Question1 An AVL tree uses the simple recursive structural constraint that the heights of the left and right subtrees of any node can differ by at most 1. However, this does not put a ixed constraint on the maximum difference in depth between any two given leaves of the AVL tree. In fact, the difference in depth between the shallowest and deepest leaves can be arbitrarily large given a large enough tree-but there are relative limits. a) Determine the minimim possible depth of other leaves as a function of dmax, the depth of the deepest leaf. (I.e., state a claim like "the depth of the shallowest leaf can be no less than the depth of the deepest leaf minus 2 (dmax - 2)) b) Draw an AVL tree where there is at least a 3-level difference between some pair of leaves. Make sure that what you drew is a legal AVL tree! Question 2 [If you are using the tree template, trim unnecessary branches, and replace all of the 'X's with either B' or 'r' (don't use uppercase 'R'--too similar to 'B')] For this question, assume we are talking about the version of red-black trees with dummy leaf nodes, i.e., all leaf nodes are black, and leaf nodes do not contain data. Also, we here define the black depth of a leaf to be the number of black nodes in the path from the root to the leaf, including the root but not counting the leaf node itself. Recall that in a red-black tree, all leaves in our tree must have the same black depth