AP CSA 2.12 Exercise 1: Counting the Steps

Unit 2: Selection and Iteration · Lesson 2.12 · Exercise 1

Counting the Steps

Informal Run-Time Analysis. Write real Java, run it, and submit it to be graded against hidden test cases.

Back to the Lesson 2.12 page All Unit 2 lessons

Why this one is worth doing

Run time analysis is counting, and counting is something a program can do to itself. Print the real step counts for three loop shapes and the growth rates stop being abstractions.

What to write

Read one integer n, which is at least 1.
Count and print how many times the body of a single loop from 1 to n runs.
Count and print how many times the body of a nested loop, both from 1 to n, runs.
Count and print how many times a loop that starts at n and halves each pass runs before reaching 0.
Count and print how many times the body of a triangular nested loop runs, where the inner loop goes from 1 to the outer counter.

Your program reads

A single integer of at least 1.

Your program prints

Four counts, one per line: linear, quadratic, halving and triangular.

Worked examples

These are the cases you can see. There are more you cannot, and they use different values, so an answer that prints these numbers as constants will fail.

Example 1 input

Example 1 output

Example 2 input

Example 2 output

Your answer

Main.java

import java.util.Scanner;

public class Main {
  public static void main(String[] args) {
    Scanner input = new Scanner(System.in);
    int n = input.nextInt();

    // Actually run the loops and count. Do not use a formula.
  }
}

Input for the Run button

Run sends whatever is in the input box below. Submitting runs your program against every test case, including hidden ones with different input.

Stuck?

Hint 1

The nested count should come out as exactly n times n. If it does not, one of the loops has the wrong bound.

Hint 2

Integer division is what makes the halving loop end: 1 / 2 is 0, so the last pass is the one that finishes it.

Hint 3

The triangular count is about half the nested one. Both are quadratic, which is why the exam calls them the same order of growth.

Where to go next

Rework the Lesson 2.12 page Pick another Unit 2 lesson

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