AP CSA 2.12 Exercise 2: Informal Run-Time Analysis Applied Practice

Unit 2: Selection and Iteration · Lesson 2.12 · Exercise 2

Informal Run-Time Analysis: Applied Practice

Six scenarios on counting operations rather than seconds, and why the input size is what matters.

Back to the Lesson 2.12 pageAll Unit 2 lessons

How this one is different

The exercise-1 editor asks you to compare implementations. These six ask how the work GROWS, which is the only comparison that survives changing computers.

Applied Practice

6 questions · scenario driven · every answer is recorded for your teacher

Question 1 of 6Apply
A single loop over n elements performs one comparison per element.
How does the number of comparisons grow with n?
Incorrect. More data means more comparisons.
Incorrect. Constant work would mean the loop does not depend on n.
Correct. Correct. This is linear growth.
Incorrect. Quadratic growth requires nesting.
Question 2 of 6Analyze
One algorithm takes 3n + 100 steps and another takes n squared steps.
Which is preferable for very large n?
Incorrect. The constant is irrelevant once n is large.
Correct. Correct, and note the quadratic one can genuinely win for SMALL n, which is why it is not simply worse.
Incorrect. They diverge sharply as n grows.
Incorrect. The growth rates settle it decisively.
Question 3 of 6Apply
A search examines elements until it finds a match, and the match happens to be the first element.
What does that tell you about the algorithm?
Correct. Correct. Best case, worst case and average case are separate claims.
Incorrect. A single loop is not quadratic.
Incorrect. It terminates at the match.
Incorrect. One lucky input does not characterize the algorithm.
Question 4 of 6Analyze
A loop halves the remaining search space on every pass.
How many passes does it need for n items?
Incorrect. Halving reduces work rather than multiplying it.
Incorrect. The count depends on n.
Incorrect. Linear growth means examining every item, which halving avoids.
Correct. Correct: this is logarithmic growth, and it is why binary search scales so well.
Question 5 of 6Evaluate
A student times two algorithms on their laptop and concludes one is better.
What is the weakness of that evidence?
Incorrect. They can be genuinely different algorithms.
Incorrect. Timing is useful evidence, just not sufficient on its own.
Correct. Correct. Growth rate is a claim about scaling and needs more than one point to observe.
Incorrect. Irrelevant to the reasoning.
Question 6 of 6Apply
Two nested loops each run n times, and the inner body contains 5 statements.
How is the total work described?
Incorrect. That accounts for only one loop.
Correct. Correct, and dropping constants is what makes growth rates comparable across implementations.
Incorrect. The 5 is not squared; only the loop counts multiply.
Incorrect. The work clearly depends on n.

Where to go next

Try the Lesson 2.12 coding exercise Pick another Unit 2 lesson

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