In the Least Recently Used (LRU) page replacement

Solution

LRU page replacement works by replacing the page that has not been used for the longest time. For the reference string 4, 2, 4, 1, 5, 2, 3, 4 with 3 frames, the page faults occur as follows: • Insert 4 (fault), Insert 2 (fault), Access 4 (hit), Insert 1 (fault), Insert 5 (fault, replace 4), Access 2 (hit), Insert 3 (fault, replace 1), Access 4 (fault, replace 5). Thus, there are 6 page faults in total. LRU minimizes page faults compared to other algorithms by always keeping the most recently used pages in memory. Why other options are wrong: A) 3 faults would require the reference string to contain repeated pages with no replacements. B) 5 faults underestimate the replacements required after the first few frames fill up. D) 7 faults occur in algorithms with more aggressive replacements like FIFO. E) 8 faults assume no page hits at all, which is incorrect since some pages are reused before replacement.