gb_trees(3)

🦋 gb_trees(3) 🦋

Erlang Module Definition — yes bestie, we are deep in the Erlang manual pages and this one is about gb_trees, the general balanced tree module 💖

---

✨ NAME ✨

gb_trees — General balanced trees. That's it, that's the name section, and honestly it ate. 👑

🌸 DESCRIPTION 🌸

okay so, this module hands you Prof. Arne Andersson's General Balanced Trees 🎀 and the flex here is real: they have no storage overhead compared to unbalanced binary trees, and their performance is better than AVL trees. Not me hyping a data structure at 2am but here we are 💅

One thing you need to internalize fr fr: this module considers two keys as different if and only if they do not compare equal (==). That's the vibe. Key comparison = ==, no cap.

🧚 Data Structure

Trees and iterators here are built using opaque data structures — and that means you should not be pattern-matching them from outside this module. Don't peek behind the curtain, bestie, it's not for you 🙈

There is no attempt to balance trees after deletions. As deletions do not increase the height of a tree, this should be OK. 🌸

And the lore drop: the original balance condition h(T) <= ceil(c * log(|T|)) has been changed to the similar (but not quite equivalent) condition 2 ^ h(T) <= |T| ^ c. This should also be OK. ✨

See Also

dict, gb_sets, maps

---

🎀 DATA TYPES 🎀

iter() :: iter(_, _).

-opaque iter(Key, Value)

A general balanced tree iterator. Very demure, very opaque 💜

tree() :: tree(_, _).

-opaque tree(Key, Value)

A general balanced tree. The main character of this entire page, obviously 👑

---

💖 FUNCTIONS 💖

balance(Tree1) -> Tree2 when Tree1 :: tree(Key, Value), Tree2 :: tree(Key, Value).

Rebalances Tree1. 🔄

Note that this is rarely necessary, but can be motivated when many nodes have been deleted from the tree without further insertions. Rebalancing can then be forced to minimize lookup times, as deletion does not rebalance the tree. So like, if you've been deleting and deleting and never inserting, this is your moment to scrub the timeline 🧼

Examples

1> Tree1 = gb_trees:from_list([{I,2*I} || I <- lists:seq(1, 100)]).
2> Delete = fun gb_trees:delete/2.
3> Tree2 = lists:foldl(Delete, Tree1, lists:seq(1, 50)).
4> gb_trees:size(Tree2).
50
5> Tree3 = gb_trees:balance(Tree2).

delete(Key, Tree1) -> Tree2 when Tree1 :: tree(Key, Value), Tree2 :: tree(Key, Value).

Removes the node with key Key from Tree1, returning the new tree — and it raises an exception if Key is not present 🚨 so no, it will not just quietly pretend everything is fine. It's giving consequences.

Examples

1> Tree1 = gb_trees:from_list([{a,1},{b,2}]).
2> Tree2 = gb_trees:delete(a, Tree1).
3> gb_trees:to_list(Tree2).
[{b,2}]

delete_any(Key, Tree1) -> Tree2 when Tree1 :: tree(Key, Value), Tree2 :: tree(Key, Value).

The chill version of delete 💅 Removes the node with key Key from Tree1 if present and returns the resulting tree; otherwise, returns Tree1 unchanged. No drama, no exception, just vibes.

Examples

1> Tree1 = gb_trees:from_list([{a,1},{b,2}]).
2> Tree2 = gb_trees:delete_any(a, Tree1).
3> gb_trees:to_list(Tree2).
[{b,2}]
4> Tree3 = gb_trees:delete_any(z, Tree2).
5> Tree2 == Tree3.
true

empty() -> tree(none(), none()).

Returns a brand new empty tree 🌱 starter pack, immaculate, nothing in it.

Examples

1> gb_trees:to_list(gb_trees:empty()).
[]

enter(Key, Value, Tree1) -> Tree2 when Tree1 :: tree(Key, Value), Tree2 :: tree(Key, Value).

The "insert or update, idc which" icon 🌈 Inserts Key with value Value into Tree1 if not present, or updates the value for Key to Value if present; returns the new tree. Either way you're leaving with a tree. Slay.

Examples

1> Tree1 = gb_trees:from_list([{a,1},{b,2}]).
2> Tree2 = gb_trees:enter(c, 10, Tree1).
3> Tree3 = gb_trees:enter(a, 100, Tree2).
4> gb_trees:to_list(Tree3).
[{a,100},{b,2},{c,10}]

from_list(List) -> Tree when List :: [{Key, Value}], Tree :: tree(Key, Value).

