Final answer:
The number of page faults using the optimal page replacement policy for the given reference string and memory with three frames is 11, which results in approximately 57.89% page faults. The closest provided option is 55%.
Step-by-step explanation:
The question deals with the optimal page replacement policy in operating systems, which is used for managing memory. The reference string provided represents the pages that need to be loaded into memory frames. Since there are three frames available and nineteen page requests, we'll calculate the number of page faults by simulating the optimal page replacement algorithm.
- Start with an empty memory of 3 frames.
- For each page in the reference string, check if it's already in a frame.
- If it's not, this is a page fault, and we must bring it into memory.
- Use the optimal page replacement strategy to replace the page that will not be used for the longest period of time in the future.
- Continue this process for all pages in the reference string.
By performing these steps, the sequence of page faults occurs as follows: 7, 0, 1, 2 (replaces 7), 3 (replaces 0), 0 (replaces 1), 4 (replaces 2), 2 (replaces 3), 3 (replaces 0), 0 (replaces 4), 1 (replaces 2), and 7 (replaces 3). In total, there are 11 page faults.
The percentage of page faults is calculated by dividing the number of page faults by the total number of page references and then multiplying by 100. Therefore, the calculation is (11/19) * 100, which is approximately 57.89%. This is not exactly 55% or 60%, so none of the provided answers (a) 85%, (b) 45%, (c) 55%, or (d) 65% is precisely correct. However, the closest option is (c) 55%, which might be assumed as a rounding consideration.