Homework Answers
AVL Tree:Balancing Factor(BF) = Height of Left Subtree -
Height of Right Subtree
This Balancing Factor(BF) is either 0,1,-1 then AVL Tree is
balanced
Step 1: Insert keys 17
After Insertion the tree is Not balanced so Perform Double Rotate Right
Step 2: Insert key 40
Step 3: Insert key 10
After Insertion the tree is Not balanced so Perform Double Rotate Right
Step 4: Insert key 90
Step 5: Insert key 5
After Insertion the tree is Not balanced so Perform Single Rotate Right
Step 6: Insert key 100
After Insertion the tree is Not balanced so Perform Single Rotate Left
Which is Required AVL Tree after performing all Insertions
b) Given Tree from Part (a)
Delete Root: Delete 25
Node to delete has two childrens so find largest element in the left subtree
Copy largest value of the left subtree into Node to Delete
Which is Required Red/Black Tree after performing Deletion of Root
Add Answer to:
2. a) Consider the following AVL Tree. 50 / 25 75 10 Insert the following values...
The task here is to show a trace of the operations needed to insert objects with your (list of) keys, one by one, into an initially empty AVL tree with restoration of AVL balance (if necessary) after each insertion for Key: [74, 92, 75, 46, 60, 3, 90, 78,
[74, 92, 75, 46, 60, 3, 90, 78, 7]The task here is to show a trace of the operations needed to insert objects with your (list of) keys, one by one, into an initially empty AVL tree with restoration of AVL balance (if necessary) after each insertion.Your submission should have the section heading 'AVL trace' followed by the coded trace of operations: Ixx to insert key xx at the root of the previously empty AVL tree; IxxLyy to insert key...
Please show rotation and balancing factors 1) Insert 13,10,15,5,11,16,4,6,7 in an AVL Tree 2) Insert 43,18,22,9,21,6,8...
Please show rotation and balancing factors 1) Insert 13,10,15,5,11,16,4,6,7 in an AVL Tree 2) Insert 43,18,22,9,21,6,8 in an AVL Tree 3) Insert 14, 4, 21, 3, 9, 15, 28, 2, 7, 10, 18, 26, 35 in an AVL Tree. Also, Remove 2, 3, 10, 18 from the AVL Tree.
AVL Tree Initial status is empty. Insert 50, 25, 10, 5, 7, 3, 30, 20, 8,...
AVL Tree Initial status is empty. Insert 50, 25, 10, 5, 7, 3,
30, 20, 8, 15 into this AVL tree in order. Draw every status of the
tree
Question 3: AVL Tree Initial status is empty. Insert 50, 25, 10, 5, 7, 3, 30, 20, 8, 15 into this AVL tree in order. Draw every status of the tree
[DSW] Create a balanced binary tree from the tree in figure 1 using DSW algorithm. Show...
[DSW] Create a balanced binary tree from the
tree in figure 1 using DSW algorithm. Show step-by-step process
including the process of
creating backbone and
perfectly balanced tree
[AVL]
Delete node 9 from tree in figure 1, then determine balance
factor for each remaining node, and create a balanced AVL tree from
it.
Delete node 3 from tree in figure 1 by using Delete-by-Copying
procedure, determine balance factor for each remaining node, and
create a balanced AVL tree...
Binary Search Trees (a) 5 pointsl Insert 5, 12, 7, 1, 6, 3, 13, 2, 10,...
Binary Search Trees
(a) 5 pointsl Insert 5, 12, 7, 1, 6, 3, 13, 2, 10, 11 into an empty binary search tree in the given order. Show the resulting BST after every insertion. (b) 5 points) What are the preorder, inorder, and postorder traversals of the BST you have after (a)? (c) 5 points Delete 2, 7, 5, 6, 11 from the BST you have after (a) in the given order Show the resulting BST after every deletion.
a) Show balance factor of every node after each insertion by creating an AVL tree with...
a) Show balance factor of every node after each insertion by creating an AVL tree with 4,2,2,0,1,4,5,9,7,1,5,3,6 number. Express all operations (single/double rotation) necessary to restore the balance. b) Create min and max heap using the same input as in part (a) by showing all the necessary steps.
