Exam-style question
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Explain why the size of the problem must be considered when comparing two algorithms. Include both time-wise and space-wise efficiency in your answer.
Model answer
What a good answer should say
- The size of the problem affects how the algorithms behave as the amount of data or work increases.
- An algorithm may take less time for a small problem but become slower than another algorithm as the problem grows.
- The amount of memory required can also change with problem size, so an algorithm may be more or less space-efficient depending on how much data must be stored.
- Complexity expresses an algorithm's behaviour as a function relative to problem size.
Explanation
Why this works
A comparison based only on one small example may not show the overall efficiency of an algorithm. Considering how time and memory requirements change as the problem size increases gives a more meaningful comparison.
Common mistake
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