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What is the time complexity of calling the prepare_recipe method in the Template Method Pattern implementation for a beverage, assuming each step runs in constant time?

medium🪤 Complexity Trap Q13 of Q15
OOP & Design Patterns - Template Method Pattern - Define Skeleton, Override Steps
What is the time complexity of calling the prepare_recipe method in the Template Method Pattern implementation for a beverage, assuming each step runs in constant time?
AO(1), since the number of steps is fixed and each step runs in constant time
BO(log n), due to the hook method optimizing optional steps
CO(n^2), because each step may call other steps recursively
DO(n), where n is the number of steps in the recipe
Step-by-Step Solution

  1. Step 1: Identify number of steps

    The template method defines a fixed sequence of steps (boil_water, brew, pour_in_cup, add_condiments).

  2. Step 2: Analyze step execution time

    Each step runs in constant time; the hook method only conditionally calls add_condiments but does not affect asymptotic complexity.

  3. Final Answer:

    Option D -> Option D

  4. Quick Check:

    Fixed steps with constant time each -> O(1) total [OK]
Quick Trick: Fixed step count -> constant time complexity [OK]
Common Mistakes:
MISTAKES
  • Confusing n as input size
  • Assuming recursion adds complexity
Trap Explanation:
PITFALL
  • Option A looks plausible if candidate thinks steps scale with input size, but steps are fixed.
Interviewer Note:
CONTEXT
  • Checks understanding of complexity in design patterns with fixed algorithm skeleton.
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