Returns a tree of the key-value tuples in List, where List can be unordered and can contain duplicate keys 🫶 so you can just dump your chaos in here and it'll sort itself out. Queen behavior.

Examples

1> Unordered = [{x, 1}, {y, 2}, {a, 3}, {x, 4}, {y, 5}, {b, 6}].
2> gb_trees:to_list(gb_trees:from_list(Unordered)).
[{a,3},{b,6},{x,4},{y,5}]

from_orddict(List) -> Tree when List :: [{Key, Value}], Tree :: tree(Key, Value).

Turns an ordered list List of key-value tuples into a tree. ✨

Important bestie: the list must not contain duplicate keys. No duplicates, I'm serious, do not test me 🙅

Examples

1> Tree = gb_trees:from_orddict([{a,1},{b,2}]).
2> gb_trees:to_list(Tree).
[{a,1},{b,2}]

get(Key, Tree) -> Value when Tree :: tree(Key, Value).

Retrieves the value stored with Key in Tree — and raises an exception if Key is not present 😭 no soft landings here, it's all or nothing.

Examples

1> Tree = gb_trees:from_list([{a,1},{b,2}]).
2> gb_trees:get(b, Tree).
2

insert(Key, Value, Tree1) -> Tree2 when Tree1 :: tree(Key, Value), Tree2 :: tree(Key, Value).

Inserts Key with value Value into Tree1, returning the new tree — and it raises an exception if Key is already present 💀 because duplicates are not the move. Use enter if you want the flexible one.

Examples

1> Tree1 = gb_trees:from_list([{a,1},{b,2}]).
2> Tree2 = gb_trees:insert(c, 10, Tree1).
3> gb_trees:to_list(Tree2).
[{a,1},{b,2},{c,10}]

is_defined(Key, Tree) -> boolean() when Tree :: tree(Key, Value :: term()).

Returns true if Key is present in Tree; otherwise, returns false. Simple. Clean. A yes-or-no girlie ✨

Examples

1> Tree = gb_trees:from_list([{a,1},{b,2},{c,3}]).
2> gb_trees:is_defined(a, Tree).
true
3> gb_trees:is_defined(x, Tree).
false

is_empty(Tree) -> boolean() when Tree :: tree().

Returns true if Tree is an empty tree; otherwise, returns false. Vibe check on your tree 🌸

Examples

1> gb_trees:is_empty(gb_trees:empty()).
true
2> gb_trees:is_empty(gb_trees:from_list([{a,99}])).
false

iterator(Tree, Order) -> Iter when Tree :: tree(Key, Value), Iter :: iter(Key, Value), Order :: ordered | reversed.

Returns an iterator that can be used for traversing the entries of Tree in either ordered or reversed direction; see next/1. 🦋

And the tech tea: the implementation is very efficient — traversing the whole tree using next/1 is only slightly slower than getting the list of all elements using to_list/1 and traversing that. The main advantage of the iterator approach is that it avoids building the complete list of all elements in memory at once. Memory? Never met her. 💅

Examples

1> Tree = gb_trees:from_list([{a,1},{b,2},{c,3}]).
2> Iter0 = gb_trees:iterator(Tree, ordered).
3> {a,1,Iter1} = gb_trees:next(Iter0).
4> RevIter0 = gb_trees:iterator(Tree, reversed).
5> {c,3,RevIter1} = gb_trees:next(RevIter0).

iterator_from(Key, Tree, Order) -> Iter when Tree :: tree(Key, Value), Iter :: iter(Key, Value), Order :: ordered | reversed.

Returns an iterator over the entries of Tree in the given Order, starting from Key or, if absent, the first key that follows in the iteration order, if any; see next/1. 🎯 mid-tree entry, no problem.

Examples

1> Tree = gb_trees:from_list([{a,1},{b,2},{c,3},{d,4}]).
2> Iter0 = gb_trees:iterator_from(aa, Tree, ordered).
3> {b,2,Iter1} = gb_trees:next(Iter0).
4> RevIter0 = gb_trees:iterator_from(c, Tree, reversed).
5> {c,3,RevIter1} = gb_trees:next(RevIter0).
6> {b,2,RevIter2} = gb_trees:next(RevIter1).

keys(Tree) -> [Key] when Tree :: tree(Key, Value :: term()).

