AvlTree is an implementation of a AVL Tree,a self-balancing binary search-tree.

The implementation is basically a port from the implementation in Java by Justin Wheterell.

This implementation provides two custom features usually not present in AVL trees:

1. The methods add, remove, or contains not only accept a value to be added, removed, or tested, but optionally also a compare function to be used in this very invocation only. This comes in handy, if a more efficient compare function can be used in a specific invocation. Example: the dynamically changing search tree of intersecting line segments in the Bentley-Ottman-Algorithm.

2. The tree can (optionally) store multiple values which are equal with respect to the tree ordering, but not identical with respect to Darts identical() function. One application is again the implementation of the Y-structure in the Bentley-Ottman-Algorithm, where multiple overlapping line segments can be handled as equivalence class of line segments.

A simple tree of ints

 // create a tree, and use some methods, use the standard
 // int.compareTo function for ordering
 var tree = new AvlTree<int>();
 tree.addAll(0,1,2);
 print(tree.inorder.toList());  // -> 0,1,2
 tree.remove(2);
 print(tree.inorder.toList());  // -> 0,1
 print(tree.contains(0));       // true

A tree of strings in reverse lexicographic order

// a balanced tree of strings, ordered in reverse lexicographical
// order
var order = (String s1, String s2) => s2.compareTo(s1);
var tree = new AvlTree<String>(compare: order);
tree.addAll("aaa", "zzz");
print(tree.inorder.toList);     // "zzz", "aaa"

A tree of strings, lowercase ordering, with equivalence classes

lowerCaseCompare(s,t) => s.toLowerCase().compareTo(t.toLowerCase());
var tree = new AvlTree<String>(compare:lowerCaseCompare,
    withEquivalenceClasses: true);
tree.addAll("aaa", "zzz", "AAA");
print(tree.smallest);         // -> "aaa", "AAA"