Write an insertion algorithm for B+ tree and Construct a tree for the following set of key values: 2, 3, 5, 7, 11, 17, 19, 23, 29, 31 Assume that the tree is initially empty and values are added in ascending order. Let the number of points that will fit in one node to be 5.

Given the following tree, calculate the postorder traversal order of its e lements. F A В D E

Problem Description Using the binary search tree (BST) data structure, we can sort a sequence of n elements by first calling an insertion procedure for n times to maintain a BST, and then performing an INORDER-TREE-WALK on the BST to output the elements in sorted order. To insert a node, we've discussed the TREE-INSERT procedure in class (also from page 294 of the text- book). This TREE-INSERT procedure can actually be improved to reduce the number of key comparisons so that each node's key is compared with the new node's key for at most once during each insertion. For example, given the following BST, The improved insertion procedure will make • 2 comparisons to insert a node with key = 1 • 3 comparisons to insert a node with key = 3 • 2 comparisons to insert a node with key = 8 5. Program Requirements In this programming assignment, you will implement in Java this sorting algorithm using BST, by using the improved insertion procedure. Note that each node of a BST is an object…

3. In a B*-tree, there can be at most 4 search-key values in each node. Assume that the height of the B*-tree is 2. The height of the tree is the length of the path from the root to a leaf node. a) What is the maximum number of leaf nodes this tree can have? Answer: b) Let N1 be a node in the tree. N1 is neither a leaf nor the root. What is the minimum number of children that N1 can have? Answer: