[Solved] What is the time complexity of accessing the nth data block in a file using an inode with direct, single, double, and triple indirect pointers, assuming each indirect block contains M pointers? | Operating Systems

Operating Systems - Inode Structure - File Metadata & Block Pointers

What is the time complexity of accessing the nth data block in a file using an inode with direct, single, double, and triple indirect pointers, assuming each indirect block contains M pointers?

AO(1) for direct blocks; O(1) for indirect blocks due to fixed pointer levels

BO(M) for indirect blocks because each indirect block must be scanned linearly

CO(n) for all blocks because indirect pointers require sequential traversal

DO(1) for direct blocks; O(log_M n) for indirect blocks due to multi-level indirection

Step-by-Step Solution

Solution:

Step 1: Analyze direct block access
Direct pointers provide immediate access, so O(1).
Step 2: Analyze indirect block access
Indirect pointers form a tree with branching factor M. Accessing nth block requires traversing up to 3 levels, each indexing into a block of size M, so complexity is O(log_M n).
Step 3: Evaluate other options
O(1) for direct blocks; O(1) for indirect blocks due to fixed pointer levels incorrectly claims O(1) for indirect blocks ignoring traversal. O(n) for all blocks because indirect pointers require sequential traversal wrongly assumes sequential traversal. O(M) for indirect blocks because each indirect block must be scanned linearly assumes scanning entire indirect block linearly, which is not needed.
Final Answer:
Option D -> Option D
Quick Check:
Indirect pointers form a tree, so access is logarithmic in M [OK]

Quick Trick: Indirect pointers form a tree, so access is O(log base M) [OK]

Common Mistakes:

MISTAKES

Assuming indirect access is O(1) or O(n) due to misunderstanding traversal

Trap Explanation:

PITFALL

Candidates confuse fixed pointer levels with constant time or think indirect blocks require scanning all pointers.

Interviewer Note:

CONTEXT

Tests understanding of time complexity of multi-level indirect pointer traversal.

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Solution Trace

More Operating Systems Quizzes

What is the time complexity of accessing the nth data block in a file using an inode with direct, single, double, and triple indirect pointers, assuming each indirect block contains M pointers?

Step 1: Analyze direct block access

Step 2: Analyze indirect block access

Step 3: Evaluate other options

Final Answer:

Quick Check:

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