Homework Answers
1)answer)
AVL tree is a self balanced binary tree with a balance factor ,meaning every node in the tree the
height of the left and right subtree can differ by at most 1.
2)answer)
The height of the AVL tree is O(log n)
3)answer)
Assume the following notation/operations on AVL trees. An empty AVL tree is denoted E. A non-empty AVL tree T has three...
Assume the following notation/operations on AVL trees. An empty AVL tree is denoted E. A non-empty AVL tree T has three attributes The key T.key is the root node's key. The left child T.left is Ts left subtree, which is an AVL tree (possibly E). The right child T.right is T's right subtree, which is an AVL tree (possibly E). (a) 5 marsl Write a function RANGECOUNT(T, lo, hi) to count the number of nodes in an AVL tree with...
Assume the following notation/operations on AVL trees. An empty AVL tree is denoted E. A non-empty AVL tree T has three...
Assume the following notation/operations on AVL trees. An empty AVL tree is denoted E. A non-empty AVL tree T has three attributes: • The key T.key is the root node’s key. • The left child T.left is T’s left subtree, which is an AVL tree (possibly E). • The right child T.right is T’s right subtree, which is an AVL tree (possibly E). (a) [5 marks] Write a function RangeCount(T, lo, hi) to count the number of nodes in an...
Consider the AVL Tree built by inserting the following sequence of integers, one at a time:...
Consider the AVL Tree built by inserting the following sequence of integers, one at a time: 5, 2, 8, 7,9 Then we insert 11. After we insert 11, before we perform any necessary rotations, is the tree balanced? And if not, which is the root of the lowest imbalanced subtree? (a) None, since the tree is already balanced after inserting 11. (b) The node containing 5. (c) The node containing 8. (d) The node containing 11. (e) The node containing...
4. Consider the following subtree of a balanced AVL tree a b AA d X Y d+1 d+2 Now, suppose that subtrees (i.e., subtree...
4. Consider the following subtree of a balanced AVL tree a b AA d X Y d+1 d+2 Now, suppose that subtrees (i.e., subtree X and subtree Y) to be both two levels deeper than its right subtree (i.e., subtree Z) so that we have the following unbalanced AVL tree node at the bottom of subtree Z is deleted, causing its two left a a b d d+1 X d+2 Describe how the AVL tree can be rebalanced. Draw the...
PYTHON QUESTION... Building a Binary Tree with extended Binary Search Tree and AVL tree. Create a...
PYTHON QUESTION... Building a Binary Tree with extended Binary Search Tree and AVL tree. Create a class called MyTree with the methods __init__(x), getLeft(), getRight(), getData(), insert(x) and getHeight(). Each child should itself be a MyTree object. The height of a leaf node should be zero. The insert(x) method should return the node that occupies the original node's position in the tree. Create a class called MyBST that extends MyTree. Override the method insert(x) to meet the definitions of a...
A balanced binary tree is a binary tree structure in which the left and right subtrees of every node differ
Data structures C++1- A balanced binary tree is a binary tree structure in which the left and right subtrees of every node differ in height by no more than 1 Out of the following choices, which is the minimum set of nodes, if removed, will make the BST balanced?2- Which of the following is true for Red-Black Trees ? Select all choices that apply! Select one or more: a. For each node in the tree, all paths from that node to any leaf nodes contain...
(b) You are given the AVL Tree in the figure below. Assume that the nodes are...
(b) You are given the AVL Tree in the figure below. Assume that the nodes are sorted in alphabetical order. E J B D K A F L H Draw the resulting BST after node E is removed. To construct the new BST replace node E with an appropriate node from the left subtree of E. Do not rebalance the resulting tree. Label each node in the resulting tree with its balance factor. (e) Now rebalance the tree from the...
(true/false) All nodes in the right subtree of a node must be smaller in value than...
(true/false) All nodes in the right subtree of a node must be smaller in value than their parent (true/false) Each node in a binary search tree may contain zero, one, or two children nodes. (true/false) It is possible to recursively process a binary search tree to print all the data in a binary search tree in sorted order. (true/false) The value of a parent must be less than all its children. (true/false) All nodes in the right subtree of a...
C++ Question 5 5 pts In a min-heap of N elements, if we want to find...
C++
Question 5 5 pts In a min-heap of N elements, if we want to find the max element, we have to search all the leaves. What is the big-o running time of findMax? O(N^2) Oſlog N) O(N) OIN log N) Question 6 5 pts An AVL tree is a Binary Search Tree that has the following additional property for every node in the tree, the height of the left and right subtrees is the same none of the above...
The INORDER traversal output of a binary tree is U,N,I,V,E,R,S,I,T,Y and the POSTORDER traversal output of the same tree is N,U,V,R,E,T,I,S,I,Y
a. The INORDER traversal output of a binary tree is U,N,I,V,E,R,S,I,T,Y and the POSTORDER traversal output of the same tree is N,U,V,R,E,T,I,S,I,Y. Construct the tree and determine the output of the PREORDER traversal output. b. One main difference between a binary search tree (BST) and an AVL (Adelson-Velski and Landis) tree is that an AVL tree has a balance condition, that is, for every node in the AVL tree, the height of the left and right subtrees differ by at most 1....
Assume the following notation/operations on AVL trees. An empty AVL tree is denoted E. A non-empty AVL tree T has three attributes The key T.key is the root node's key. The left child T.left is Ts left subtree, which is an AVL tree (possibly E). The right child T.right is T's right subtree, which is an AVL tree (possibly E). (a) 5 marsl Write a function RANGECOUNT(T, lo, hi) to count the number of nodes in an AVL tree with...
Consider the AVL Tree built by inserting the following sequence of integers, one at a time: 5, 2, 8, 7,9 Then we insert 11. After we insert 11, before we perform any necessary rotations, is the tree balanced? And if not, which is the root of the lowest imbalanced subtree? (a) None, since the tree is already balanced after inserting 11. (b) The node containing 5. (c) The node containing 8. (d) The node containing 11. (e) The node containing...
4. Consider the following subtree of a balanced AVL tree a b AA d X Y d+1 d+2 Now, suppose that subtrees (i.e., subtree X and subtree Y) to be both two levels deeper than its right subtree (i.e., subtree Z) so that we have the following unbalanced AVL tree node at the bottom of subtree Z is deleted, causing its two left a a b d d+1 X d+2 Describe how the AVL tree can be rebalanced. Draw the...
(b) You are given the AVL Tree in the figure below. Assume that the nodes are sorted in alphabetical order. E J B D K A F L H Draw the resulting BST after node E is removed. To construct the new BST replace node E with an appropriate node from the left subtree of E. Do not rebalance the resulting tree. Label each node in the resulting tree with its balance factor. (e) Now rebalance the tree from the...
(true/false) All nodes in the right subtree of a node must be smaller in value than their parent (true/false) Each node in a binary search tree may contain zero, one, or two children nodes. (true/false) It is possible to recursively process a binary search tree to print all the data in a binary search tree in sorted order. (true/false) The value of a parent must be less than all its children. (true/false) All nodes in the right subtree of a...
C++
Question 5 5 pts In a min-heap of N elements, if we want to find the max element, we have to search all the leaves. What is the big-o running time of findMax? O(N^2) Oſlog N) O(N) OIN log N) Question 6 5 pts An AVL tree is a Binary Search Tree that has the following additional property for every node in the tree, the height of the left and right subtrees is the same none of the above...
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