3. What is the minimum number of nodes in an AVL tree of height 7? Articulate your answer

4. Suppose we allow storing duplicated keys in a Balanced Binary Search Tree. That is, two elements can have the same key. Describe how to perform the operation findAllElements(k), which returns all the items with keys equal to k in a balanced search tree, and show that it runs in O(logn + s), where n is the number of nodes in the tree and s is the number of nodes with key equal to k.

5. Suppose we have 20 singleton sets, numbered 0 through 19, and we call the operation union(find(i),fin(i+5)), for i = 0,1,2,.....,14. Draw a picture of the tree-based representation of the sets that results, assuming we dont implement the union-by-size and path compression techniques