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Avl Tree Builder
AVL Tree. 1. Algorithms AVL Tree. Balanced binary tree ● The disadvantage of a binary search tree is that its height can be as large as N-1 ● This means that the time needed to perform insertion and deletion and many other operations can be O(N) in the worst case ● We want a tree with small height ● A binary tree with N node has height at least (log N) ● Thus, our goal is to keep the height of a binary search tree O(log N) ● Such trees are called balanced binary search trees. Examples are AVL tree, red-black tree. Binary Search Tree - Best Time ● All BST operations are O(h), where d is tree depth ● minimum d is for a binary tree with N nodes ■ What is the best case tree? ■ What is the worst case tree?
Avl & Software
● So, best case running time of BST operations is O(log N) 2h log N. Binary Search Tree - Worst Time ● Worst case running time is O(N) ■ What happens when you Insert elements in ascending order? ○ Insert: 2, 4, 6, 8, 10, 12 into an empty BST ■ Problem: Lack of “balance”: ○ compare depths of left and right subtree ■ Unbalanced degenerate tree. Balanced and unbalanced BST 4 2 5 1 3 1 5 2 4 3 7 6 4 2 6 5 71 3 Is this “balanced”?