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What is the time complexity of computing the cost() method when stacking k decorators on a core object using the Decorator Pattern with dynamic behavior injection?

medium🪤 Complexity Trap Q13 of Q15

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

What is the time complexity of computing the cost() method when stacking k decorators on a core object using the Decorator Pattern with dynamic behavior injection?

AO(1) because each decorator adds a fixed cost

BO(k) because each decorator delegates the call to the next one

CO(k^2) because each decorator calls all previous decorators recursively

DO(log k) because decorators form a balanced tree structure

Step-by-Step Solution

Step 1: Identify call chain length
Each decorator's cost() calls the wrapped object's cost(), forming a chain of length k.
Step 2: Calculate total calls
Cost computation requires traversing all k decorators once, so time complexity is O(k).
Final Answer:
Option B -> Option B
Quick Check:
Each decorator adds constant work, total linear in k [OK]

Quick Trick: Decorator calls chain length equals number of decorators [OK]

Common Mistakes:

MISTAKES

Assuming O(1) because cost is a simple addition
Mistaking recursive calls as quadratic

Trap Explanation:

PITFALL

O(1) looks plausible but ignores delegation chain; O(k^2) confuses recursion depth with repeated calls.

Interviewer Note:

CONTEXT

Checks understanding of delegation and call stack in decorator chains.

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