Part 1 unbalanced binary search trees Add the following numbers, in the order given, to a binary search tree, and draw a diagram of the resulting tree. For this part of the assignment, you need only show the final tree. 36 21 70 20 14 88 96 74 81 16 64 99 19 83 68 93 Label the height of each node in the final tree.

Database System Concepts
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Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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Chapter1: Introduction
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**Exercise 4 – Random Order**

Add the following numbers, in the specified order, to a balanced BST (Binary Search Tree).

12, 95, 63, 16, 27, 21, 69, 51,
85, 45, 83, 73, 24, 33, 28, 52

---

This exercise involves inserting given numbers into a Binary Search Tree to maintain balance. 

*Binary Search Tree (BST)*: A node-based data structure where each node has a key greater than all the keys in the node’s left subtree and less than those in its right subtree. Balancing ensures efficient operations.
Transcribed Image Text:**Exercise 4 – Random Order** Add the following numbers, in the specified order, to a balanced BST (Binary Search Tree). 12, 95, 63, 16, 27, 21, 69, 51, 85, 45, 83, 73, 24, 33, 28, 52 --- This exercise involves inserting given numbers into a Binary Search Tree to maintain balance. *Binary Search Tree (BST)*: A node-based data structure where each node has a key greater than all the keys in the node’s left subtree and less than those in its right subtree. Balancing ensures efficient operations.
**Part 1: Unbalanced Binary Search Trees**

Add the following numbers, in the order given, to a binary search tree, and draw a diagram of the resulting tree. For this part of the assignment, you need only show the final tree.

36, 21, 70, 20, 14, 88, 96, 74, 81, 19, 83, 68, 93, 16, 64, 99

Label the height of each node in the final tree.

---

**Part 2: Balanced Binary Search Trees**

In this part of the assignment, you will draw four AVL trees, balancing them as you add items.

Every time you need to rebalance the tree, you must label it to show:

- Which of the 4 cases it is (right/right, right/left, left/right, or left/left).
- Which rotations (left or right) are performed.

If a single rebalancing operation requires two rotations, you may either show the end result after both rotations, or show both rotations separately.

Every time a tree is rebalanced, you should draw the resulting tree in black, and draw the newly-added nodes (up to the next rebalancing) in a different color. The last section of this assignment shows an example of what I’m looking for.

---

Note, however, that this does not tell you which case each rebalance operation was, nor which rotations were performed. It just shows the end product.

**Exercise 1 – Ascending Order**

Add the numbers 1 to 12 to a balanced BST in ascending order.

**Exercise 2 – Descending Order**

Add the numbers 1 to 12 to a balanced BST in descending order.

**Exercise 3 – Random Order**

Add the numbers from Part 1 of this assignment to a balanced BST in the order given.
Transcribed Image Text:**Part 1: Unbalanced Binary Search Trees** Add the following numbers, in the order given, to a binary search tree, and draw a diagram of the resulting tree. For this part of the assignment, you need only show the final tree. 36, 21, 70, 20, 14, 88, 96, 74, 81, 19, 83, 68, 93, 16, 64, 99 Label the height of each node in the final tree. --- **Part 2: Balanced Binary Search Trees** In this part of the assignment, you will draw four AVL trees, balancing them as you add items. Every time you need to rebalance the tree, you must label it to show: - Which of the 4 cases it is (right/right, right/left, left/right, or left/left). - Which rotations (left or right) are performed. If a single rebalancing operation requires two rotations, you may either show the end result after both rotations, or show both rotations separately. Every time a tree is rebalanced, you should draw the resulting tree in black, and draw the newly-added nodes (up to the next rebalancing) in a different color. The last section of this assignment shows an example of what I’m looking for. --- Note, however, that this does not tell you which case each rebalance operation was, nor which rotations were performed. It just shows the end product. **Exercise 1 – Ascending Order** Add the numbers 1 to 12 to a balanced BST in ascending order. **Exercise 2 – Descending Order** Add the numbers 1 to 12 to a balanced BST in descending order. **Exercise 3 – Random Order** Add the numbers from Part 1 of this assignment to a balanced BST in the order given.
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