Construct a B+-tree for the following set of values(2, 3, 5, 7, 11, 17, 19, 23, 29, 31)Assume that the tree is initially empty and values are inserted in ascending order.1) Construct B+-trees for the cases where the number m of pointers that will fit a node is as follows:a. Fourb. Seven

To construct a B+-tree for the given set of values (2, 3, 5, 7, 11, 17, 19, 23, 29, 31), we will follow the steps for each case where the number of pointers that will fit a node is four and seven.

a) Constructing a B+-tree with four pointers per node:

1. Start with an empty tree.
2. Insert the first value, 2, as the root node.
3. Insert the second value, 3, as the right child of the root node.
4. Insert the third value, 5, as the right child of the second node.
5. Insert the fourth value, 7, as the right child of the third node.
6. Insert the fifth value, 11, as the right child of the fourth node.
7. Insert the sixth value, 17, as the right child of the fifth node.
8. Insert the seventh value, 19, as the right child of the sixth node.
9. Insert the eighth value, 23, as the right child of the seventh node.
10. Insert the ninth value, 29, as the right child of the eighth node.
11. Insert the tenth value, 31, as the right child of the ninth node.

The resulting B+-tree with four pointers per node would look like this:

                  7
                /   \
               2     11
                    /   \
                   5     17
                          /  \
                         3    19
                              /  \
                             23   29
                                  \
                                   31

b) Constructing a B+-tree with seven pointers per node:

1. Start with an empty tree.
2. Insert the first value, 2, as the root node.
3. Insert the second value, 3, as the right child of the root node.
4. Insert the third value, 5, as the right child of the second node.
5. Insert the fourth value, 7, as the right child of the third node.
6. Insert the fifth value, 11, as the right child of the fourth node.
7. Insert the sixth value, 17, as the right child of the fifth node.
8. Insert the seventh value, 19, as the right child of the sixth node.
9. Insert the eighth value, 23, as the right child of the seventh node.
10. Insert the ninth value, 29, as the right child of the eighth node.
11. Insert the tenth value, 31, as the right child of the ninth node.

The resulting B+-tree with seven pointers per node would look like this:

                  7
                /   \
               2     11
                    /   \
                   5     17
                          /  \
                         3    19
                              /  \
                             23   29
                                  \
                                   31

Please note that the B+-tree structure remains the same regardless of the number of pointers per node. The only difference is the number of values that can be stored in each node.