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CGAL : Computational Geometry Algorithms Library in C++ contains a robust implementation of Range Trees; Boost.Icl offers C++ implementations of interval sets and maps. IntervalTree (Python) - a centered interval tree with AVL balancing, compatible with tagged intervals; Interval Tree (C#) - an augmented interval tree, with AVL balancing ...
To split an AVL tree into two smaller trees, those smaller than key k, and those greater than key k, first draw a path from the root by inserting k into the AVL. After this insertion, all values less than k will be found on the left of the path, and all values greater than k will be found on the right.
There is no standard implementation of associative arrays in C, but a 3rd-party library, C Hash Table, with BSD license, is available. [1] Another 3rd-party library, uthash, also creates associative arrays from C structures. A structure represents a value, and one of the structure fields serves as the key. [2]
The order of enumeration is always deterministic for a given set of keys by sorting. This is the case for tree-based implementations, one representative being the <map> container of C++. [16] The order of enumeration is key-independent and is instead based on the order of insertion.
Join follows the right spine of t 1 until a node c which is balanced with t 2. At this point a new node with left child c, root k and right child t 2 is created to replace c. The new node may invalidate the balancing invariant. This can be fixed with rotations. The following is the join algorithms on different balancing schemes. The join ...
Most operations on a binary search tree (BST) take time directly proportional to the height of the tree, so it is desirable to keep the height small. A binary tree with height h can contain at most 2 0 +2 1 +···+2 h = 2 h+1 −1 nodes. It follows that for any tree with n nodes and height h: + And that implies:
Boehm GC is also distributed with a C string handling library called cords. This is similar to ropes in C++ ( trees of constant small arrays), but instead of using reference counting for proper deallocation, it relies on garbage collection to free objects.
The weak AVL tree is defined by the weak AVL rule: Weak AVL rule: all rank differences are 1 or 2, and all leaf nodes have rank 0. Note that weak AVL tree generalizes the AVL tree by allowing for 2,2 type node. A simple proof shows that a weak AVL tree can be colored in a way that represents a red-black tree.