To find the kth smallest element in the tree, create a recursive algorithm that accepts a BST and an integer k as inputs. Remember that all the nodes in the right subtree are bigger than the root, while all the nodes in the left subtree are smaller.

Design an recursive algorithm that uses a treetraversal algorithm on a proper binary tree to check if the tree satisfies someproperty.

To 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)...

Make a binary tree implementation utilising the chapter's discussed recursive method. In this strategy, every node is a binary tree. A binary tree thus contains references to both its left and right subtrees as well as the element stored at its root.A mention of its parent may also be appropriate.

To 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...

Given the following tree, calculate the postorder traversal order of its e lements. F A В D E

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.

The Delete algorithm for a binary search tree retrieves and deletes the inorder successor when the node being deleted has two children. In this case the inorder successor is found as: O a. the smallest value in the left subtree. O b. the largest value in the right subtree. O c. the largest value in the left subtree. O d. None of these are correct O e. the smallest value in the right subtree.

In a binary search tree, to remove a node N that has left child C1 and right child C2, we do the following: Group of answer choices We make C1 the left child of N’s parent and C2 the right child of N’s parent We make C1 the right child of N’s parent and C2 the left child of N’s parent We find the largest item L in N’s left subtree, copy the contents of L to N, and remove L We find the smallest item S in N’s right subtree, copy the contents of S to N, and remove N We find the largest item L in N's right subtree, copy the contents of L to N, and remove L

Kruskal's Algorithm: Kruskal's algorithm is a minimum-spanning-tree algorithm which finds an edge of the least possible weight that connects any two trees in the forest. This algorithm is a Greedy Algorithm. The steps to find a MST using this algorithm are as follows: Sort all the edges in non-decreasing order of their weight. Pick the smallest edge. Check if it forms a cycle with the spanning tree formed so far. If cycle is not formed, include this edge. Else, discard it. Repeat step2 until there are (V-1) edges in the spanning tree. Example with 10 vertices and 20 weighted edges:

A Binary Search Tree (BST) can be used to efficiently implement a sorted set. It stores uniquevalues and offers an efficient membership method (contains).A binary search tree (BST) is a binary tree with the additional binary search tree property.The binary search tree property states that for every node n in the tree1. n.data is greater than the data value of all nodes in the sub-tree rooted with n.left.2. n.data is less than the data value of all nodes in the sub-tree rooted with n.right.As we are implementing a set, all data (strings) in the tree will be unique. Every node in the treewill have its own distinct string. Strings will be compared using the canonical way (as defined bythe compareTo() method in the String class).For example, the binary tree on the left (below) IS a binary search tree and the one on the rightis NOT.You will implement several methods in the BinaryTree and BST classes. The BST class mustextend the BinaryTree class. Methods that you must complete (implement or...

Draw a binary search tree by inserting the following numbers and determine the predecessor and successor of 10, 1, and 6. numbers to insert {8,1,5,4,9,10,6,3,15}

Given the following binary tree below, find the Inorder, Postorder and Preorder traversals. Also state which graph traversal algorithm was used in all three traversals