In the worst-case situation, binary tree sort using a self-balancing binary search tree requires O(n log n) time, which is slower than merge sort.

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) Postorder

Suppose you have a binary search tree with 100 nodes and you want to find the node with the maximum value. What is the time complexity of this operation?

Construct a Binary Search Tree (BST) for the following array elements  [50, 15, 62, 5, 20, 58, 91, 3, 8, 37, 60, 24] Delete element 15 from the constructed BST After deletion, using the new BST, add element 12 to the BST

Use a simple recursive technique to determine whether a binary tree is BST?

Create an implementation of a binary tree using the recursive approach introduced in the chapter. In this approach, each node is abinary tree. Thus a binary tree contains a reference to the elementstored at its root as well as references to its left and right subtrees.You may also want to include a reference to its parent.

7. For a binary tree like what follows. Please use deletion by merging to delete node 32. Show your work(step by step) 29 89 14 32 20 50 43 78 44

Q1 PLEASE QUESTION 1:(a) Draw a binary search tree (BST) after the insertion of keys: 8, 3, 2, 1, 4, and 9, in this order.(b) List the node keys of the above BST in pre-order, in-order, and post-order, respectively.

Create a binary linked tree, and traverse the tree by using the recursive function. The structure of the tree is as follow:   You should input the nodes in pre-order sequence. If a child of a node is NULL, input a space. Write the function of create binary tree, pre-order to print the nodes, in-order to print the nodes and post-order to print the nodes. Count the height of the tree.   Header file typedef char ElemType;   typedef struct node//define the type of binary tree node {                                       }BTnode;       Source file #include <stdio.h> #include <stdlib.h> #include "tree.h"   BTnode * createTree()//create the binary tree，return the root {             BTnode *tnode;// tnode is the root             char elem;                                ;//input the character                            //if the input is a space，set the pointer as NULL               Else// if the input is not a space，generate the binary node and create its left sub-tree and right…