Problem 4. Insert the following set of keys {1, 4, 3, 5, 8, 9, 0, 7, 2, 6} in an empty red-black tree in the order they are listed.

Consider a traversal of a binary tree. Suppose that visiting a node means to simply display the data in the node. What are the results of each of the following traversals of the tree in the following figures according to: a. Pre-order technique b. Post-order technique c. In-order technique A B D E F G H

B. Consider the following three binary trees. (a) 22 38 35 31 20 25 (b) 35 21 38 18 24 37 39 17 23 31 32 63 32 82 28 38 110 16 34 39 i) Which of these binary trees is an AVL tree? Justify your answer. ii) Insert key "40" into that AVL tree. Show all your steps and how the tree looks like.

What is the Postorder Traversal of the following tree E H I) F, J, I, H, G, E, D II) G, H, I, J, E, D, F III) D, F, E, H, I, J, G IV) D, E, G, H, I, J, F V) G, J, I, H, E, F, D (F)

2. This question is about binary search tree.a. Show the final result after inserting 3, 1, 4, 6, 9, 2, 8, 5, 7, 0 into an empty binary search tree.b. Show the result of deleting the root twice. If the deleted node contains 2 children, its value is replaced by the minimum value of the right subtree, and the deletion is propagated. Show the result after each deletion

What will be the Inorder traversal of the following tree?*           11, 20, 29, 32, 41, 50, 65, 72, 91, 99       11, 20, 29, 32, 50, 65, 72, 91, 99, 41       11, 32, 50, 72, 99, 29, 65, 91, 20, 41       41, 20, 11, 29, 32, 65, 50, 91, 72, 99       41, 20, 11, 65, 91, 99, 29, 32, 50, 72

What will be the resulting B- Trees (2-3 trees) for the following items?

You are given both the Post-order traversal and an in-order traversal for aunique binary tree.Post-order traversal: F A C D B EIn-order traversal: A F E C B D • Draw the unique tree defined by those traversals.• Write down the corresponding pre-order traversal for that tree.

Assuming that the array shown below represents a binary tree of nodes holding Integer objects, indicate which of the properties applies to the tree. More than one property may apply. It is also possible that none of the properties apply. (Draw the tree on scratch paper if it helps you to figure things out) The array: [8, 5, 13, null, null, 11, 20, null, null, null, null, 9] Full Tree Неар None of the above Complete Tree Binary Search Tree O AVL Tree

Write a detailed algorithm/description explaining how to efficiently solve this problem: Suppose two binary search trees (T1, T2) have already been created. Determine whether these two trees are the same--they have the same number of elements and have the same elements. You may use any of the tree and BST methods discussed in lectures, and you can choose whether the trees are implemented as linked trees, or are stored in arrays. Note: While T1 and T2 might be the same (as defined above) they do not need to have the same structure (shape). They might organize the data in the tree in different ways. Estimate the growth function and big O value ofyour algorithm; explain how you arrive at your answer.