Returns the keys in Tree as an ordered list. Just the keys, no values invited, they're not on the guest list 🎀

Examples

1> Tree = gb_trees:from_list([{a,1},{b,2},{c,3}]).
2> gb_trees:keys(Tree).
[a,b,c]
3> gb_trees:keys(gb_trees:empty()).
[]

larger(Key1, Tree) -> none | {Key2, Value} when Key1 :: Key, Key2 :: Key, Tree :: tree(Key, Value).

Returns {Key2, Value}, where Key2 is the least key strictly greater than Key1, and Value is the value associated with this key. 📈

Returns none if no such pair exists. 🫥

Examples

1> Tree = gb_trees:from_list([{a,1},{b,2},{c,3}]).
2> gb_trees:larger(c, Tree).
none
3> gb_trees:larger(bb, Tree).
{c,3}
4> gb_trees:larger(a, Tree).
{b,2}

largest(Tree) -> {Key, Value} when Tree :: tree(Key, Value).

Returns {Key, Value}, where Key is the largest key in Tree, and Value is the value associated with this key. 👑

Assumes that the tree is not empty. Do not call this on an empty tree bestie, I'm begging 🙏

Examples

1> Tree = gb_trees:from_list([{a,1},{b,2},{c,3}]).
2> gb_trees:largest(Tree).
{c,3}

lookup(Key, Tree) -> none | {value, Value} when Tree :: tree(Key, Value).

Looks up Key in Tree and returns {value, Value} if found, or none if not present. No exceptions, just answers 🔍✨ the calm one.

Examples

1> Tree = gb_trees:from_list([{a,1},{b,2},{c,3}]).
2> gb_trees:lookup(a, Tree).
{value,1}
3> gb_trees:lookup(z, Tree).
none

map(Function, Tree1) -> Tree2 when Function :: fun((K :: Key, V1 :: Value1) -> V2 :: Value2), Tree1 :: tree(Key, Value1), Tree2 :: tree(Key, Value2).

Maps Function(K, V1) -> V2 to all key-value pairs of tree Tree1, returning a new tree Tree2 with the same set of keys as Tree1 and the new set of values V2. Glow-up for the values only, the keys are staying exactly as they are 💅🌈

Examples

1> Tree0 = gb_trees:from_list([{a,1},{b,2},{c,3}]).
2> Tree1 = gb_trees:map(fun(_, V) -> 2 * V end, Tree0).
3> gb_trees:to_list(Tree1).
[{a,2},{b,4},{c,6}]

next(Iter1) -> none | {Key, Value, Iter2} when Iter1 :: iter(Key, Value), Iter2 :: iter(Key, Value).

Returns {Key, Value, Iter2}, where Key is the next key referred to by iterator Iter1, and Iter2 is the new iterator to be used for traversing the remaining nodes — or the atom none if no nodes remain. 🦋 Little step-by-step girly.

Examples

1> Tree = gb_trees:from_list([{a,1},{b,2},{c,3}]).
2> Iter0 = gb_trees:iterator(Tree).
3> {a,1,Iter1} = gb_trees:next(Iter0).
4> {b,2,Iter2} = gb_trees:next(Iter1).
5> {c,3,Iter3} = gb_trees:next(Iter2).
6> none = gb_trees:next(Iter3).

size(Tree) -> non_neg_integer() when Tree :: tree().

Returns the number of nodes in Tree. Headcount, but for trees 🧮

Examples

1> gb_trees:size(gb_trees:empty()).
0
2> gb_trees:size(gb_trees:from_list([{a,1},{b,2}])).
2

smaller(Key1, Tree) -> none | {Key2, Value} when Key1 :: Key, Key2 :: Key, Tree :: tree(Key, Value).

okay so continuing smaller/2: it returns {Key2, Value}, where Key2 is the greatest key strictly less than Key1, and Value is the value associated with this key. If no such pair exists, you get none. fr fr, no cap. 💅

Examples ✨

1> Tree = gb_trees:from_list([{a,1},{b,2},{c,3}]).
2> gb_trees:smaller(c, Tree).
{b,2}
3> gb_trees:smaller(bb, Tree).
{b,2}
4> gb_trees:smaller(a, Tree).
none

---

smallest(Tree) -> {Key, Value} 👑

when Tree :: tree(Key, Value).

Returns {Key, Value}, where Key is the smallest key in Tree, and Value is the value associated with this key.

⚠️ Assumes that the tree is not empty. Do not run this on an empty tree, bestie — that is not the vibe.

