We are going to design our B+ Tree to be as optimal as possible for our old hard drives . We want to keep the tree as short as we can, and pack each disk block in the filesystem as tightly as possible. We also want to access our data in sorted order for printing out reports, so each leaf node will have a pointer to the next one.

CPU architecture: Intel Xeon with 64 bit cores Filesystem: Ext4 with 4KB (4096 byte) blocks The customer records are keyed by a random UUID of 128 bits Customers Data record definition from the header file: #include struct CustomerData { uuid_t uuid; // Customer 128 bit key char[32] name; // Customer name (char is 1 byte each) uint32_t ytd_sales; // Customer year to date sales };

A. Calculate the size of the internal nodes (M) for our B-tree:

B. Calculate the size of the B-tree leaf nodes (L) for this tree make sure to include the pointer (note CPU architecture!) to keep the list of leaf nodes:

UUID UUID UUID UUIDJUUID UUID CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData Figure #1: Visualization of our B+ Tree of height 2, customer data records, and pointers between the leaf nodes UUID UUID UUID UUIDJUUID UUID CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData CustomerData Figure #1: Visualization of our B+ Tree of height 2, customer data records, and pointers between the leaf nodes