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Considering space complexity, what is the primary reason the Banker's Algorithm requires O(P * R) auxiliary space, and why might candidates mistakenly think it is O(P + R)?

medium🪤 Complexity Trap Q6 of Q15
Operating Systems - Banker's Algorithm - Safe State & Resource Allocation
Considering space complexity, what is the primary reason the Banker's Algorithm requires O(P * R) auxiliary space, and why might candidates mistakenly think it is O(P + R)?
ABecause it only stores the Available vector and one process's allocation at a time, which sums to P plus R.
BBecause it stores the Need matrix for all processes and resource types, which is P multiplied by R in size.
CBecause it uses recursion stacks proportional to P plus R during safety checks.
DBecause it stores all possible safe sequences explicitly, which is exponential in P and R.
Step-by-Step Solution
Solution:

  1. Step 1: Identify data structures used

    The algorithm maintains matrices like Allocation, Max, and Need, each sized P by R.

  2. Step 2: Calculate space complexity

    Storing Need alone requires O(P * R) space, dominating auxiliary space.

  3. Step 3: Why candidates pick O(P + R)

    They confuse vectors (Available size R, process flags size P) with matrices, underestimating space.

  4. Final Answer:

    Option B -> Option B

  5. Quick Check:

    Need matrix size is P times R [OK]
Quick Trick: Need matrix requires P*R space, not just P+R [OK]
Common Mistakes:
MISTAKES
  • Confusing vectors with matrices in space calculation
  • Ignoring Need matrix storage
  • Assuming recursion stack dominates space
Trap Explanation:
PITFALL
  • Candidates often overlook the matrix nature of Need and Allocation, leading to underestimation.
Interviewer Note:
CONTEXT
  • Evaluates understanding of space requirements in Banker's Algorithm.
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