Homework Balanced Trees (1)

Option+Explanation

Exercise 2: AVL Trees Construct AVL trees by inserting the elements successively, starting with the empty tree. a) 1, 2, 3, 4, 5, 6 b) 6, 5, 4, 3, 2, 1 c) 3, 6, 5, 1, 2, 4 (Note: Observe the final trees and you will find that although all of them have the same data, the tree are not necessarily the same.)

Avl tree

2. Insert the following numbers into an empty BST and draw the resulting tree. 23, 42, 12, 57, 5, 16, 46, 1. a) What is the height of the tree? 3. Remove the following numbers from the BST from step 2 using lazy removal: 42, 16, 57. Draw the resulting tree. a) What is the height of the tree? 4. Now insert the following numbers into the BST from step 3: 40, 20, 16, 42. Draw the resulting tree. a) What is the height of the tree?

2-3 tree & binary tree  SOLVE THIS ONLY IF YOU REALLY KNOW THE CONCEPT. OTHERWISE DONT TOUCH IT. SOLVE IT COMPLETELY AND ACCURATELY. REWARD : 4 LIKES.

AVL TREE On empty AVL Tree: Insert these values: 6, 27, 19, 11, 36, 14, 81, 63, 75 and then Delete the following values: 14, 75, 36, 19, 11.

Algorithm

Tree (avl). Incorrect answer will be directly downvoted.

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Insert the following values into an initially empty red-black tree in the order given. Insert: 73, 35, 68, 94, 26, 29, 16, 44, 38, 81, 59, 61 show side by side the RBT and 2-4 tree.

(No coding) Insert the following values into a binary search tree in the given order.(Draw the tree) Then traverse this tree using inorder, preorder ve postorder methods. List the values for each one. Then delete 40.(draw the resulting tree) 20, 40,14,5,12,25,55,13,1,34,8,90,50,3

Balanced Trees a) Draw the 2-3-4-trees that results when you insert the keys 1   12   7   15  18   9   20   8   13   19   26 in that order into an initially empty tree. Draw the 2-3-4-tree before and after every split of a node. When inserting new values into the tree, they should only be inserted into the leaves.

a) Show all the steps in creating a Red-Black tree by inserting the following sequentialy, 25, 33, 12,46,19,16,17 and 25. b) After creating the Red-Black tree as indicated above, delete the node representing 19 and display the RedBlack tree Show everything step by step please

(Drawing and code) 1. Show the BST after deleting 15 from the following BST.You must show the tree and the pseudocode of deleting 15.Show the BST after inserting 60,15,100,57,67,107,49,64 into an empty BST.2. Show the BST after deleting 60 from the following BST.Delete 67 instead of 60. After you delete 15, delete 67. You must show the tree and the pseudocode of deleting 67.3. Show the inorder, preorder, and postorder of the following BST.You must show it on original tree included all nodes.

Correct sequence

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Option+Explanation

Binary Search Tree (BST)A. Draw the binary search tree after you insert the following values40,20,10,25,30,22,50 Hint: BST has property that right child node is greater than root whileThe left child node is smaller than the root.B. Run then traverse the tree using inorder, preorder, and postorderHint: ( inorder: left root right , preorder: root left right, postorder: left right root ) Write the pseudo code to delete ..... then draw the tree.D. Write the pseudo code to delete ....then draw the tree.E. Write the pseudo code to delete ..... then draw the tree.F.  What is the search running time for trees that are not balanced?G.  What is the search running time for a tree that is balanced?

Q 3 - Given Postorder and Inorder traversals, construct the tree. (10) a) Inorder = {F, E, T, V, O, S, R, N} b) Postorder = {E, F, V, T, S, N, R, O}

Construct AVL trees by inserting the elements successively, starting with the empty tree. a) 1, 2, 3, 4, 5, 6 b) 6, 5, 4, 3, 2, 1 c) 3, 6, 5, 1, 2, 4 (Note: Observe the final trees and you will find that although all of them have the same data, the tree are not necessarily the same.)

8. What tree results when you add the values 44, 88, 55, 77, 33, 99, 66, 22, 25 and 75 to each of the following initially empty trees. (For each question, show only the final result) a) Binary Search Tree b) Based on the answer in question of 7(a): i) ii) c) AVL tree delete node '55' and redraw the tree. delete node '44' (after deleting node 55) and redraw the tree.

Which ones are correct for the tree T drawn below? (Select all that applies.) look at the picture sent Group of answer choices a) A preorder traversal of the tree yields 100 , 20 , 10 , 30 , 200 , 150 , 300. b) A preorder traversal of the tree yields 100, 20, 30, 10, 200, 150, 300. c) An inorder traversal of the tree yields 10, 20, 30, 100, 150, 200, 300. d) An inorder traversal of the tree yields 10, 20, 100, 30, 150, 200, 300. e) A postorder traversal of the tree yields 10, 30, 20, 100, 150, 300, 200. f) A postorder traversal of the tree yields 10, 30, 20, 150, 300, 200, 100.

Bonus section Given the following sequence of numbers to insert into a tree data structure:8 10 2 4 5 1 6 3 7 9Answer the following questions:1) What will the binary search tree look like after the numbers are inserted in the givenorder?2) From the tree you finished in 1), what will the tree look like each time after thefollowing numbers are deleted (use the delete algorithm discussed in the slideswhere the successor is found in the right child subtree):a. Delete(7)b. Delete(10)c. Delete(2)3) From the tree you finished in 2), what will the preorder and postorder outputtraversals look like?

Direction: (a) Use predecessor instead of successor. When there are choices between single or double rotate, please choose single rotation. Explain the process. From the following tree, please simulate insertion of: G, E, R, H O

Postorder: 7  6  8  5  2  9  4  10  3  1 Inorder:      6  7  2  5  8  1  4  9  3  10   After drawing the tree, what is the weight of the tree? (Numeric Answer ONLY)

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11. Preorder Traversal What is the preorder traversal order of the following tree: 3 Pick ONE option 1, 2, 4, 5, 3 4, 2, 5, 1, 3 4,5, 2, 3, 1 1,2, 3, 4, 5 Clear Selection

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