For 3 page frames, the following is the reference string: 7 2 3 2 1 3 0 6 2 3 0 4 2 1 3 2 1 7 1 8 How many page faults does the LRU page replacement algorithm produceAnswer( Please choose a correct answer )   CLEAR10151216

To solve this problem, we need to simulate the Least Recently Used (LRU) page replacement algorithm. Here are the steps:

1. Start with an empty memory of 3 page frames.
2. For each page in the reference string, do the following:
   • If the page is already in memory, continue to the next page.
   • If the page is not in memory and there is an empty frame, load the page into the empty frame and continue to the next page.
   • If the page is not in memory and there are no empty frames, find the page that was least recently used and replace it with the current page. This is a page fault.
3. Count the number of page faults.

Let's apply these steps to the given reference string:

7 2 3 2 1 3 0 6 2 3 0 4 2 1 3 2 1 7 1 8

• Start with empty memory: [_, _, _]
• Load 7 into memory: [7, _, _] (1 page fault)
• Load 2 into memory: [7, 2, _] (2 page faults)
• Load 3 into memory: [7, 2, 3] (3 page faults)
• 2 is already in memory.
• Replace 7 with 1: [1, 2, 3] (4 page faults)
• 3 is already in memory.
• Replace 1 with 0: [0, 2, 3] (5 page faults)
• Replace 3 with 6: [0, 2, 6] (6 page faults)
• Replace 6 with 2: [0, 2, 2] (7 page faults)
• 3 is not in memory, replace 0 with 3: [3, 2, 2] (8 page faults)
• 0 is not in memory, replace 2 with 0: [3, 0, 2] (9 page faults)
• Replace 2 with 4: [3, 0, 4] (10 page faults)
• Replace 4 with 2: [3, 0, 2] (11 page faults)
• Replace 2 with 1: [3, 0, 1] (12 page faults)
• 3 is not in memory, replace 0 with 3: [3, 3, 1] (13 page faults)
• 2 is not in memory, replace 1 with 2: [3, 3, 2] (14 page faults)
• 1 is not in memory, replace 3 with 1: [1, 3, 2] (15 page faults)
• 7 is not in memory, replace 1 with 7: [7, 3, 2] (16 page faults)
• 1 is not in memory, replace 2 with 1: [7, 3, 1] (17 page faults)
• 8 is not in memory, replace 1 with 8: [7, 3, 8] (18 page faults)

So, the LRU page replacement algorithm produces 18 page faults for the given reference string with 3 page frames.