These problems need to be solved using java coding **Transcription for Educational Website:**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 \( N = 2^{h+1} - 1 \) 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. ### Understanding Binary Trees and AVL Trees**3. Binary Trees**Binary trees are structured as follows:```javapublic class BTNode { private E data; private BTNode left, right;}```In this context, a binary tree `t1` is considered a prefix of another binary tree `t2` if `t2` can be transformed into `t1` by removing zero or more leaves from `t2`. To implement this, write a method:```javapublic static boolean prefix(BTNode t1, BTNode t2)```This method should determine if `t1` is indeed a prefix of `t2`.**4. Node Depth in Binary Search Trees**The depth of a node is defined as the length of the unique path from the root to that specific node. For a full binary search tree with a height `h` and `N = 2^(h+1) - 1` nodes, you are tasked with finding the average depth of all `N` nodes.**5. AVL Tree Insertions and Deletions**Illustrate the process of inserting elements `9, 1, 2, 8, 10, 5, 4, 3, 7, 6` into an initially empty AVL tree. Following the insertions, if the root is deleted, it should be replaced by the smallest key in the right subtree. Visualize the AVL tree after each insertion, deletion, and rotation with an indication of the type of each rotation.

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Description: These problems need to be solved using java coding **Transcription for Educational Website:**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 = 2^{h+1}

// Java program for insertion in AVL Tree class Node { int key, height; Node left, right;…

Engineering

Computer Science

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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