Pythagorean Triplet

Easy
13
82.9% Acceptance

In this lab, you will implement a method in Java named isPythagoreanTriplet. This method will take an array of three numbers as input and return a boolean value indicating whether these numbers form a Pythagorean triplet.

What is a Pythagorean Triplet?

A Pythagorean triplet consists of three positive integers (a), (b), and (c), such that (a^2 + b^2 = c^2). For example, (3, 4, 5) is a Pythagorean triplet because 3² + 4² = 5².

Task

Your task is to create a method isPythagoreanTriplet(int[] numbers) in the Main class. This method should:

  • Take an array of three integers as its parameter.
  • Check if these integers can form a Pythagorean triplet.
  • Return true if they form a Pythagorean triplet, and false otherwise.

Implementation Guidelines

  • Sorting: Consider sorting the array first. This can simplify the process of comparing the squares of the numbers.
  • Math Operations: You'll need to perform squaring and sum operations to check if the numbers satisfy the Pythagorean condition.
  • Edge Cases: Be sure to handle edge cases such as negative numbers or zeros, as these do not form valid triplets.

Remember, no external libraries are required; standard Java functions are sufficient to complete this task.

Goal

Successfully implement the isPythagoreanTriplet method to pass all the challenges, proving that your method can accurately identify Pythagorean triplets as well as reject non-triplets.

Challenges

Challenge 1: Test Basic Pythagorean Triplet

  • Input: An array [5, 4, 3]
  • Expected Behavior: Your function should return true as 5, 4, and 3 form a Pythagorean triplet (5² + 4² = 3²).
  • Task: Implement the isPythagoreanTriplet method in the Main class to correctly identify this triplet.

Challenge 2: Test Larger Pythagorean Triplet

  • Input: An array [5, 12, 13]
  • Expected Behavior: Your function should return true since 5, 12, and 13 form a valid Pythagorean triplet (5² + 12² = 13²).
  • Task: Ensure that your isPythagoreanTriplet method can handle larger integers and still accurately determine a Pythagorean triplet.

Challenge 3: Test with Non-Triplet

  • Input: An array [2, 3, 4]
  • Expected Behavior: The function should return false because 2, 3, and 4 do not satisfy the Pythagorean triplet equation (2² + 3² ≠ 4²).
  • Task: Modify isPythagoreanTriplet to correctly reject arrays that do not form a Pythagorean triplet.

Challenge 4: Test Complex Pythagorean Triplet

  • Input: An array [7, 25, 24]
  • Expected Behavior: Your function should return true, as these numbers form a Pythagorean triplet (7² + 24² = 25²).
  • Task: This challenge tests the function's ability to recognize less obvious triplets. Ensure your method can identify such cases accurately.

Challenge 5: Test Another Non-Triplet

  • Input: An array [1, 5, 8]
  • Expected Behavior: The function should return false as these numbers do not form a Pythagorean triplet (1² + 5² ≠ 8²).
  • Task: Confirm that your isPythagoreanTriplet method can effectively identify and reject invalid triplets.