Please show steps clearly 4. Consider a binary search tree where each node v has a field v.height that stores the height of the subtreerooted at v.(Note: The height is not the same as the size field we discussed in class. In particular, v.height is thenumber of edges in the longest path from v to a leaf of the subtree rooted at v.)(a) Modify the TreeInsert procedure (discussed in class and described in the course notes) to updatethe height fields so that all the .height fields of the tree are corrected after applying the Tree Insertoperation. (Assume that all the .height fields were correct before the TreeInsert operation.) Yourmodified algorithm should take the same asymptotic running time as the original TreeInsertoperation. Explain your modification and give pseudo-code for the modified algorithm.(b) Analyze the running time of your modified procedure in terms of the height of the binary searchtree. If your solution involves incrementing the height of all nodes on the path to the root when the inserted node does not have a sibling, then, you should explicitlystate that you will be assuming that the inserted node is at the lowest level of the tree, namely, the inserted node is on the longest path from the root to a leaf.Note that if you do not make this assumption and the inserted node does not have a sibling, then the height of some nodes on the path to the root may not needto be incremented and an additional check is required at each node on the path to the root.If you want to provide the most general solution without making the assumption above, then you need to carefully think about what needs to be checked at eachnode on the path to the root when the inserted node does not have a sibling. In particular, when the inserted node does not have a sibling, then rather than directlyincrementing the height of every node on the path to the root, there should be another formula to update the height of each node on that path.

(a) To modify the TreeInsert procedure to update the height fields, we can add a new function called…

Consider a binary search tree where each node v has a field v.height that store Doted at v. Note: The height is not the same as the size field we discussed in class. In umber of edges in the longest path from v to a leaf of the subtree rooted at (a) Modify the Tree Insert procedure (discussed in class and described in t the height fields so that all the height fields of the troo or porrooted ofte:

Consider a binary search tree where each node v has a field v.height that store Doted at v. Note: The height is not the same as the size field we discussed in class. In umber of edges in the longest path from v to a leaf of the subtree rooted at (a) Modify the Tree Insert procedure (discussed in class and described in t the height fields so that all the height fields of the troo or porrooted ofte:

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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Question

Please show steps clearly

4. Consider a binary search tree where each node v has a field v.height that stores the height of the subtree
rooted at v.
(Note: The height is not the same as the size field we discussed in class. In particular, v.height is the
number of edges in the longest path from v to a leaf of the subtree rooted at v.)
(a) Modify the TreeInsert procedure (discussed in class and described in the course notes) to update
the height fields so that all the .height fields of the tree are corrected after applying the Tree Insert
operation. (Assume that all the .height fields were correct before the TreeInsert operation.) Your
modified algorithm should take the same asymptotic running time as the original TreeInsert
operation. Explain your modification and give pseudo-code for the modified algorithm.
(b) Analyze the running time of your modified procedure in terms of the height of the binary search
tree.

If your solution involves incrementing the height of all nodes on the path to the root when the inserted node does not have a sibling, then, you should explicitly
state that you will be assuming that the inserted node is at the lowest level of the tree, namely, the inserted node is on the longest path from the root to a leaf.
Note that if you do not make this assumption and the inserted node does not have a sibling, then the height of some nodes on the path to the root may not need
to be incremented and an additional check is required at each node on the path to the root.
If you want to provide the most general solution without making the assumption above, then you need to carefully think about what needs to be checked at each
node on the path to the root when the inserted node does not have a sibling. In particular, when the inserted node does not have a sibling, then rather than directly
incrementing the height of every node on the path to the root, there should be another formula to update the height of each node on that path.

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