive the arguments in a fresh
list and apply the #{vector-immutable} function. It's possible that
inlining at the Racket or Chez Scheme level works better than I think,
but I don't think the intermediate list allocations will be optimized
away.

• in utils.rhm, don't wrap racket's vector->immutable-vector in a rhombus function, just export and rename to vec
• make leaf a macro instead of a function

Test concatenating trees of differing heights

The main structure of the code is there, now, but it is not yet working as intended in some ways. The result of some_tree.concat(other_tree).to_list() will always be as expected, but there are performance issues lurking and a lack of thorough testing involving trees of varied sizes as well as trees created through complex-ish series of operations including concats, appends, sets, etc.

• fix #5 may not need fixing, see comments on #5
• needs more thorough testing
  • #7
  • randomized tests
  • test very large trees

as proposed in racket/rhombus-prototype#351

• method get(index)
• method set(index, element)
• method add(element) # Adds to the end of the list
• method insert(index, element)
• method remove(element) # Removes first occurrence of element from list
• method removeAt(index)
• method sublist(start, end) # Returns a view

leftwise-dense nodes should not have sizes arrays. Currently all nodes created via concatenation except leaf nodes end up with sizes arrays. This means some future operations will take the slow path that should not. Example:

> check: Tree(leaf(& List.iota(32)), 32, 0).concat(Tree(leaf(& List.iota(32)), 32, 0)).root.sizes
         ~is #false
    
check: failed
  got: Array(32, 64)
  expected: #false

Note, though, that only the nodes along the join path of the new tree will get sizes arrays always set. So, for example:

> def (t, l, r):
      def l:
        for values(t = Tree()):
          each i: List.iota(32^3)
          t.add(i)
      def r:
        for values(t = Tree()):
          each i: List.iota(32^3)
          t.add(i + 32^3)
      values(l.concat(r), l, r)
      
> values(l.balanced, r.balanced)
#true
#true
> t.root.balanced
#false
> t.root.size
2
> values(t.root.get(0).balanced, t.root.get(1).balanced)
#false
#false
> for values(balanced = #true):
    each i: 0 .. t.root.get(0).size - 1
    balanced && t.root.get(0).get(i).balanced
    
#true
> t.root.get(t.root.size - 1).balanced
#false
> for values(balanced = #true):
    each i: 1 .. t.root.get(1).size
    balanced && t.root.get(1).get(i).balanced
    
#true
> t.root.get(1).get(0).balanced
#false```

For ease of testing, it's nice to be able to change the branch factor / max width of a tree (it's much easier to write out a manual test for a 2 or 4-way branching tree than a 32-way branching tree), but in the end, this configuration capability is probably not needed and also probably negatively affects performance. What Clojure does is maintain separate copies of the code where one is parameterized and one is not (see here). We could do something like that, if maintaining parameterized capability is desired (maybe for future dev work / testing, maybe there is some actual production code use case)

• change [this stuff] (https://github.com/OxSon/rrb.rhm/blob/use_array/rrbtree.rhm#L12) to just be constants rather than Parameters
• adjust tests to remove with_shift_inc(....) stuff