rbtrees.pl -- Red black trees

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
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.

rb_previous(+Tree, +Key, -Previous, -Value) is semidet

Previous is the previous element after Key in Tree, and is associated with Val.

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)

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.

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.

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.

rb_visit(+Tree, -Pairs)

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) is det

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)

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. Fails if or if call(G,Val0,ValF) is not satisfiable for all Val0. Assumes keys are not repeated.

rb_keys(+Tree, -Keys)

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.

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. 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 valide Red-Black tree.