Consider the following page reference string:1,2,3,4,5,3,4,1,2,7,8,7,8,9,7,8,9,5,4,5. How many page faults would occur for the following replacement algorithm, assuming four frames:a) FIFOb) LRU

Consider the following page reference string:
1,2,3,4,5,3,4,1,2,7,8,7,8,9,7,8,9,5,4,5. How many page faults would occur for the following replacement algorithm, assuming four frames:
a) FIFO
b) LRU

a) FIFO (First In First Out) algorithm:

Using the FIFO algorithm with four frames and the given page reference string, the page faults occur as follows:

Page	Frame 0	Frame 1	Frame 2	Frame 3	Page Fault?
1	1				Yes
2	1	2			Yes
3	1	2	3		Yes
4	1	2	3	4	Yes
5	5	2	3	4	Yes
3	5	2	3	4	No
4	5	2	3	4	No
1	5	2	3	4	No
2	5	2	3	4	No
7	5	7	3	4	Yes
8	5	7	8	4	Yes
7	5	7	8	4	No
8	5	7	8	4	No
9	5	7	8	9	Yes
7	5	7	8	9	No
8	5	7	8	9	No
9	5	7	8	9	No
5	5	7	8	9	No
4	5	4	8	9	Yes
5	5	4	8	9	No

Therefore, the total number of page faults is 9.

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b) LRU (Least Recently Used) algorithm:

Using the LRU algorithm with four frames and the given page reference string, the page faults occur as follows:

Page	Frame 0	Frame 1	Frame 2	Frame 3	Page Fault?
1	1				Yes
2	1	2			Yes
3	1	2	3		Yes
4	1	2	3	4	Yes
5	5	2	3	4	Yes
3	5	2	3	4	No
4	5	2	3	4	No
1	1	2	3	4	Yes
2	1	2	3	4	No
7	1	2	7	4	Yes
8	1	2	7	8	Yes
7	1	2	7	8	No
8	1	2	7	8	No
9	1	2	7	9	Yes
7	1	2	7	9	No
8	1	2	8	9	Yes
9	1	2	8	9	No
5	1	2	5	9	Yes
4	1	2	5	4	Yes
5	1	2	5	4	No

Therefore, the total number of page faults is 10.