Organizing and accessing data are essential for effective programming. Every graduate student in computer science or computer engineering should know how to design and use data structures to create elegant, efficient, and effective code. You should also be able to analyze data structures and algorithms for time and space complexity and how to select, implement, and test the best data structures for complex programming tasks. 1. Suppose the following values are inserted, in the given order, into an empty AVL tree: 1,12,31,35,40. What value is the left child of 35 ? (You may answer "NULL" if 35 has no right child.) 2. Suppose the following words were inserted into a compressed alphabet trie, using the symbol $ to represent the end of a word: cat, cats, bat, bats, battery. How many nodes would the re'sulting tree contain? 3. How many nodes of this K-D tree are visited (e.g. searched or explored) in performing the range query "find all points within 15 units of (25,50)