A DESCRIPTION OF THE PROBLEM :
The current binarySearch implementations in java.util.Arrays require direct comparability between array elements and the search key. However, in many real-world scenarios, data structures contain objects where the search should be based on a derived key rather than the object itself.

To address this, the proposed methods provide:
1. A binarySearch method that extracts keys using a Function<? super T, Comparable<? super K>> and performs a binary search based on the natural ordering of the extracted keys.
2. A binarySearch method that allows specifying a Comparator<? super K> for cases where a custom ordering is needed.

Proposed Method Signatures:

public static <T, K> int binarySearch(T[] array, K key, Function<? super T, Comparable<? super K>> fn)

public static <T, K> int binarySearch(T[] array, K key, Function<? super T, K> fn, Comparator<? super K> c)

Use Cases:

1. Searching in an Array of Objects by a Specific Field

record Person(String name, int age) {}
Person[] people = {
    new Person("Alice", 30),
    new Person("Bob", 25),
    new Person("Charlie", 35)
};
Arrays.sort(people, Comparator.comparingInt(Person::age));
int index = Arrays.binarySearch(people, 30, Person::age);

2. Searching with a Custom Comparator

int index = Arrays.binarySearch(people, "Alice", Person::name, String.CASE_INSENSITIVE_ORDER);