Answer :
The first node that becomes an Alpha node (balance factor exceeds 1 or -1) during the construction of the AVL tree is 35 after inserting 27. Detailed steps describe how each value is inserted and the resulting rotations needed for balancing. An AVL tree maintains balance after each insertion to ensure search efficiency.
Building an AVL Tree :
An AVL tree is a self-balancing binary search tree where the difference between the heights of the left and right subtrees of any node is no more than one.
Step-by-Step Construction :
- Insert 35: The tree is empty, so 35 becomes the root.
- Insert 49: 49 is greater than 35, so it becomes the right child of 35.
- Insert 22: 22 is less than 35, so it becomes the left child of 35.
- Insert 27: 27 is greater than 22 but less than 35, so it becomes the right child of 22.
- Right subtree of 22 (height 1) exceeds left subtree (height 0) by 1, hence balanced.
- Insert 64: 64 is greater than 35 and 49, so it becomes the right child of 49.
- Right subtree of 49 exceeds left subtree by 1, creating a minor imbalance.
- Insert 60: 60 is less than 64 but greater than 49, so it becomes the left child of 64.
- Height of right subtree of 49 becomes 2. The tree becomes unbalanced with balance factor 2, requiring rotations.
- Perform left rotation on 49. 60 becomes the right child of 35, right of 49, and 49 becomes left child of 60.
The first node that becomes an Alpha node (balance factor exceeds 1 or -1) during insertion is 35 after inserting 27
Creating an AVL tree, the value indicating the first alpha node would be 49 because the alpha node is the node that needs to be rebalanced. A node is basic unit of data structures such as a linked list or tree data structure.
What does AVL tree mean?
AVL tree is a kind of binary search tree. Like a binary search tree, it consists of a "root" node and "leaf" nodes. Each node has at most two children, the left child being smaller than the parent and the right child being larger than the parent. However, binary search trees can be either unbalanced or balanced.
What is the balance factor of the nodes in the AVL tree?
The balance factor for a node in an AVL tree is the height difference between the left and right subtrees of that node. The self-balancing property of the AVL tree is maintained by the balancing factor. The correction factor value must always be -1, 0, or +1.
How can I find a node in the AVL tree?
Start at the root of the tree and compare the key to the node's value. Returns a node if the key is equal to the value. If the key is greater, search from the right child, otherwise continue searching from the left child.
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