Construct a B+-tree for the following set of search key values, where each node can contain at most 3 keys. 20, 100, 50, 10, 5, 30, 45, 38, 80, 64, 150, 65, 120, 180, 140 Assume the tree is initially empty and values are added sequentially one by one. You must draw the tree and give a proper explanation for each insertion.

Another important property of a binary search tree is being able to easily find the maximum and minimum key in the tree. Discuss a simple rule to identify these keys. What is the output of a BFS traversal in a normal binary search tree if the key insert order is "1,2,3,4,5,6,7"?

Question: In a binary search tree (BST), what is the relationship between a node's left child and its parent? A) The left child is greater than the parent. B) The left child is less than the parent. C) The left child is equal to the parent. D) There is no specific relationship between the left child and the parent in a BST.

In a B+-tree, there can be at most 4 search-key values in each node. Assume that the height of the B+-tree is 2. The height of the tree is the length of the path from the root to a leaf node.  a. What is the maximum number of leaf nodes this tree can have? b. Let N1 be a node in the tree. N1 is neither a leaf nor a root. What is the minimum number of children that N1 can have?

Examine a traversal of a binary tree. Let's say that visiting a node means to display the data in the node. What are the result of each of the following traversals of the tree included? It is preorder, postorder, inorder or level order?

The pre-order traversal of binary search tree is 10, 5, 1, 7, 40, 50. What is the post-order traversal of the tree?

Given a binary tree with the array representation as the table below: a) Draw the diagram of the given binary tree. b) What is the number of internal nodes of the given binary tree? c) If node item L has a right child, what is the index of this right child of L? * Binary tree must be clearly drawn, to indicate the left/right children if any. index 1 2 3 4 6 7 8 9 10 11 item A D G K L

Consider the Binary Search Tree below: (a) Give the order in which the nodes will be visited in a preorder traversal. (b) List all the nodes in level 3 of the tree. (c) How many leaf nodes does the tree have? (d) If we delete node 80, which node should be its replacement? (e) Is the given tree an AVL tree? If it is an AVL tree, discuss how it conforms to the definition of an AVL tree. If it is not an AVL tree, explain how you will change the tree into an AVL tree.

Exercise 8. In a red-black tree which is initially empty, we insert in order nodes with keys 1,2,3,4. Draw the tree after these insertions (single-circled nodes are black, and double-circled nodes are red).