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.
Caveats
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 {mutable left : ('k, 'v) t;key : 'k;mutable value : 'v;mutable height : int;mutable right : ('k, 'v) t;
}| Leaf of {key : 'k;mutable value : 'v;
}
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 is_empty : (_, _) t -> boolval invariant : ('k, 'v) t -> compare:('k -> 'k -> int) -> unitChecks invariants, raising an exception if any invariants fail.
val add :
('k, 'v) t ->
replace:bool ->
compare:('k -> 'k -> int) ->
added:bool Stdlib.ref ->
key:'k ->
data:'v ->
('k, 'v) tAdds 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) optionval last : ('k, 'v) t -> ('k * 'v) optionval find : ('k, 'v) t -> compare:('k -> 'k -> int) -> 'k -> 'v optionIf 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) ->
'afind_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 find_and_call1 :
('k, 'v) t ->
compare:('k -> 'k -> int) ->
'k ->
a:'a ->
if_found:('v -> 'a -> 'b) ->
if_not_found:('k -> 'a -> 'b) ->
'bval find_and_call2 :
('k, 'v) t ->
compare:('k -> 'k -> int) ->
'k ->
a:'a ->
b:'b ->
if_found:('v -> 'a -> 'b -> 'c) ->
if_not_found:('k -> 'a -> 'b -> 'c) ->
'cval findi_and_call :
('k, 'v) t ->
compare:('k -> 'k -> int) ->
'k ->
if_found:(key:'k -> data:'v -> 'a) ->
if_not_found:('k -> 'a) ->
'aval findi_and_call1 :
('k, 'v) t ->
compare:('k -> 'k -> int) ->
'k ->
a:'a ->
if_found:(key:'k -> data:'v -> 'a -> 'b) ->
if_not_found:('k -> 'a -> 'b) ->
'bval findi_and_call2 :
('k, 'v) t ->
compare:('k -> 'k -> int) ->
'k ->
a:'a ->
b:'b ->
if_found:(key:'k -> data:'v -> 'a -> 'b -> 'c) ->
if_not_found:('k -> 'a -> 'b -> 'c) ->
'cval mem : ('k, 'v) t -> compare:('k -> 'k -> int) -> 'k -> boolReturns true if key is present in the tree, and false otherwise.
val remove :
('k, 'v) t ->
removed:bool Stdlib.ref ->
compare:('k -> 'k -> int) ->
'k ->
('k, 'v) tRemoves 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.
val fold :
('k, 'v) t ->
init:'acc ->
f:(key:'k -> data:'v -> 'acc -> 'acc) ->
'accval iter : ('k, 'v) t -> f:(key:'k -> data:'v -> unit) -> unitval mapi_inplace : ('k, 'v) t -> f:(key:'k -> data:'v -> 'v) -> unitMap over the the tree, changing the data in place.
val choose_exn : ('k, 'v) t -> 'k * 'v