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# Module Avltree

### Signature

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.

***************** Points of Ugliness *****************

* compare is passed in to every function where it is used. If you pass a different compare to functions on the same tree, then all bets are off as far as what it does, and it's all your fault. 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 Core_hashtbl's memory overhead isn't higher than INRIA's, even though it uses a tree instead of a list for buckets.

* But you said 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.

* 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 actually), with the same memory overhead, with sane add semantics (the add semantics they used were a performance hack), and with worst case log(N) insertion, lookup, and removal. I'd say that's worth it. But for those of you who will feel morally compelled to put in a CR about this interface. I challenge you to write a better interface, implement a hash table with it, and show that your table has better performance than Core_hashtbl.

type
('k, 'v)
t
= private

We expose `t`

to allow an optimization in Hashtbl that makes iter and fold more than
twice as fast.

It is however private so that `'k`

and `'v`

are invariant. This avoids the following
segfault. The segfault works by creating a tree containing `[`A of string]`

keys,
mutating it to contain `[`A of string | `B of int]`

keys, and then pattern matching
against keys at the first type.

```
let added = ref false in
let tree =
Avltree.add Avltree.empty ~key:0 ~data:(`A "Hello, world!") ~compare
~added ~replace:true
in
let x : (int, [ `A of string ]) Avltree.t = tree in
ignore (Avltree.add tree ~key:0 ~data:(`B 0) ~compare
~added ~replace:true : (_, _) Avltree.t);
match Avltree.find x 0 ~compare:compare with
| None -> assert false
| Some (`A str) -> print_string str (* BOOM! *)
```

val
empty : ('k, 'v) t

val
invariant : ('k, 'v) t -> compare:('k -> 'k -> int) -> unit

check invariants, raise an exception if any invariants fail

val
add : ('k, 'v) t -> replace:bool -> compare:('k -> 'k -> int) -> added:bool Pervasives.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.

val
first : ('k, 'v) t -> ('k
* 'v) option

Returns the first (leftmost) or last (rightmost) element in the tree

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, return 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
mem : ('k, 'v) t -> compare:('k -> 'k -> int) -> 'k -> bool

return true if key is present in the tree, otherwise return false.

val
remove : ('k, 'v) t -> removed:bool Pervasives.ref -> compare:('k -> 'k -> int) -> 'k -> ('k, 'v) t

remove key destructively from the tree if it exists, return 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, or false otherwise.

val
fold : ('k, 'v) t -> init:'a -> f:(key:'k -> data:'v -> 'a -> 'a) -> 'a

fold over the tree

val
iter : ('k, 'v) t -> f:(key:'k -> data:'v -> unit) -> unit

iterate over the tree