equals() と hashCode() を一緒にオーバーライドする必要があるのはなぜですか？

// by default, equals() compares IDENTITY (same object?), hashCode() is based on memory address
Person p1 = new Person("Ann", 30);
Person p2 = new Person("Ann", 30);
p1.equals(p2);   // false by default — different objects, even with same data

@Override
public boolean equals(Object o) {
    if (this == o) return true;
    if (o == null || getClass() != o.getClass()) return false;
    Person p = (Person) o;
    return age == p.age && Objects.equals(name, p.name);  // compare by CONTENT
}

@Override
public int hashCode() {
    return Objects.hash(name, age);   // MUST be consistent with equals()
}

Person p1 = new Person("Ann", 30);
Person p2 = new Person("Ann", 30);  // equal by our equals()

Set<Person> set = new HashSet<>();
set.add(p1);
set.contains(p2);   // ❌ likely FALSE — even though p1.equals(p2)!

1. equal objects → equal hash codes (REQUIRED for correctness)
2. unequal objects MAY have the same hash (collisions are allowed)
3. hashCode() must be consistent (same object → same code, unchanged)
4. equals() must be reflexive, symmetric, transitive, consistent

record Person(String name, int age) {}   // records auto-generate equals/hashCode/toString!