What Does The Following Method Do When Passed A Positive Int $n$?```cint Example(int N) { If (n == 0) Return 0; Else Return Example(n - 1) + N N N;}```A. Returns The Cube Of The Number $n$ B. Returns One

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Introduction

In this article, we will delve into the world of recursive functions and explore the behavior of a given method when passed a positive integer n. The method in question is a recursive function that takes an integer n as input and returns a value based on a specific condition. Our goal is to understand what this method does when passed a positive integer n.

The Recursive Function

The given recursive function is defined as follows:

int example(int n) {
    if (n == 0)
        return 0;
    else
        return example(n - 1) + n * n;
}

This function takes an integer n as input and returns a value based on the following condition:

  • If n is equal to 0, the function returns 0.
  • If n is not equal to 0, the function calls itself recursively with the argument n - 1 and adds the square of n to the result.

Analyzing the Function

To understand what this function does, let's analyze its behavior step by step.

Base Case

The base case of the function is when n is equal to 0. In this case, the function returns 0. This is the stopping point of the recursion, and the function will not call itself again.

Recursive Case

When n is not equal to 0, the function calls itself recursively with the argument n - 1. This means that the function will call itself repeatedly until n reaches 0.

Adding the Square of n

In each recursive call, the function adds the square of n to the result. This means that the function is accumulating the sum of the squares of all numbers from n down to 1.

Example Walkthrough

Let's walk through an example to see how the function behaves.

Suppose we call the function with n = 3. Here's what happens:

  1. example(3) is called, which calls example(2) recursively.
  2. example(2) is called, which calls example(1) recursively.
  3. example(1) is called, which calls example(0) recursively.
  4. example(0) returns 0, which is the base case.
  5. The result of example(1) is 0 + 1^2 = 1.
  6. The result of example(2) is 1 + 2^2 = 5.
  7. The result of example(3) is 5 + 3^2 = 14.

Therefore, the function returns 14 when called with n = 3.

Conclusion

In conclusion, the given recursive function takes a positive integer n as input and returns the sum of the squares of all numbers from n down to 1. This function is an example of a recursive function that uses a base case and a recursive case to solve a problem.

What Does the Function Do?

Based on our analysis, we can conclude that the function returns the sum of the squares of all numbers from n down to 1.

Answer

The correct answer is:

  • B. Returns the sum of the squares of all numbers from n down to 1.

Introduction

In our previous article, we explored the behavior of a given recursive function when passed a positive integer n. We analyzed the function's behavior step by step and concluded that it returns the sum of the squares of all numbers from n down to 1. In this article, we will answer some frequently asked questions about the function to help you better understand its behavior.

Q: What is the base case of the function?

A: The base case of the function is when n is equal to 0. In this case, the function returns 0.

Q: What happens when n is not equal to 0?

A: When n is not equal to 0, the function calls itself recursively with the argument n - 1. This means that the function will call itself repeatedly until n reaches 0.

Q: What is the recursive case of the function?

A: The recursive case of the function is when n is not equal to 0. In this case, the function calls itself recursively with the argument n - 1 and adds the square of n to the result.

Q: How does the function accumulate the sum of the squares?

A: The function accumulates the sum of the squares by adding the square of n to the result of each recursive call. This means that the function is adding the square of each number from n down to 1 to the result.

Q: Can you provide an example walkthrough of the function?

A: Here's an example walkthrough of the function:

Suppose we call the function with n = 3. Here's what happens:

  1. example(3) is called, which calls example(2) recursively.
  2. example(2) is called, which calls example(1) recursively.
  3. example(1) is called, which calls example(0) recursively.
  4. example(0) returns 0, which is the base case.
  5. The result of example(1) is 0 + 1^2 = 1.
  6. The result of example(2) is 1 + 2^2 = 5.
  7. The result of example(3) is 5 + 3^2 = 14.

Q: What is the time complexity of the function?

A: The time complexity of the function is O(n), where n is the input value. This is because the function makes n recursive calls, each of which takes constant time.

Q: What is the space complexity of the function?

A: The space complexity of the function is O(n), where n is the input value. This is because the function uses a recursive call stack of size n.

Conclusion

In conclusion, we have answered some frequently asked questions about the recursive function. We hope that this article has helped you better understand the behavior of the function and its time and space complexity.

Frequently Asked Questions

  • Q: What is the base case of the function?
  • A: The base case of the function is when n is equal to 0.
  • Q: What happens when n is not equal to 0?
  • A: When n is not equal to 0, the function calls itself recursively with the argument n - 1.
  • Q: What is the recursive case of the function?
  • A: The recursive case of the function is when n is not equal to 0.
  • Q: How does the function accumulate the sum of the squares?
  • A: The function accumulates the sum of the squares by adding the square of n to the result of each recursive call.
  • Q: Can you provide an example walkthrough of the function?
  • A: Yes, here's an example walkthrough of the function.
  • Q: What is the time complexity of the function?
  • A: The time complexity of the function is O(n), where n is the input value.
  • Q: What is the space complexity of the function?
  • A: The space complexity of the function is O(n), where n is the input value.