Examples 🦋

1> Tree = gb_trees:from_list([{a,1},{b,2},{c,3}]).
2> gb_trees:smallest(Tree).
{a,1}

take(Key, Tree1) -> {Value, Tree2} 🎀

when

Tree1 :: tree(Key, _),
Tree2 :: tree(Key, _),
Key :: term(),
Value :: term().

Returns a value Value from the node with key Key and a new tree Tree2 with that node removed.

⚠️ Assumes that Key is present in the tree. If it's not? That's a whole different situation, okay.

Examples 💖

1> Tree0 = gb_trees:from_list([{a,1},{b,2},{c,3}]).
2> {Value,Tree1} = gb_trees:take(b, Tree0).
3> Value.
2
4> gb_trees:to_list(Tree1).
[{a,1},{c,3}]

take_any(Key, Tree1) -> {Value, Tree2} | error 🌈

when

Tree1 :: tree(Key, _),
Tree2 :: tree(Key, _),
Key :: term(),
Value :: term().

Returns a value Value from the node with key Key and a new tree Tree2 with that node removed; returns error if Key is not present in Tree1.

No assumptions, she's flexible. 😌

Examples ⭐

1> Tree0 = gb_trees:from_list([{a,1},{b,2},{c,3}]).
2> {Value,Tree1} = gb_trees:take_any(b, Tree0).
3> Value.
2
4> gb_trees:to_list(Tree1).
[{a,1},{c,3}]
5> gb_trees:take_any(x, Tree0).
error

take_largest(Tree1) -> {Key, Value, Tree2} 🔥

when

Tree1 :: tree(Key, Value),
Tree2 :: tree(Key, Value).

Returns {Key, Value, Tree2}, where Key is the largest key in Tree1, Value is the value associated with this key, and Tree2 is this tree with the corresponding node deleted.

⚠️ Assumes that the tree is not empty. Empty tree? Absolutely not, bestie.

Examples 👑

1> Tree0 = gb_trees:from_list([{a,1},{b,2},{c,3}]).
2> {Key,Value,Tree1} = gb_trees:take_largest(Tree0).
3> Key.
c
4> Value.
3
5> gb_trees:to_list(Tree1).
[{a,1},{b,2}]

take_smallest(Tree1) -> {Key, Value, Tree2} 🌸

when

Tree1 :: tree(Key, Value),
Tree2 :: tree(Key, Value).

Returns {Key, Value, Tree2}, where Key is the smallest key in Tree1, Value is the value associated with that key, and Tree2 is the tree with the corresponding node removed.

⚠️ Assumes that the tree is not empty. Same energy as above: do not test fate.

Examples 🧚

1> Tree0 = gb_trees:from_list([{a,1},{b,2},{c,3}]).
2> {Key,Value,Tree1} = gb_trees:take_smallest(Tree0).
3> Key.
a
4> Value.
1
5> gb_trees:to_list(Tree1).
[{b,2},{c,3}]

to_list(Tree) -> [{Key, Value}] 📝

when Tree :: tree(Key, Value).

Converts a tree into an ordered list of key-value tuples. Slay.

Examples 💜

1> Tree = gb_trees:from_list([{a,1},{b,2},{c,3}]).
2> gb_trees:to_list(Tree).
[{a,1},{b,2},{c,3}]
3> gb_trees:to_list(gb_trees:empty()).
[]

update(Key, Value, Tree1) -> Tree2 🫶

when

Tree1 :: tree(Key, Value), Tree2 :: tree(Key,
Value).

Updates Key to value Value in Tree1 and returns the new tree.

⚠️ Assumes that the key is present in the tree. If it's not present, this is not the function you're looking for, iykyk.

Examples ✨

1> Tree1 = gb_trees:from_list([{a,1},{b,2}]).
2> Tree2 = gb_trees:update(a, 99, Tree1).
3> gb_trees:to_list(Tree2).
[{a,99},{b,2}]

values(Tree) -> [Value] 🍓

when Tree :: tree(Key :: term(), Value).

Returns the values in Tree as an ordered list, sorted by their corresponding keys.

Duplicates are not removed. They stay. Periodt.

Examples 🌟

1> Tree = gb_trees:from_list([{a,1},{b,2},{c,3},{d,1}]).
2> gb_trees:values(Tree).
[1,2,3,1]

---

and that's the whole page, bestie. the footer says Ericsson AB · stdlib 8.0.4 · gb_trees(3) — date wasn't in this chunk, but the energy is timeless. bye, go balance your trees 💖