Suppose that you just finished inserting several records into a heap file, and now you want to sort those records. Assume that the DBMS uses external sort and makes efficient use of the available buffer space when it sorts a file. Here is some potentially useful information about the newly loaded file and the DBMS software that is available to operate on it:
The number of records in the file is 4,500. The sort key for the file is four bytes long. You can assume that rids are eight bytes long and page ids are four bytes long. Each record is a total of 48 bytes long. The page size is 512 bytes. Each page has 12 bytes of control information on it. Four buffer pages are available.

1. How many sorted subfiles will there be after the initial pass of the sort, and how long will each subfile be?

2. How many passes (including the initial pass considered above) will be required to sort this file?

3. What will be the total I/O cost for sorting this file?

4. What is the largest file, in terms of the number of records, that you can sort with just four buffer pages in two passes? How would your answer change if you had 257 buffer pages?

5. Suppose that you have a B+ tree index with the search key being the same as the desired sort key. Find the cost of using the index to retrieve the records in sorted order for each of the following cases:

? The index uses Alternative (1) for data entries.

? The index uses Alternative (2) and is not clustered. (You can compute the worstcase cost in this case.)

? How would the costs of using the index change if the file is the largest that you can sort in two passes of external sort with 257 buffer pages? Give your answer for both clustered and unclustered indexes.