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If an object is wrapped by k decorators, each adding a constant time operation in the cost() method, what is the overall time complexity of calling cost() on the outermost decorator?

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OOP & Design Patterns - Decorator Pattern - Wrapping Behaviour Without Subclassing

If an object is wrapped by k decorators, each adding a constant time operation in the cost() method, what is the overall time complexity of calling cost() on the outermost decorator?

AO(1)

BO(k)

CO(k^2)

DO(log k)

Step-by-Step Solution

Solution:

Step 1: Analyze the call chain
Each decorator calls cost() on the wrapped object, adding constant time.
Step 2: Calculate total time
With k decorators, calls chain linearly, so total time is proportional to k.
Final Answer:
Option A -> Option A
Quick Check:
Each decorator adds constant time, calls chain linearly [OK]

Quick Trick: Decorator calls chain linearly, so time is O(k) [OK]

Common Mistakes:

MISTAKES

Assuming constant time ignoring the chain of calls.
Mistaking it for O(k^2) by double counting.
Thinking logarithmic due to recursion, which is incorrect here.

Trap Explanation:

PITFALL

Ignoring the recursive call chain leads to underestimating time complexity.

Interviewer Note:

CONTEXT

Tests understanding of performance implications of stacked decorators.

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