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# GATE | GATE-CS-2014-(Set-1) | Question 65

• Difficulty Level : Basic
• Last Updated : 11 Sep, 2019

Assume that there are 3 page frames which are initially empty. If the page reference string is 1, 2, 3, 4, 2, 1, 5, 3, 2, 4, 6, the number of page faults using the optimal replacement policy is__________.
(A) 5
(B) 6
(C) 7
(D) 8

Explanation: In optimal page replacement replacement policy, we replace the place which is not used for longest duration in future.

```Given three page frames.

Reference string is 1, 2, 3, 4, 2, 1, 5, 3, 2, 4, 6

Initially, there are three page faults and entries are
1  2  3

Page 4 causes a page fault and replaces 3 (3 is the longest
distant in future), entries become
1  2  4
Total page faults =  3+1 = 4

Pages 2 and 1 don't cause any fault.

5 causes a page fault and replaces 1, entries become
5  2  4
Total page faults =  4 + 1 = 5

3 causes a page fault and replaces 5, entries become
3  2  4
Total page faults =  5 + 1 = 6

3, 2 and 4 don't cause any page fault.

6 causes a page fault.
Total page faults =  6 + 1 = 7```

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