11. In the 2-3 tree given below (i.e., NOT a 2-3-4 tree), execute insert(28), insert(99), and...
11. In the 2-3 tree given below (i.e., NOT a 2-3-4 tree), execute insert(28), insert(99), and insert(58), in that order, making sure to rebalance after each insertion. Draw the resulting 2-3 tree after executing these operations. 45 20 70 30 60 80 90 2(4(10 11) (25) (40) (50 55) (65) (71 75)(85) (92 96
True or false? (a) An insertion in an AVL tree with n nodes requires Θ (log(n))...
True or false? (a) An insertion in an AVL tree with n nodes requires Θ (log(n)) rotations. (b) A set of numbers are inserted into an empty BST in sorted order and inserted into an empty AVL tree in random order. Listing all elements in sorted order from the BST is O (n), while listing them in sorted order from the AVL tree is O (log(n)). (c) If items are inserted into an empty BST in sorted order, then the...
1. Construct an AVL tree for the list C, S, U, M, B, W, I, N....
1. Construct an AVL tree for the list C, S, U, M, B, W, I, N. Use the alphabetical ascending order of the letters and insert them successively starting with the empty tree. Your answer should present the rotation operations clearly for each letter addition. 2. Present an insertion order for the keys C, S, U, M, B, W, I, and N that leads to a 2-3 tree of height 1. In the problem, you should use the alphabetical ascending...
1- Insert in the given order the following values into an intially empty 2-3-4 tree: 100,...
1- Insert in the given order the following values into an intially empty 2-3-4 tree: 100, 200, 300, 400, 500, 600, 700, 110, 120, 130, 800, 750, 690. Show how the tree evolves after each value is inserted. In other words, draw a picture of the tree after each insertion. 2- Insert the same sequence as above into an initially empty red-black tree. Again draw a picture of the tree after each insertion, and indicate which rotations and/or color flips...
AVL Tree Initial status is empty. Insert 50, 25, 10, 5, 7, 3,
30, 20, 8, 15 into this AVL tree in order. Draw every status of the
tree
Question 3: AVL Tree Initial status is empty. Insert 50, 25, 10, 5, 7, 3, 30, 20, 8, 15 into this AVL tree in order. Draw every status of the tree
[DSW] Create a balanced binary tree from the
tree in figure 1 using DSW algorithm. Show step-by-step process
including the process of
creating backbone and
perfectly balanced tree
[AVL]
Delete node 9 from tree in figure 1, then determine balance
factor for each remaining node, and create a balanced AVL tree from
it.
Delete node 3 from tree in figure 1 by using Delete-by-Copying
procedure, determine balance factor for each remaining node, and
create a balanced AVL tree...
Binary Search Trees
(a) 5 pointsl Insert 5, 12, 7, 1, 6, 3, 13, 2, 10, 11 into an empty binary search tree in the given order. Show the resulting BST after every insertion. (b) 5 points) What are the preorder, inorder, and postorder traversals of the BST you have after (a)? (c) 5 points Delete 2, 7, 5, 6, 11 from the BST you have after (a) in the given order Show the resulting BST after every deletion.
11. In the 2-3 tree given below (i.e., NOT a 2-3-4 tree), execute insert(28), insert(99), and insert(58), in that order, making sure to rebalance after each insertion. Draw the resulting 2-3 tree after executing these operations. 45 20 70 30 60 80 90 2(4(10 11) (25) (40) (50 55) (65) (71 75)(85) (92 96
True or false? (a) An insertion in an AVL tree with n nodes requires Θ (log(n)) rotations. (b) A set of numbers are inserted into an empty BST in sorted order and inserted into an empty AVL tree in random order. Listing all elements in sorted order from the BST is O (n), while listing them in sorted order from the AVL tree is O (log(n)). (c) If items are inserted into an empty BST in sorted order, then the...
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