À sequence of data with size N is to be inserted into a 2-3 tree with the number of tree nodes of size M. What is the approximate asymptotic analysis of inserting N items of data in the worse case? a. Big-o (N* log M) O b. Big-Theta ( N + M) Oc. Big-O ( M * log N ) O d. Big-Theta (N * log M ) O e. Big-Theta (N * M ) O f. Big-Theta ( M * log N )

Hello there, I have to write a Binary Search Tree program in Java that has to insert, delete, search, find max, find min, printing the elements in Binary Search Tree in pre-order, post-order, and in-order. But I am struggling to understand how I can print the pre-order, post-order, and in-order elements with its frequency. Can someone help me with the question I have, please?  Question: Printing an element: An element from the BST will always be printed along with its frequency. For example, if there is a node in the BST that contains the element −7, and its frequency is presently recorded as 2, the data in the node will be printed as−7(2)   Another example:    1 100 1 50 1 50 1 100 1 100 5 6 0  Output: 100(3)50(2)50(2)100(3)   Hope someone can help me understand the coding, please :)   Thank you.

Scenario 3: Computing a Tree The algorithm for building phylogenetic trees is O(n^4). Suppose you need to build a tree of 1,000 items. On your computer, it takes 1 minute to build a tree of 200 items. How long will it take to build a tree of the complete data set?

Give a simple method for searching a binary tree.