What does the AP CSA 4.16 FRQ practice question ask you to do?

Base Cases That Return the Right Thing: (a) public static int sumTo(int n) returns 1 + 2 + ... + n recursively, and 0 when n is 0. (b) public static int factorial(int n) returns n! recursively, and 1 when n is 0. (c) public static int countDigits(int n) returns how many digits n has, recursively. The number 0 has one digit. (d) public static int power(int base, int exp) returns base to the exp, recursively, and 1 when exp is 0.

Do you write a whole program or just a method for AP CSA 4.16?

Nothing is given. Write a class named Recurse. Assume n is at least 0. Do not write a main method. A hidden driver calls your code, so the value each method RETURNS is what is scored and nothing you print is measured.

How is the AP CSA 4.16 FRQ practice scored?

Out of 4 points, one per rubric row: (a) public static int sumTo(int n) returns 1 + 2 + ... + n recursively, and 0 when n is 0. (b) public static int factorial(int n) returns n! recursively, and 1 when n is 0. (c) public static int countDigits(int n) returns how many digits n has, recursively. The number 0 has one digit. (d) public static int power(int base, int exp) returns base to the exp, recursively, and 1 when exp is 0. Your answer runs against 5 test cases, 3 of them hidden, and the fraction you pass becomes the score. That is not how a human AP reader marks a rubric, so treat the rows above as the thing being practised.

What is a common mistake on AP CSA 4.16?

part (a) bottoms out at 1 instead of 0, so every sum is one too large. It is one of 4 error(s) this question is built to catch.

AP CSA 4.16 FRQ Practice: Base Cases That Return the Right Thing

Unit 4: Data Collections · Lesson 4.16 · FRQ Practice

Base Cases That Return the Right Thing

A free response question in the shape the exam uses: a stated contract, four rubric parts, and no main method handed to you. Worth 4 points.

Back to the Lesson 4.16 page All Unit 4 lessons

Why this question is worth four points

A missing base case makes recursion crash, and everyone learns to look for that. A base case that returns the WRONG VALUE is the mistake that actually appears on student work: the method terminates, the recursion is shaped correctly, and every answer is off by the same factor. A sum that bottoms out at 1 and a product that bottoms out at 0 are the same error.

What you are given

Nothing is given. Write a class named Recurse. Assume n is at least 0. Do not write a main method.

The question

(a) public static int sumTo(int n) returns 1 + 2 + ... + n recursively, and 0 when n is 0.
(b) public static int factorial(int n) returns n! recursively, and 1 when n is 0.
(c) public static int countDigits(int n) returns how many digits n has, recursively. The number 0 has one digit.
(d) public static int power(int base, int exp) returns base to the exp, recursively, and 1 when exp is 0.

What the reader is looking for

Write class Recurse with the four static methods described. No main method.
Every part here has a base case that must return a SPECIFIC value. A sum bottoms out at 0 and a product bottoms out at 1, and swapping those two is the whole question.
Every recursive call must move toward the base case, or the method never returns.

Worked examples

These show what a correct answer prints. There are more cases you cannot see, and they use different values, so an answer built around just these numbers will fail.

Example 1 input

5 2 3

Example 1 output

Example 2 input

0 7 0

Example 2 output

Your answer

Main.java

class Recurse {
  // (a) sumTo(int n) -> int

  // (b) factorial(int n) -> int

  // (c) countDigits(int n) -> int

  // (d) power(int base, int exp) -> int
}

Input for the Run button

How this is scored: your answer runs against every test case, and the fraction it passes becomes your score out of 4. That is not how a human AP reader marks a rubric, so treat the score as a check on whether your code works, and the rubric above as the thing you are actually practising.

Stuck?

Hint 1

The base case value is the identity of whatever the recursion combines. Addition combines with 0 and multiplication combines with 1.

Hint 2

Part (c) bottoms out at any single digit number, which includes 0. Testing n == 0 instead throws away the last digit of every number.

Hint 3

The recursive call must be smaller. n - 1 and n / 10 both reach their base cases; n itself never does.

Before you submit

4 mistake(s) that lose points on this question

Each of these is a real error the grader catches. Check your answer against them before you submit, not instead of trying.

part (a) bottoms out at 1 instead of 0, so every sum is one too large
part (b) bottoms out at 0, so every factorial is 0
part (d) bottoms out at 0, so every power is 0
part (c) discards the result of its recursive call

Where to go next

Rework the Lesson 4.16 page Try the from-scratch exercise for this lesson Try the debugging exercise for this lesson

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