A modified optimal page replacement algorithm predicts only up to the next 4 page references (includ

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Question

A modified optimal page replacement algorithm predicts only up to the next 4 page references (including the current page). Process accesses pages: 1, 3, 2, 4, 2, 3, 1, 2, 4, 3, 1, 4. System has 3 frames initially empty. Number of page faults is ______.

Accepted Answer

Answer: 6Concept — Modified Optimal Page Replacement: Similar to Belady's optimal algorithm, but eviction decisions use only the next 4 reference positions (including the current one). When eviction is needed, the page whose next use (within the lookahead window) is farthest away is evicted. If a page is not in the next 4 references, it is considered "never used" (evict first).Reference string: 1, 3, 2, 4, 2, 3, 1, 2, 4, 3, 1, 4 (positions 1–12)   StepPageFramesLookahead (next 4 incl. current)EvictFault?     11{1}1,3,2,4—Yes  23{1,3}3,2,4,2—Yes  32{1,3,2}2,4,2,3—Yes  44Full! Lookahead: 4,2,3,1. Frames {1,3,2}. Next uses: 1→pos7, 3→pos6, 2→pos5. Farthest=1 at pos7. Evict 1.—{3,2,4}Yes  52{3,2,4}2,3,1,2HitNo  63{3,2,4}3,1,2,4HitNo  71Full! Lookahead: 1,2,4,3. Frames {3,2,4}. Next uses: 3→pos10, 2→pos8, 4→pos9. Farthest=3 at pos10. Evict 3.—{1,2,4}Yes  82{1,2,4}2,4,3,1HitNo  94{1,2,4}4,3,1,4HitNo  103Full! Lookahead: 3,1,4,—. Frames {1,2,4}. Next uses: 1→pos11, 4→pos12, 2→not in next 4 (evict first). Evict 2.—{1,4,3}Yes  111{1,4,3}1,4,—HitNo  124{1,4,3}4,—HitNo   Total page faults: positions 1, 2, 3, 4, 7, 10 = 6 faults

A modified optimal page replacement algorithm predicts only up to the next 4 page references (including the current page). Process accesses pages: 1, 3, 2, 4, 2, 3, 1, 2, 4, 3, 1, 4. System has 3 frames initially empty. Number of page faults is ______.

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A modified optimal page replacement algorithm predicts only up to the next 4 page references (including the current page). Process accesses pages: 1, 3, 2, 4, 2, 3, 1, 2, 4, 3, 1, 4. System has 3 frames initially empty. Number of page faults is ______.

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