A standard method to reduce the search time for very large data bases is to implement a B+ tree of order m. an m-way search trie, where the role of internal nodes is to guide search as quickly as possible to the leaf node that must contain the key if it is present in the structure. Don't forget to review the definition on the first page of this problem. The questions in this problem are about members of the B-tree family of order m. You are expected to use the definitions provided below in your answers. Please read the questions carefully to make sure that you are addressing the correct structure in your answer. A B tree of order m is an m-way search tree. A B+ tree and B* tree of order m are m-way search tries. The root is either a leaf or has at least two non-empty child subtrees. . All the leaves are at the same level, and leaves have no child pointers. All internal nodes except the root must have at least [] non-empty child pointers for a B tree or a B+ tree. A non-root internal B*-tree node must have least [2] non-empty child pointers. All elements in the B-tree family of order m (B tree, B+ tree, or B* tree) have a maximum of p keys per leaf unless otherwise stated. The B tree and B+ tree must have at least [5] keys per leaf. The B* tree must have at least [keys per leaf. Please answer the following questions regarding the B tree family using the rules given above. 3.7 Derive an expression for the maximum number of keys that can be present in a B+ tree of order m with depth g. 3.8 Briefly explain how the value of m is selected for a B+ tree of order m that is to represent an extremely large data set. 3.10 Give a lower bound on the asymptotic complexity of search in a B+ tree of order m. Explain your answer for full credit. 3.11 Give an upper bound on the asymptotic complexity of search in a B+ tree of order m. Explain your answer for full credit. 3.12 By definition, the contents of the internal and external nodes of a B+ tree of order m are different because they play different roles in the structure. Briefly explain how the challenge of working with two distinct node types is handled when managing a B+ tree of order m.