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Mediumpaginglrupage fault

~165s

Counting LRU page faults

A process references the pages 7, 0, 1, 2, 0, 3, 0, 4. With three frames and LRU replacement, how many page faults occur?

Show the answer and the worked solution

Correct answer: C.

6

Worked solution

  1. 7, 0 and 1 fault into the empty frames, leaving [7, 0, 1] with 7 the least recently used.
  2. 2 faults and evicts 7, giving [0, 1, 2].
  3. The reference to 0 is a hit and makes 0 the most recently used, so 1 becomes the least recently used.
  4. 3 faults and evicts 1, giving [0, 2, 3]; the next reference to 0 is a hit, leaving 2 least recently used.
  5. 4 faults and evicts 2. The faults are on 7, 0, 1, 2, 3 and 4 — 6 in total.

Answer: 6.

The idea

LRU approximates the optimal policy by assuming the recent past predicts the near future. Its cost is the bookkeeping: real systems approximate it with reference bits or a second-chance clock.

Shortcut. Only the two re-references to 0 hit, because 0 is always recent when it returns, so 8 − 2 = 6 faults.

Common trap. 7 is the FIFO count: evicting the oldest-loaded page throws 0 out at the reference to 3, so the next 0 faults as well.

OS, DBMS & Networks

9 of 40

Level

Medium

Target time

~165s

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Counting LRU page faults — Aptitude Question

Counting LRU page faults: A process references the pages 7, 0, 1, 2, 0, 3, 0, 4. With three frames and LRU… Answer and worked solution on CodeKairo.

Question

A process references the pages 7, 0, 1, 2, 0, 3, 0, 4. With three frames and LRU replacement, how many page faults occur?

Options

  1. 4
  2. 5
  3. 6
  4. 7
Show the answer and the worked solution

Correct answer: C. 6

Worked solution

  1. 7, 0 and 1 fault into the empty frames, leaving [7, 0, 1] with 7 the least recently used.
  2. 2 faults and evicts 7, giving [0, 1, 2].
  3. The reference to 0 is a hit and makes 0 the most recently used, so 1 becomes the least recently used.
  4. 3 faults and evicts 1, giving [0, 2, 3]; the next reference to 0 is a hit, leaving 2 least recently used.
  5. 4 faults and evicts 2. The faults are on 7, 0, 1, 2, 3 and 4 — 6 in total.

Answer: 6.

The idea

LRU approximates the optimal policy by assuming the recent past predicts the near future. Its cost is the bookkeeping: real systems approximate it with reference bits or a second-chance clock.

Shortcut. Only the two re-references to 0 hit, because 0 is always recent when it returns, so 8 − 2 = 6 faults.

Common trap. 7 is the FIFO count: evicting the oldest-loaded page throws 0 out at the reference to 3, so the next 0 faults as well.

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