Given information:

Suppose I have a relation Grades(student_id, assignment_id, score). I have 200 students and 20 assignments. I would grade all submissions of one assignment based on the submission order, and then insert the records. As a result, based on my insertion nature, the student_id is not sorted, but the assignment_id is. I choose heap file as my file organization. My page is quite small it can only store 40 records, or 200 bytes in one page. The SearchKeySize is 2 bytes and PointerSize is 2 bytes. My buffer size is also small, 4 pages.

100pages needed to store :

1. 1. I want to improve the I/O cost. I am debating if I need to build index for student_id, or to sort based on student_id. So I need to do some estimation. Please help me by answering the following questions.
2. 1. What is the I/O cost of multi-way merge sort if I sort the relation after I enter all records?

Please Answer the following question with an explanation .