Page replacement algorithms (FIFO, LRU, Optimal) in Operating Systems - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding FIFO Page Replacement

Consider a system using the FIFO (First-In-First-Out) page replacement algorithm with 3 page frames. Given the page reference string: 7, 0, 1, 2, 0, 3, 0, 4, how many page faults will occur?

A 7

B 5

C 6

D 4

💡 Hint

Remember, FIFO replaces the oldest loaded page first.

With 3 frames, the pages loaded and replaced in order cause 7 page faults for the given string.

🔍 Analysis

intermediate

LRU Page Replacement Behavior

Using the LRU (Least Recently Used) algorithm with 4 page frames, analyze the page reference string: 1, 2, 3, 4, 1, 2, 5, 1, 2, 3, 4, 5. How many page faults will occur?

A 10

B 9

C 8

D 7

💡 Hint

LRU replaces the page that was least recently used when a replacement is needed.

Tracking the pages shows 9 page faults for the given reference string with 4 frames under LRU.

❓ Comparison

advanced

Optimal vs FIFO Page Replacement

Given the page reference string 2, 3, 2, 1, 5, 2, 4, 5, 3, 2, 5, 2 and 3 page frames, which algorithm results in fewer page faults: FIFO or Optimal?

A FIFO results in fewer page faults

B Cannot determine without frame size

C Optimal results in fewer page faults

D Both have the same number of page faults

💡 Hint

Optimal algorithm replaces the page that will not be used for the longest time in the future.

Optimal always results in the least number of page faults compared to FIFO for the same reference string and frame size.

❓ Reasoning

advanced

Identifying Page Faults in LRU

With 2 page frames and the reference string 1, 2, 3, 2, 1, 4, 5, which pages cause page faults under the LRU algorithm?

A 1, 2, 3, 4, 5

B 1, 2, 3, 5

C 1, 2, 3, 4

D 1, 3, 4, 5

💡 Hint

Page faults occur when a page is not in any frame at the time of reference.

Pages 1, 2, 3, 4, and 5 cause faults; 2 and 1 are hits on second references.

📋 Factual

expert

Optimal Page Replacement Algorithm Property

Which statement correctly describes the Optimal page replacement algorithm?

A It replaces the page that was loaded first in memory

B It replaces the page that has the highest frequency of use

C It replaces the page that was least recently used

D It replaces the page that will not be used for the longest time in the future

💡 Hint

Think about how Optimal predicts future page references.

Optimal replaces the page that will not be needed for the longest time in the future, minimizing page faults.

Practice

1. Which page replacement algorithm removes the page that has been in memory the longest, regardless of usage?

easy

A. FIFO (First In First Out)

B. LRU (Least Recently Used)

C. Optimal

D. Random

Solution

1. Step 1: Understand FIFO behavior

   FIFO removes the oldest page loaded into memory first, ignoring how often it is used.

2. Step 2: Compare with other algorithms

   LRU removes the least recently used page, Optimal removes the page not needed for the longest future time, Random removes any page randomly.

3. Final Answer:

   FIFO (First In First Out) -> Option A

4. Quick Check:

   Oldest page removed = FIFO [OK]

Hint: Oldest page out means FIFO [OK]

Common Mistakes:

• Confusing FIFO with LRU
• Thinking Optimal removes oldest page
• Assuming Random is FIFO

2. Which of the following is the correct description of the LRU page replacement algorithm?

easy

A. Removes the page that will not be used for the longest time in the future

B. Removes the least recently used page

C. Removes the oldest page loaded into memory

D. Removes a random page

Solution

1. Step 1: Recall LRU definition

   LRU removes the page that has not been used for the longest time recently.

2. Step 2: Match options with definitions

   Removes the page that will not be used for the longest time in the future describes Optimal, C describes FIFO, B is random removal.

3. Final Answer:

   Removes the least recently used page -> Option B

4. Quick Check:

   Least recently used = LRU [OK]

Hint: Least recent use means LRU [OK]

Common Mistakes:

• Mixing LRU with Optimal
• Confusing LRU with FIFO
• Choosing random removal as LRU

3. Given the page reference string 7, 0, 1, 2, 0, 3, 0, 4 and 3 page frames, how many page faults occur using the FIFO algorithm?

medium

A. 6

B. 5

C. 7

D. 4

Solution

1. Step 1: Simulate FIFO with 3 frames

   Load pages in order: 7 (fault), 0 (fault), 1 (fault), then 2 replaces 7 (fault), 0 is in memory (no fault), 3 replaces 0 (fault), 0 replaces 1 (fault), 4 replaces 2 (fault).

2. Step 2: Count total faults

   Faults occur at 7,0,1,2,3,0,4 = 7 faults, but 0 at position 6 is already in memory, so no fault there. Total faults = 6.

3. Final Answer:

   6 -> Option A

4. Quick Check:

   Count page faults in FIFO = 6 [OK]

Hint: Count faults when page not in frames FIFO order [OK]

Common Mistakes:

• Counting repeated pages as faults
• Mixing FIFO with LRU results
• Forgetting to replace oldest page

4. Identify the error in this LRU page replacement simulation with 2 frames and reference string 1, 2, 3, 2, 1, 4: The algorithm replaces page 1 first instead of page 3.

medium

A. Algorithm should replace page 2 first

B. Algorithm should replace oldest page, which is page 1

C. Algorithm should replace least recently used page, which is page 3

D. Algorithm should replace a random page

Solution

1. Step 1: Simulate LRU up to replacement point

   1(fault)[1], 2(fault)[1,2], 3 replaces LRU=1 [2,3], 2(hit) updates LRU=3 MRU=2 [3,2]. Next 1 should replace LRU=3.

2. Step 2: Check replacement choice

   The error is replacing page 1 instead of the least recently used page 3.

3. Final Answer:

   Algorithm should replace least recently used page, which is page 3 -> Option C

4. Quick Check:

   LRU replaces least recently used page [OK]

Hint: Replace least recently used page in LRU [OK]

Common Mistakes:

• Replacing oldest page instead of least used
• Confusing LRU with FIFO
• Replacing wrong page due to usage order

5. You have 4 page frames and the reference string 1, 2, 3, 4, 2, 1, 5, 1, 2, 3, 4, 5. Using the Optimal page replacement algorithm, how many page faults will occur?

hard

A. 7

B. 8

C. 9

D. 6

Solution

1. Step 1: Simulate Optimal with 4 frames

   1,2,3,4 (4 faults). 2 hit, 1 hit. 5 replaces 4 (farthest next at pos11, fault 5). 1 hit, 2 hit, 3 hit. 4 replaces 1 (no future use, fault 6). 5 hit.

2. Step 2: Count total faults

   Total faults = 6.

3. Final Answer:

   6 -> Option D

4. Quick Check:

   Optimal page faults counted = 6 [OK]

Hint: Replace page not needed longest in future [OK]

Common Mistakes:

• Counting repeated pages as faults
• Using FIFO or LRU logic instead of Optimal
• Forgetting to check future references