A low-level, mutable AVL tree.
It is not intended to be used directly by casual users. It is used for implementing other data structures. The interface is somewhat ugly, and it's that way for a reason: the goal of this module is minimum memory overhead and maximum performance.
1. compare
is passed to every function where it is used. If you pass a different
compare
to functions on the same tree, then behavior is indeterminate. Why? Because
otherwise we'd need a top-level record to store compare
, and when building a hash
table, or other structure, that little t
is a block that increases memory
overhead. However, if an empty tree is just a constructor Empty
, then it's just a
number, and uses no extra memory beyond the array bucket that holds it. That's the
first secret of how Hashtbl's memory overhead isn't higher than INRIA's, even though
it uses a tree instead of a list for buckets.
2. But if it's mutable, why do all the "mutators" return t
? Answer: it is mutable,
but the root node might change due to balancing. Since we have no top-level record to
hold the current root node (see point 1), you have to do it. If you fail to do it, and
use an old root node, you're responsible for the (sure to be nasty) consequences.
3. What on earth is up with the ~removed
argument to some functions? See point 1:
since there is no top-level node, it isn't possible to keep track of how many nodes
are in the tree unless each mutator tells you whether or not it added or removed a
node (vs. replacing an existing one). If you intend to keep a count (as you must in a
hash table), then you will need to pay attention to this flag.
After all this, you're probably asking yourself whether all these hacks are worth it. Yes! They are! With them, we built a hash table that is faster than INRIA's (no small feat) with the same memory overhead, sane add semantics (the add semantics they used were a performance hack), and worst-case log(N) insertion, lookup, and removal.
type ('k, 'v) t
= private
| Empty | |||||
| Node of {
}
| |||||
| Leaf of {
}
|
We expose t
to allow an optimization in Hashtbl that makes iter and fold more than
twice as fast. We keep the type private to reduce opportunities for external code to
violate avltree invariants.
val empty : ('k, 'v) t
val invariant : ('k, 'v) t ‑> compare:('k ‑> 'k ‑> int) ‑> unit
Checks invariants, raising an exception if any invariants fail.
val add : ('k, 'v) t ‑> replace:bool ‑> compare:('k ‑> 'k ‑> int) ‑> added:bool Base__.Import.ref ‑> key:'k ‑> data:'v ‑> ('k, 'v) t
Adds the specified key and data to the tree destructively (previous t
's are no
longer valid) using the specified comparison function. O(log(N)) time, O(1) space.
The returned t
is the new root node of the tree, and should be used on all further
calls to any other function in this module. The bool ref
, added, will be set to
true
if a new node is added to the tree, or false
if an existing node is replaced
(in the case that the key already exists).
If replace
(default true) is true then add
will overwrite any existing mapping for
key
. If replace
is false, and there is an existing mapping for key, then add
has
no effect.
Returns the first (leftmost) or last (rightmost) element in the tree.
val first : ('k, 'v) t ‑> ('k * 'v) option
val last : ('k, 'v) t ‑> ('k * 'v) option
val find : ('k, 'v) t ‑> compare:('k ‑> 'k ‑> int) ‑> 'k ‑> 'v option
If the specified key exists in the tree, returns the corresponding value. O(log(N)) time and O(1) space.
val find_and_call : ('k, 'v) t ‑> compare:('k ‑> 'k ‑> int) ‑> 'k ‑> if_found:('v ‑> 'a) ‑> if_not_found:('k ‑> 'a) ‑> 'a
find_and_call t ~compare k ~if_found ~if_not_found
is equivalent to:
match find t ~compare k with Some v -> if_found v | None -> if_not_found k
except that it doesn't allocate the option.
val findi_and_call : ('k, 'v) t ‑> compare:('k ‑> 'k ‑> int) ‑> 'k ‑> if_found:(key:'k ‑> data:'v ‑> 'a) ‑> if_not_found:('k ‑> 'a) ‑> 'a
val mem : ('k, 'v) t ‑> compare:('k ‑> 'k ‑> int) ‑> 'k ‑> bool
Returns true if key is present in the tree, and false otherwise.
val remove : ('k, 'v) t ‑> removed:bool Base__.Import.ref ‑> compare:('k ‑> 'k ‑> int) ‑> 'k ‑> ('k, 'v) t
Removes key destructively from the tree if it exists, returning the new root node.
Previous root nodes are not usable anymore; do so at your peril. The removed
ref
will be set to true if a node was actually removed, and false otherwise.