File allocation methods (contiguous, linked, indexed) in Operating Systems - Time & Space Complexity

Time Complexity: File allocation methods (contiguous, linked, indexed)

O(n)

Understanding Time Complexity

When managing files on a disk, the way files are stored affects how long it takes to access them.

We want to understand how the time to find or read a file grows as the file size or disk size increases.

Scenario Under Consideration

Analyze the time complexity of accessing a file using different allocation methods.

// Example: Accessing all blocks of a file
for (int i = 0; i < file_size; i++) {
    read_block(block_address[i]);
}
    

This code reads each block of a file one by one using the block addresses stored according to the allocation method.

Identify Repeating Operations

We look at how many times the system must find and read blocks.

• Primary operation: Reading each block of the file.
• How many times: Once per block, repeated for all blocks in the file.

How Execution Grows With Input

As the file size grows, the number of blocks to read grows too.

Input Size (blocks)	Approx. Operations (block reads)
10	10 reads
100	100 reads
1000	1000 reads

Pattern observation: The number of operations grows directly with the file size.

Final Time Complexity

Time Complexity: O(n)

This means the time to access the whole file grows linearly with the number of blocks in the file.

Common Mistake

[X] Wrong: "Accessing any block in a file always takes the same time regardless of allocation method."

[OK] Correct: Different allocation methods affect how quickly the system finds each block, so access time can vary.

Interview Connect

Understanding how file storage methods affect access time helps you explain system design choices clearly and confidently.

Self-Check

What if we used an indexed allocation with a multi-level index? How would that change the time complexity of accessing a block?

Practice

1. Which file allocation method stores all file blocks in one continuous sequence on disk?

easy

A. Hybrid allocation

B. Linked allocation

C. Indexed allocation

D. Contiguous allocation

Solution

1. Step 1: Understand file storage methods

   Contiguous allocation stores all file blocks one after another in a continuous space on disk.

2. Step 2: Compare with other methods

   Linked allocation stores blocks scattered with pointers; indexed uses an index block. Only contiguous is continuous.

3. Final Answer:

   Contiguous allocation -> Option D

4. Quick Check:

   Continuous blocks = Contiguous allocation [OK]

Hint: Continuous blocks mean contiguous allocation [OK]

Common Mistakes:

• Confusing linked allocation with contiguous
• Thinking indexed allocation stores blocks continuously
• Assuming hybrid is a standard method

2. Which of the following is the correct way to describe linked allocation?

easy

A. File blocks are stored in a continuous sequence

B. Each file block contains a pointer to the next block

C. An index block contains pointers to all file blocks

D. File blocks are stored in a fixed-size table

Solution

1. Step 1: Recall linked allocation structure

   In linked allocation, each file block stores a pointer to the next block, forming a chain.

2. Step 2: Eliminate other options

   Continuous sequence is contiguous; index block is indexed allocation; fixed-size table is unrelated.

3. Final Answer:

   Each file block contains a pointer to the next block -> Option B

4. Quick Check:

   Pointers in blocks = Linked allocation [OK]

Hint: Pointers inside blocks mean linked allocation [OK]

Common Mistakes:

• Mixing up index block with linked pointers
• Thinking linked allocation stores blocks continuously
• Confusing fixed-size table with file allocation

3. Consider a file stored using indexed allocation with an index block containing pointers to data blocks 5, 9, and 12. Which block does the system read first to access the file?

medium

A. The index block

B. Block 5

C. Block 9

D. Block 12

Solution

1. Step 1: Understand indexed allocation access

   The system first reads the index block to find pointers to all data blocks.

2. Step 2: Identify the first block read

   Before accessing data blocks 5, 9, or 12, the index block must be read to know their locations.

3. Final Answer:

   The index block -> Option A

4. Quick Check:

   Index block read first in indexed allocation [OK]

Hint: Index block is always read first in indexed allocation [OK]

Common Mistakes:

• Choosing a data block instead of the index block
• Confusing linked allocation with indexed
• Assuming direct access without index

4. A file system uses linked allocation but the file's blocks are stored non-contiguously without pointers linking them. What is the main problem here?

medium

A. File blocks are stored contiguously, causing slow access

B. File blocks are fragmented but linked correctly

C. Pointers are missing, so file blocks cannot be accessed sequentially

D. Index block is corrupted

Solution

1. Step 1: Understand linked allocation requirements

   Linked allocation requires each block to have a pointer to the next block for sequential access.

2. Step 2: Identify the problem without pointers

   Without pointers, the system cannot follow the chain, so blocks cannot be accessed in order.

3. Final Answer:

   Pointers are missing, so file blocks cannot be accessed sequentially -> Option C

4. Quick Check:

   Missing pointers break linked allocation chain [OK]

Hint: No pointers means linked allocation fails [OK]

Common Mistakes:

• Assuming fragmentation is not a problem
• Confusing contiguous storage with linked allocation
• Thinking index block is involved in linked allocation

5. A file of size 12 blocks is stored using contiguous allocation starting at block 20. If block 25 is corrupted, what is the impact on the file access?

hard

A. The entire file becomes inaccessible due to break in continuity

B. File access continues using pointers from block 25

C. Only block 25 is lost; other blocks are accessible

D. Index block redirects access around block 25

Solution

1. Step 1: Recall contiguous allocation properties

   Files are stored in continuous blocks; any corruption breaks the sequence.

2. Step 2: Analyze impact of corrupted block 25

   Since block 25 is in the middle, the file cannot be read beyond that point, making the entire file inaccessible.

3. Final Answer:

   The entire file becomes inaccessible due to break in continuity -> Option A

4. Quick Check:

   Corruption breaks contiguous file access [OK]

Hint: Contiguous files fail if any block is corrupted [OK]

Common Mistakes:

• Assuming only corrupted block is lost
• Thinking pointers or index block help in contiguous allocation
• Confusing linked or indexed allocation behavior