Jest-Fast-Check: Property-Based Testing for Robust Functions

This challenge is about integrating property-based testing into your Jest test suite using fast-check. Property-based testing helps you write more robust and comprehensive tests by defining general properties that your functions should uphold, rather than testing specific input/output pairs. You will create a simple function and then write Jest tests for it using fast-check to ensure its correctness across a wide range of inputs.

Problem Description

Your task is to implement a function that takes an array of numbers and returns a new array containing only the even numbers from the input array. After implementing this function, you will write Jest tests for it using the fast-check library. These tests should verify that the function correctly filters even numbers by defining and testing properties that should hold true for any valid input array.

Key Requirements:

1. Implement filterEvenNumbers function:

   • The function should accept an array of numbers (number[]).
   • It should return a new array containing only the even numbers from the input array, preserving their original order.
   • If the input array is empty or contains no even numbers, it should return an empty array.

2. Write Jest tests using fast-check:

   • You need to define properties that characterize a correct filterEvenNumbers implementation.
   • Use fast-check's fc.assert function within your Jest tests to verify these properties.

Expected Behavior:

• The filterEvenNumbers function should correctly identify and return only even numbers.
• The Jest tests should pass, indicating that the function satisfies the defined properties.

Edge Cases to Consider:

• Empty input array.
• Arrays containing only odd numbers.
• Arrays containing only even numbers.
• Arrays containing a mix of positive, negative, and zero values.

Examples

Example 1:

Input: [1, 2, 3, 4, 5, 6]
Output: [2, 4, 6]
Explanation: The function correctly identifies and returns the even numbers 2, 4, and 6.

Example 2:

Input: [1, 3, 5, 7, 9]
Output: []
Explanation: The input array contains no even numbers, so an empty array is returned.

Example 3:

Input: []
Output: []
Explanation: An empty input array results in an empty output array.

Constraints

• The input array will contain only numbers.
• The function should not mutate the original input array.
• The fast-check library should be used for property-based testing.
• Tests should be written in TypeScript.

Notes

• To use fast-check with Jest, you'll typically need to install it: npm install --save-dev fast-check @types/jest.
• Consider properties such as:
  • Every number in the output array must be even.
  • The order of even numbers in the output array must be the same as in the input array.
  • The output array should not contain any numbers that were not present in the input array.
• Think about how fast-check can generate various types of number arrays for testing.