Red-Black trees are balanced search binary trees. They are named because
nodes can be classified as either red or black. The code we include is
based on "Introduction to Algorithms", second edition, by Cormen,
Leiserson, Rivest and Stein. The library includes routines to insert,
lookup and delete elements in the tree.
A Red black tree is represented as a term t(Nil, Tree)
, where Nil is the
Nil-node, a node shared for each nil-node in the tree. Any node has the
form colour(Left, Key, Value, Right)
, where colour is one of red
or
black
.
- author
- - Vitor Santos Costa, Jan Wielemaker, Samer Abdallah,
Peter Ludemann.
- See also
- - "Introduction to Algorithms", Second Edition Cormen, Leiserson,
Rivest, and Stein, MIT Press
- rb_new(-Tree) is det
- Create a new Red-Black tree Tree.
- deprecated
- - Use rb_empty/1.
- rb_empty(?Tree) is semidet
- Succeeds if Tree is an empty Red-Black tree.
- rb_lookup(+Key, -Value, +Tree) is semidet
- True when Value is associated with Key in the Red-Black tree Tree.
The given Key may include variables, in which case the RB tree is
searched for a key with equivalent, as in (==)/2, variables. Time
complexity is O(log N) in the number of elements in the tree.
- rb_min(+Tree, -Key, -Value) is semidet
- Key is the minimum key in Tree, and is associated with Val.
- rb_max(+Tree, -Key, -Value) is semidet
- Key is the maximal key in Tree, and is associated with Val.
- rb_next(+Tree, +Key, -Next, -Value) is semidet
- Next is the next element after Key in Tree, and is associated with
Val. Fails if Key isn't in Tree or if Key is the maximum key.
- rb_previous(+Tree, +Key, -Previous, -Value) is semidet
- Previous is the previous element after Key in Tree, and is
associated with Val. Fails if Key isn't in Tree or if Key is the
minimum key.
- rb_update(+Tree, +Key, +NewVal, -NewTree) is semidet
- rb_update(+Tree, +Key, ?OldVal, +NewVal, -NewTree) is semidet
- Tree NewTree is tree Tree, but with value for Key associated with
NewVal. Fails if it cannot find Key in Tree.
- rb_apply(+Tree, +Key, :G, -NewTree) is semidet
- If the value associated with key Key is Val0 in Tree, and if
call(G,Val0,ValF)
holds, then NewTree differs from Tree only in that
Key is associated with value ValF in tree NewTree. Fails if it
cannot find Key in Tree, or if call(G,Val0,ValF)
is not satisfiable.
- rb_in(?Key, ?Value, +Tree) is nondet
- True when Key-Value is a key-value pair in red-black tree Tree. Same
as below, but does not materialize the pairs.
rb_visit(Tree, Pairs), member(Key-Value, Pairs)
Leaves a choicepoint, even if Key is instantiated; to avoid a
choicepoint, use rb_lookup/3.
- rb_insert(+Tree, +Key, ?Value, -NewTree) is det
- Add an element with key Key and Value to the tree Tree creating a
new red-black tree NewTree. If Key is a key in Tree, the associated
value is replaced by Value. See also rb_insert_new/4.
- rb_insert_new(+Tree, +Key, ?Value, -NewTree) is semidet
- Add a new element with key Key and Value to the tree Tree creating a
new red-black tree NewTree. Fails if Key is a key in Tree.
- rb_delete(+Tree, +Key, -NewTree)
- rb_delete(+Tree, +Key, -Val, -NewTree)
- Delete element with key Key from the tree Tree, returning the value
Val associated with the key and a new tree NewTree.
Fails if Key is not in Tree.
- rb_del_min(+Tree, -Key, -Val, -NewTree)
- Delete the least element from the tree Tree, returning the key Key,
the value Val associated with the key and a new tree NewTree.
Fails if Tree is empty.
- rb_del_max(+Tree, -Key, -Val, -NewTree)
- Delete the largest element from the tree Tree, returning the key
Key, the value Val associated with the key and a new tree NewTree.
Fails if Tree is empty.
- rb_visit(+Tree, -Pairs) is det
- Pairs is an infix visit of tree Tree, where each element of Pairs is
of the form Key-Value.
- rb_map(+T, :Goal) is semidet
- True if
call(Goal, Value)
is true for all nodes in T.
- rb_map(+Tree, :G, -NewTree) is semidet
- For all nodes Key in the tree Tree, if the value associated with key
Key is Val0 in tree Tree, and if
call(G,Val0,ValF)
holds, then the
value associated with Key in NewTree is ValF. Fails if
call(G,Val0,ValF)
is not satisfiable for all Val0.
- rb_fold(:Goal, +Tree, +State0, -State)
- Fold the given predicate over all the key-value pairs in Tree,
starting with initial state State0 and returning the final state
State. Pred is called as
call(Pred, Key-Value, State1, State2)
Determinism depends on Goal.
- rb_clone(+TreeIn, -TreeOut, -Pairs) is det
- `Clone' the red-back tree TreeIn into a new tree TreeOut with the
same keys as the original but with all values set to unbound values.
Pairs is a list containing all new nodes as pairs K-V.
- rb_partial_map(+Tree, +Keys, :G, -NewTree)
- For all nodes Key in Keys, if the value associated with key Key is
Val0 in tree Tree, and if
call(G,Val0,ValF)
holds, then the value
associated with Key in NewTree is ValF, otherwise it is the value
associated with the key in Tree. Fails if Key isn't in Tree or if
call(G,Val0,ValF)
is not satisfiable for all Val0 in Keys. Assumes
keys are sorted and not repeated (fails if this is not true).
- rb_keys(+Tree, -Keys) is det
- Keys is unified with an ordered list of all keys in the Red-Black
tree Tree.
- list_to_rbtree(+List, -Tree) is det
- Tree is the red-black tree corresponding to the mapping in List,
which should be a list of Key-Value pairs. List should not contain
more than one entry for each distinct key, but this is not validated
by list_to_rbtree/2.
- ord_list_to_rbtree(+List, -Tree) is det
- Tree is the red-black tree corresponding to the mapping in list
List, which should be a list of Key-Value pairs. List should not
contain more than one entry for each distinct key, but this is not
validated by ord_list_to_rbtree/2. List is assumed
to be sorted according to the standard order of terms.
- rb_size(+Tree, -Size) is det
- Size is the number of elements in Tree.
- is_rbtree(@Term) is semidet
- True if Term is a valid Red-Black tree. Processes the entire tree,
checking the coloring of the nodes, the balance and the ordering of
keys. It does not validate that keys are sufficiently instantiated
to ensure the tree remains valid if a key is further instantiated.
Undocumented predicates
The following predicates are exported, but not or incorrectly documented.
- rb_delete(Arg1, Arg2, Arg3, Arg4)
- rb_update(Arg1, Arg2, Arg3, Arg4, Arg5)