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If the Library Management System uses inheritance to model different types of users (Member, Librarian, Guest), what is the space complexity impact when adding new user types frequently?

medium🪤 Complexity Trap Q6 of Q15
OOP & Design Patterns - Design a Library Management System - LLD with Relationships & Edge Cases
If the Library Management System uses inheritance to model different types of users (Member, Librarian, Guest), what is the space complexity impact when adding new user types frequently?
AO(n) -- linear increase proportional to the number of user types due to separate class metadata
BO(1) -- no additional space since inheritance shares base class memory
CO(log n) -- logarithmic due to class hierarchy tree depth
DO(n²) -- quadratic due to duplicated fields in subclasses
Step-by-Step Solution
Solution:

  1. Step 1: Understand memory usage in inheritance

    Each subclass adds its own metadata and possibly fields, increasing space usage.

  2. Step 2: Analyze impact of adding multiple user types

    Adding n user types adds roughly O(n) space for class metadata and unique fields.

  3. Step 3: Reject constant and quadratic assumptions

    Inheritance does not share all memory; no quadratic duplication unless fields are copied.

  4. Final Answer:

    Option A -> Option A

  5. Quick Check:

    Each new subclass adds metadata -> linear space [OK]
Quick Trick: New subclasses add metadata -> O(n) space [OK]
Common Mistakes:
MISTAKES
  • Assuming inheritance shares all memory (O(1))
  • Overestimating to quadratic space
  • Confusing hierarchy depth with space
Trap Explanation:
PITFALL
  • Candidates often think inheritance is memory-free or constant space, ignoring class metadata overhead.
Interviewer Note:
CONTEXT
  • Evaluates understanding of inheritance memory overhead and scalability.
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