Write a technique that quickly identifies whether two nodes u and v in a tree T whose root node is s are descendants or ancestors.
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Write a technique that quickly identifies whether two nodes u and v in a tree T whose root node is s are descendants or ancestors.
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- You are familiar with the parent → child relationship in a binary tree. Write a function which determines if two nodes in a binary tree are cousins. Two nodes are cousins if they are on the same level and have different parents. In the following example: D B с A checkCousins ("D", "C") = False checkCousins ("D", "F") = True checkCousins ("D", "B") = False E FTo delete a key in a B-tree: Step 1. If the key k is in node x and x is a leaf, delete the key k from x. Step 2. If the key k is in node x and x is an internal node, do the following: 2a) If the child y that precedes k in node x has at least t keys, then find the predecessor k’ of k in the sub-tree rooted at y. Recursively delete k’, and replace k by k’ in x. (We can find k’ and delete it in a single downward pass.) 2b) If y has fewer than t keys, then, symmetrically, examine the child z that follows k in node x. If z has at least t keys, then find the successor k’ of k in the subtree rooted at z. Recursively delete k’, and replace k by k’ in x. (We can find k’ and delete it in a single downward pass.) 2c) Otherwise, if both y and z have only t-1 keys, merge k and all of z into y, so that x loses both k and the pointer to z, and y now contains 2t-1 keys. Then free z and recursively delete k from y. Answer the following regarding insertion/deletion of keys in a B-Tree: (1)…Implement a function to verify if a binary tree is balanced. A balanced tree, for the purposes of this question, is one in which the heights of the two subtrees of any node never differ by more than one.
- Given the preorder and inorder traversals of a binary tree, you build that binary tree. Preorder: X In-order: A Y A E Y EX C C K D D L KLQuestion 5 Draw a binary tree T that simultaneously satisfies the following: 1. Each internal node of Tstores a single character. 2. A preorder traversal of Tyields EXAMFUN. 3. An inorder traversal of Tyields MAFXUEN. Your Answer. Note You may upload your handwritten solution as an attachment ORTo delete a key in a B-tree: Step 1. If the key k is in node x and x is a leaf, delete the key k from x. Step 2. If the key k is in node x and x is an internal node, do the following: 2a) If the child y that precedes k in node x has at least t keys, then find the predecessor k’ of k in the sub-tree rooted at y. Recursively delete k’, and replace k by k’ in x. (We can find k’ and delete it in a single downward pass.) 2b) If y has fewer than t keys, then, symmetrically, examine the child z that follows k in node x. If z has at least t keys, then find the successor k’ of k in the subtree rooted at z. Recursively delete k’, and replace k by k’ in x. (We can find k’ and delete it in a single downward pass.) 2c) Otherwise, if both y and z have only t-1 keys, merge k and all of z into y, so that x loses both k and the pointer to z, and y now contains 2t-1 keys. Then free z and recursively delete k from y. 1) Write pseudo code for Step (1) for function B-Tree-Delete-Key(x, k). Make…
- A tree is said to be an AVL tree or height balanced if, for every noden, the heights of the subtrees of n differ by no more than 1. Write a staticBinaryTree method that determines if a tree rooted at the referenced node isheight balanced.Write an algorithm to find the "next" node (i.e., in-order successor) of a given node in a binary search tree. You may assume that each node has a link to its parent.True or False? The number of nodes in a non-empty tree is equal to the number of nodes in its left subtree plus the number of nodes in its right subtree plus 1. please explain
- Implement the binary tree ADT using a linked structure as we developed in class, add the following methods: - def countK(self, num): function that takes in num and counts number of times num appears in the binary tree - def equal(self, other: BinaryTree): function thats takes in another binary tree (other) as parameter and returns true if both binary trees are equal, otherwise function returns False.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 HConsider the following Binary Tree. root A B D E F C G H K If we perform an postorder traversal, which value is displayed FOURT Enter the node's label (A,B,C,D,E,F,G,H,K) in the space provided.