For the AVL Tree what values could you insert to cause a right-right imbalance and at which node does the imbalance occur? Please show and explain based on the tree provided.
For the AVL Tree what values could you insert to cause a right-right imbalance and at which node does the imbalance occur? Please show and explain based on the tree provided.
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For the AVL Tree what values could you insert to cause a right-right imbalance and at which node does the imbalance occur?
Please show and explain based on the tree provided.
Transcribed Image Text:The diagram illustrates a binary search tree (BST), a data structure used in computer science to facilitate fast data retrieval and organization. Below is a detailed description of the tree structure:
- The root of the tree is the node with the value 10.
- The left subtree of the root contains:
- Node 5, which branches into:
- Node 2 on the left.
- Node 8 on the right, with Node 13 further branching from Node 15 on the left.
- The right subtree of the root contains:
- Node 20, which branches into:
- Node 15 on the left, with further branches:
- Node 13 on the left.
- Node 17 on the right, which branches into:
- Node 18 on the right.
- Node 25 on the right, which branches into:
- Node 23 on the left.
- Node 30 on the right.
The binary search tree ensures that for each node, all values in the left subtree are smaller, and all values in the right subtree are larger, relative to the node's value. This order aids in efficient search operations, typically achieving a time complexity of O(log n) for balanced trees.
Expert Solution
Step 1: Introduction
AVL tree is a type of self balanced binary tree which contains balancing factor for each node as 1,-1 or 0. Balancing factor is the height of left sub tree minus right sub tree. If any node contains balancing factor other than -1, 1 or 0 then it is said to be imbalanced.
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