Show the process of inserting 9, 1, 2, 8, 10, 5, 4, 3, 7, 6 into an initially empty AVL tree. Then the root is deleted and replaced by the smallest key in the right subtree. Show the tree after each insertion, deletion, and rotation. Indicate the type of each rotation.
Show the process of inserting 9, 1, 2, 8, 10, 5, 4, 3, 7, 6 into an initially empty AVL tree. Then the root is deleted and replaced by the smallest key in the right subtree. Show the tree after each insertion, deletion, and rotation. Indicate the type of each rotation.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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These problems need to be solved using java coding
![4. The depth of a node is the length of the unique path from the root to the node. Consider a
full binary search tree with height h and N = 24+1 – 1 nodes. What is the average depth of
the N nodes?
5. Show the process of inserting 9, 1, 2, 8, 10, 5, 4, 3, 7, 6 into an initially empty AVL tree.
Then the root is deleted and replaced by the smallest key in the right subtree. Show the tree
after each insertion, deletion, and rotation. Indicate the type of each rotation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4735b9fe-1f62-4c1c-b375-80e5700bde0c%2F525f0957-1b51-422e-a224-4bd6c8157f54%2F1sp406j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. The depth of a node is the length of the unique path from the root to the node. Consider a
full binary search tree with height h and N = 24+1 – 1 nodes. What is the average depth of
the N nodes?
5. Show the process of inserting 9, 1, 2, 8, 10, 5, 4, 3, 7, 6 into an initially empty AVL tree.
Then the root is deleted and replaced by the smallest key in the right subtree. Show the tree
after each insertion, deletion, and rotation. Indicate the type of each rotation.
![3. Assume that binary trees are defined as
public class BTNode<E>
{
private E data;
private BTNode<E> left, right;
}
We say that a binary tree t1 is a prefix of a binary tree t2 if t2 can be made identical to t1
by removing zero or more leaves of t2. Write a method
public static boolean prefix(BTNode<Integer> t1, BTNode<Integer> t2)
that determines whether t1 is a prefix of t2.
4. The depth of a node is the length of the unique path from the root to the node. Consider a
full binary search tree with height h and N = 2h+1
1 nodes. What is the average depth of
the N nodes?
5. Show the process of inserting 9, 1, 2, 8, 10, 5, 4, 3, 7, 6 into an initially empty AVL tree.
Then the root is deleted and replaced by the smallest key in the right subtree. Show the tree
after each insertion, deletion, and rotation. Indicate the type of each rotation.
ch](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4735b9fe-1f62-4c1c-b375-80e5700bde0c%2F525f0957-1b51-422e-a224-4bd6c8157f54%2F7j006e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Assume that binary trees are defined as
public class BTNode<E>
{
private E data;
private BTNode<E> left, right;
}
We say that a binary tree t1 is a prefix of a binary tree t2 if t2 can be made identical to t1
by removing zero or more leaves of t2. Write a method
public static boolean prefix(BTNode<Integer> t1, BTNode<Integer> t2)
that determines whether t1 is a prefix of t2.
4. The depth of a node is the length of the unique path from the root to the node. Consider a
full binary search tree with height h and N = 2h+1
1 nodes. What is the average depth of
the N nodes?
5. Show the process of inserting 9, 1, 2, 8, 10, 5, 4, 3, 7, 6 into an initially empty AVL tree.
Then the root is deleted and replaced by the smallest key in the right subtree. Show the tree
after each insertion, deletion, and rotation. Indicate the type of each rotation.
ch
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