For a tree which uses lazy deletion, implement a function which counts the # of deleted nodes.
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- Draw a tree with a depth of 3 and indicate all the nodes as either a parent, child, root, or leaf node(s).Write a technique that quickly determines if any two nodes u and v in a tree T whose root node is s are descendants or ancestors.Write a function, singleParentWithLeftChild, that returns the number of nodes in a binary tree (pointed by p) that have only one left child. Your program should NOT count the nodes with one right child. (30 point) // find the number of singles parent nodes in a binary subtree pointed by p int BST::singleParentWithLeftChild(TreeNode* p) { // write your code here! }
- the main function, define a binary tree and fill it with 10random integers.For the given Binary Tree, list the keys in the order they are visited by each of the following traversal methods (a) Preorder (b) Inorder (c) PostorderWrite a technique that quickly identifies whether u is a descendant or ancestor of v in a tree T whose root node is s.
- construct a binary search tree using a set of numbers, similar to the example mentioned in the class. after constructing the BST, you need to give the pre-order traversal of the tree. Finally, you’re required to remove the root of tree. Please show me step by step how to do this!Apply tree traversals on the following binary tree picture inserted below..Attached is an image of a binary tree: Write the order of the nodes visited in: An in-order traversal: A pre-order traversal: A post-order traversal: What is the height of the above binary tree?
- 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.Implement a binary tree with the following criteria: - Minimum 5 nodes (including root) - Arbitrary value for each node - At least 1 node has leftChild and rightChild Then print / output the binary tree. Examples of expected output: 10 / \ 6 12 / \ \ 5 8 14To 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)…