2-3-4 Trees Java Programming Given the following sequence of numbers: 4.0 5.0 6.0 1.0 2.0 3.0 2.5 3.5 7.0 3.9 8.0 3.8 6.5 6.7 9.0 Show what the 2-3-4 tree looks like after each insert. This means you start with a blank tree and then show the 2-3-4 tree after inserting 4.0. Then, from that 2-3-4 tree, show what it looks like after you insert 5.0 into it. Repeat for the remaining numbers. There are 15 numbers to insert so you should be showing 15 trees progressively being built. Assume we are maintaining numbers in ascending order correctly within the tree as discussed in the slides. From the tree you have from completing question 1, which of the following is true (remember that more than one answer may apply) There are 6 leaf nodes in the tree No matter what the next number is to insert, there will definitely be a node that will be split Each non-leaf node in the final tree has exactly 2 children None of the above Finally, which of the following concepts about a 2-3-4 tree are true (again, remember that more than one answer may apply) A 2-3-4 tree can be unbalanced if all the numbers are entered in ascending order Insert in a 2-3-4 tree is O(log n) Deleting a node in a 2-3-4 tree is easy – search for the node with the data item and simply remove it from the data item array None of the above

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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2-3-4 Trees

Java Programming

Given the following sequence of numbers:

4.0

5.0

6.0

1.0

2.0

3.0

2.5

3.5

7.0

3.9

8.0

3.8

6.5

6.7

9.0

Show what the 2-3-4 tree looks like after each insert. This means you start with a blank tree and then show the 2-3-4 tree after inserting 4.0. Then, from that 2-3-4 tree, show what it looks like after you insert 5.0 into it. Repeat for the remaining numbers. There are 15 numbers to insert so you should be showing 15 trees progressively being built. Assume we are maintaining numbers in ascending order correctly within the tree as discussed in the slides.
From the tree you have from completing question 1, which of the following is true (remember that more than one answer may apply)
1. There are 6 leaf nodes in the tree
2. No matter what the next number is to insert, there will definitely be a node that will be split
3. Each non-leaf node in the final tree has exactly 2 children
4. None of the above
Finally, which of the following concepts about a 2-3-4 tree are true (again, remember that more than one answer may apply)
1. A 2-3-4 tree can be unbalanced if all the numbers are entered in ascending order
2. Insert in a 2-3-4 tree is O(log n)
3. Deleting a node in a 2-3-4 tree is easy – search for the node with the data item and simply remove it from the data item array
4. None of the above

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