Final answer:
The maximum possible height for an AVL tree with 10 nodes is 4. The AVL tree balancing concept is applied to ensure the tree is as flat as possible while maintaining the balance criterion. An example includes a balanced AVL tree structure with specific node values demonstrating the maximum height.
Step-by-step explanation:
To determine the maximum possible height of an AVL tree with 10 nodes, we need to apply the concept of AVL tree balancing. An AVL tree is a self-balancing binary search tree where the difference between heights of left and right subtrees cannot be more than one for all nodes.The maximum height (h) of an AVL tree with n nodes can be found using the Fibonacci sequence: n >= F_{h+2} - 1, where F is the Fibonacci number. For 10 nodes, we find the smallest Fibonacci number greater than 10+1=11, which is 13 (the 7th Fibonacci number). Therefore, the maximum height is 5 (since Fibonacci sequence starts from index 0). However, with 10 nodes, the maximum height is 4, not reaching the theoretical maximum.
An example of an AVL tree with 10 nodes and maximum height of 4 is:
- Root: 10
- Left subtree (height 3):
- Right subtree (height 2):
The nodes are balanced to maintain the AVL property, ensuring that this tree has a maximum height with 10 nodes.An AVL tree is a balanced binary search tree in which the heights of the left and right subtrees of any node differ by at most one. To find the maximum possible height for an AVL tree with 10 nodes, we can use the formula:height = log2(n+1) - 1.Using this formula, we can calculate the height for 10 nodes:height = log2(10+1) - 1 = 3.To draw an AVL tree with 10 nodes and the maximum possible height of 3, we can arrange the nodes in a way that balances the tree.