Problem DescriptionUsing the binary search tree (BST) data structure, we can sort a sequence of n elements by first calling aninsertion procedure for n times to maintain a BST, and then performing an INORDER-TREE-WALK on theBST to output the elements in sorted order.To insert a node, we've discussed the TREE-INSERT procedure in class (also from page 294 of the text-book). This TREE-INSERT procedure can actually be improved to reduce the number of key comparisonsso that each node's key is compared with the new node's key for at most once during each insertion. Forexample, given the following BST,The improved insertion procedure will make• 2 comparisons to insert a node with key = 1• 3 comparisons to insert a node with key = 3• 2 comparisons to insert a node with key = 85.Program RequirementsIn this programming assignment, you will implement in Java this sorting algorithm using BST, by usingthe improved insertion procedure. Note that each node of a BST is an object containing four attributes:key (for the value of an element), le ft (for its left child), right (for its right child), and p (for its parent).Please add a static counter to track the number of key comparisons made by your algorithm. Your programwill output the following1. The size of the input array,2. The input array,3. The list of array elements after sorting, and4. The number of key comparisons made.TestingRun your program multiple times on different input arrays. You may try to define the input array usingrandom numbers and also try by assigning a particular number to each element. Try to answer the followingtwo questions:Q1. If the array size n is fixed, what does a worst-case input array (resulting in the maximum totalnumber of key comparisons) look like?Q2. If the array size n is fixed, what does a best-case input array (resulting in the minimum total numberof key comparisons) look like?In particular, set n = 15. Run your program by creating a worst-case input array and a best-case inputarray. For each case, include the following in the “README" file.• Take a screenshot of your program's output;• Draw the BST after all 15 keys are inserted.Write your answers to Q1 and Q2 for general n as part of the summary of your testing results in the"README" file.

Problem Description Using the binary search tree (BST) data structure, we can sort a sequence of n elements by first calling an insertion procedure for n times to maintain a BST, and then performing an INORDER-TREE-WALK on the BST to output the elements in sorted order. To insert a node, we've discussed the TREE-INSERT procedure in class (also from page 294 of the text- book). This TREE-INSERT procedure can actually be improved to reduce the number of key comparisons so that each node's key is compared with the new node's key for at most once during each insertion. For example, given the following BST,

Problem Description Using the binary search tree (BST) data structure, we can sort a sequence of n elements by first calling an insertion procedure for n times to maintain a BST, and then performing an INORDER-TREE-WALK on the BST to output the elements in sorted order. To insert a node, we've discussed the TREE-INSERT procedure in class (also from page 294 of the text- book). This TREE-INSERT procedure can actually be improved to reduce the number of key comparisons so that each node's key is compared with the new node's key for at most once during each insertion. For example, given the following BST,

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

Problem Description
Using the binary search tree (BST) data structure, we can sort a sequence of n elements by first calling an
insertion procedure for n times to maintain a BST, and then performing an INORDER-TREE-WALK on the
BST to output the elements in sorted order.
To insert a node, we've discussed the TREE-INSERT procedure in class (also from page 294 of the text-
book). This TREE-INSERT procedure can actually be improved to reduce the number of key comparisons
so that each node's key is compared with the new node's key for at most once during each insertion. For
example, given the following BST,
The improved insertion procedure will make
• 2 comparisons to insert a node with key = 1
• 3 comparisons to insert a node with key = 3
• 2 comparisons to insert a node with key = 8
5.
Program Requirements
In this programming assignment, you will implement in Java this sorting algorithm using BST, by using
the improved insertion procedure. Note that each node of a BST is an object containing four attributes:
key (for the value of an element), le ft (for its left child), right (for its right child), and p (for its parent).
Please add a static counter to track the number of key comparisons made by your algorithm. Your program
will output the following
1. The size of the input array,
2. The input array,
3. The list of array elements after sorting, and
4. The number of key comparisons made.
Testing
Run your program multiple times on different input arrays. You may try to define the input array using
random numbers and also try by assigning a particular number to each element. Try to answer the following
two questions:
Q1. If the array size n is fixed, what does a worst-case input array (resulting in the maximum total
number of key comparisons) look like?
Q2. If the array size n is fixed, what does a best-case input array (resulting in the minimum total number
of key comparisons) look like?
In particular, set n = 15. Run your program by creating a worst-case input array and a best-case input
array. For each case, include the following in the “README" file.
• Take a screenshot of your program's output;
• Draw the BST after all 15 keys are inserted.
Write your answers to Q1 and Q2 for general n as part of the summary of your testing results in the
"README" file.

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