Collatz Conjecture

Easy
16
88.6% Acceptance

In this lab, you will implement a method in Java named countSteps, which will calculate the number of steps needed to reach 1 from a given starting number using the Collatz Conjecture. Your implementation will be tested against a series of challenges to ensure accuracy and efficiency.

The Collatz Conjecture

The Collatz Conjecture is a mathematical algorithm that involves a sequence of operations on positive integers. For any given number n, the sequence is as follows:

  • If n is even, divide it by 2.
  • If n is odd, multiply it by 3 and add 1.
  • Continue this process until n becomes 1.

Task

Your task is to write a public static method countSteps in a class named Main. This method should:

  • Take an integer n as an input.
  • Return the number of steps it takes to reduce n to 1 by following the rules of the Collatz Conjecture.

Requirements

  • The method should be named countSteps and must be static.
  • It should take a single integer parameter and return an integer.
  • Ensure your method handles a range of inputs efficiently and accurately.
  • Remember, the method should return the number of steps, not print them.

Example

If the input to countSteps is 6, the method should return 8, as it takes 8 steps to reduce 6 to 1 following the Collatz Conjecture.

Challenges Information

Challenge 1: Testing with the Number 7

  • Objective: Implement the countSteps method in the Main class to correctly execute the Collatz conjecture starting from the number 7.
  • Expected Output: The method should return 16, indicating 16 steps to reduce 7 to 1 following the Collatz conjecture rules.

Challenge 2: Testing with the Number 6

  • Objective: Write the countSteps method in the Main class to process the number 6 according to the Collatz conjecture.
  • Expected Output: The method must return 8, denoting 8 steps required to reach 1 from 6.

Challenge 3: Testing with the Number 16

  • Objective: Ensure the countSteps method in the Main class correctly processes the number 16 under the Collatz conjecture.
  • Expected Output: The correct output is 4, showing that 4 steps are needed to go from 16 to 1.

Challenge 4: Testing with the Number 1

  • Objective: Test the countSteps method in the Main class with the number 1, the endpoint of the Collatz conjecture.
  • Expected Output: As 1 is already the target, the method should return 0, indicating no steps are needed.