Contiguous allocation in Operating Systems - Time & Space Complexity

Time Complexity: Contiguous allocation

O(n * m)

Understanding Time Complexity

When managing files in an operating system, contiguous allocation stores files in one continuous block on disk.

We want to understand how the time to find or allocate space grows as file size or disk size changes.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

int find_contiguous_space(int disk[], int size, int file_size) {
  for (int i = 0; i < size; i++) {
    int count = 0;
    while (count < file_size && i + count < size && disk[i + count] == 0) {
      count++;
    }
    if (count == file_size) {
      return i; // start index found
    }
  }
  return -1; // no space found
}
    

This code searches the disk array to find a continuous free space block large enough for the file.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The outer loop scans each disk block, and the inner while loop checks consecutive blocks for free space.
• How many times: The outer loop runs up to the disk size, and the inner loop runs up to the file size for each position.

How Execution Grows With Input

As the disk size grows, the search checks more starting points. For each, it may check up to the file size blocks.

Input Size (disk size n)	Approx. Operations
10	Up to 10 * file_size checks
100	Up to 100 * file_size checks
1000	Up to 1000 * file_size checks

Pattern observation: The total checks grow roughly by multiplying disk size and file size.

Final Time Complexity

Time Complexity: O(n * m)

This means the time to find space grows proportionally to the disk size times the file size.

Common Mistake

[X] Wrong: "The search time depends only on the disk size, not the file size."

[OK] Correct: Because for each disk position, the code checks up to the file size blocks to confirm continuous free space.

Interview Connect

Understanding how searching for continuous space scales helps you reason about file system efficiency and resource management.

Self-Check

What if the disk was represented as a linked list instead of an array? How would the time complexity change?

Practice

1. What is the main characteristic of contiguous allocation in operating systems?

easy

A. Files are stored in one continuous block of memory.

B. Files are stored in multiple scattered blocks.

C. Files are stored using linked lists.

D. Files are stored in indexed blocks.

Solution

1. Step 1: Understand file storage methods

   Contiguous allocation means storing a file in one continuous block of memory without breaks.

2. Step 2: Compare with other methods

   Other methods like linked or indexed allocation store files in scattered blocks or use pointers.

3. Final Answer:

   Files are stored in one continuous block of memory. -> Option A

4. Quick Check:

   Contiguous allocation = continuous block storage [OK]

Hint: Contiguous means continuous block storage [OK]

Common Mistakes:

• Confusing contiguous with linked allocation
• Thinking files are scattered in contiguous allocation
• Mixing indexed allocation with contiguous

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

easy

A. Files are divided into fixed-size blocks scattered across memory.

B. Files use pointers to link scattered blocks.

C. Files occupy a single continuous block of memory.

D. Files are stored in a tree-like index structure.

Solution

1. Step 1: Identify the definition of contiguous allocation

   Contiguous allocation means the entire file is stored in one continuous block of memory.

2. Step 2: Eliminate incorrect options

   Options A, B, and D describe other allocation methods like linked or indexed allocation.

3. Final Answer:

   Files occupy a single continuous block of memory. -> Option C

4. Quick Check:

   Continuous block = contiguous allocation [OK]

Hint: Continuous block means contiguous allocation [OK]

Common Mistakes:

• Choosing linked or indexed allocation descriptions
• Confusing fixed-size blocks with contiguous storage
• Assuming pointers are used in contiguous allocation

3. Consider a file system using contiguous allocation. If a file of size 10 blocks is stored starting at block 50, which blocks does it occupy?

medium

A. Blocks 60 to 69

B. Blocks 40 to 49

C. Blocks 51 to 60

D. Blocks 50 to 59

Solution

1. Step 1: Understand starting block and file size

   The file starts at block 50 and occupies 10 continuous blocks.

2. Step 2: Calculate occupied blocks

   Blocks occupied are from 50 up to 50 + 10 - 1 = 59.

3. Final Answer:

   Blocks 50 to 59 -> Option D

4. Quick Check:

   Start 50 + size 10 = blocks 50-59 [OK]

Hint: Start block + size - 1 = last block [OK]

Common Mistakes:

• Off-by-one errors in block range
• Starting count from 1 instead of 0
• Choosing blocks after the last block

4. A file stored using contiguous allocation needs to be extended by 5 blocks, but the next 5 blocks after the file are occupied. What is the main problem here?

medium

A. File cannot be extended because contiguous space is not available.

B. File can be extended by linking scattered blocks.

C. File size can be increased without any issue.

D. File can be moved to another location without fragmentation.

Solution

1. Step 1: Understand contiguous allocation extension

   Files must occupy continuous blocks; extension requires free blocks immediately after the file.

2. Step 2: Analyze the problem

   Since the next 5 blocks are occupied, the file cannot be extended contiguously.

3. Final Answer:

   File cannot be extended because contiguous space is not available. -> Option A

4. Quick Check:

   Extension needs free contiguous blocks [OK]

Hint: Extension needs free continuous blocks [OK]

Common Mistakes:

• Assuming scattered blocks can be linked in contiguous allocation
• Ignoring fragmentation issues
• Thinking file can grow without moving

5. You have a disk with free blocks scattered as follows: 5 blocks free at 0-4, 3 blocks free at 10-12, and 7 blocks free at 20-26. You want to store a file of size 6 blocks using contiguous allocation. Which free space can you use and why?

hard

A. Blocks 10-12, because they are in the middle of the disk.

B. Blocks 20-25, because they have enough continuous free blocks.

C. Blocks 0-4, because they are the first free blocks.

D. No space is available because all free blocks are scattered.

Solution

1. Step 1: Identify free block sizes

   Free blocks are 5 at 0-4, 3 at 10-12, and 7 at 20-26.

2. Step 2: Find a continuous free space of at least 6 blocks

   Only blocks 20-26 have 7 continuous free blocks, enough for 6 blocks.

3. Final Answer:

   Blocks 20-25, because they have enough continuous free blocks. -> Option B

4. Quick Check:

   Need ≥6 continuous blocks, only 20-26 fits [OK]

Hint: Choose free space with enough continuous blocks [OK]

Common Mistakes:

• Choosing smaller free blocks that don't fit file size
• Ignoring the need for continuous blocks
• Assuming scattered free blocks can be combined