Efficient trees : Terminology and Types.
Efficient binary trees address the shortcomings of standard binary search trees by employing mechanisms to maintain balance. This balance ensures that operations like search, insertion, and deletion have a logarithmic time complexity, preventing worst-case scenarios where BSTs can degrade to linear time. These trees automatically reorganize their structure to maintain balance after modifications.
1. AVL Tree
Definition
An AVL tree (named after inventors Adelson-Velsky and Landis) is a self-balancing binary search tree. This means it’s a BST with a specific property that guarantees its balance: for every node in the tree, the height difference between its left and right subtrees is at most 1. This difference is called the balance factor.
AVL trees address a critical weakness of regular BSTs: potential imbalance. In the worst-case scenario, a BST can degenerate into a linked list if elements are inserted in sorted order, leading to O(n) search time. AVL trees prevent this by performing rotations whenever an insertion or deletion operation disrupts the balance factor constraint.
Rotations are local operations that change the structure of the subtree rooted at the unbalanced node, restoring balance without affecting the BST properties. AVL tree rotations and examples are explained in detail in next tutorial.
2. Red-Black Trees
Definition:
A red-black tree is a self-balancing binary search tree where each node has an extra bit representing its “color” (red or black). Specific rules govern the arrangement of red and black nodes, maintaining a roughly balanced tree.
Red-black trees use a set of properties involving node colors and their relationships to ensure that no path from the root to a leaf is more than twice as long as any other path. This relaxed balance constraint simplifies the balancing operations compared to AVL trees, resulting in faster insertion and deletion in many cases, although search might be slightly slower due to a potentially greater height.
Red Black Tree are explained next to AVL Trees tutorial.
3. Splay Trees
Definition:
A splay tree is a self-balancing binary search tree that reorganizes itself after every access operation (search, insert, delete). This reorganization, called “splaying,” moves the accessed node to the root of the tree.
Splay trees don’t enforce a strict balance factor like AVL or red-black trees. Instead, they rely on the splaying operation to bring frequently accessed nodes closer to the root, optimizing for access patterns where certain elements are more likely to be accessed than others.
Play tress are explained in the tutorial next to Red Black Tree.
