1. (20 points) Based on the problem type in parentheses (True/False, fill in the Blank (FIB), or briefly answer (ANS)), answer the following questions. 1-1 What is the maximum and minimum number of leaf nodes of a complete binary tree of height 5 ? Answer the same question for a complete binary tree of height k. (FIB) 1-2 Assume that a max heap with 20 nodes is represented sequentially using an array T as explained in class. Where is the largest number in T? What is the range of indexes where the smallest number may reside? (FIB) 1-3 On a binary search tree, what will happen if the root is deleted? Which node will become the new root? 1-4 Given the inorder and preorder traversal results, we can always construct a unique binary tree. (True/False) 1-5 Consider a max heap T with 30 nodes represented by an array as discussed in class. How many swapping do we need if a value smaller than all existing values is inserted? Where will the new value be placed? Answer the same questions above when a value larger than all existing values is inserted. 1-6 Given an undirected graph G which has exactly two connected components H I and H2. What is the relationship between the set of vertices V1 of H1 and the set of vertices V2 of H2 ? Let V be the set of vertices of G. What is the relationship between V,VI and V2 ? Briefly explain you answers. 1.7 Given a biconnected graph G, will the graph be connected after the removal of an edge? Will G be connected after the removal of a vertex? Consider all possible cases and briefly explain your