Scope refers to the range or boundaries within which a particular variable or code can be accessed and used. In programming, pattern variables are used to match a specific data structure, and their scope can be limited to certain conditions or statements.

Let's say we have a scenario where a user can be either an administrator or a regular user. We can use the instanceof operator to check the type of the user and then access their specific properties based on their role. In this example, the scope of the pattern variable would be limited to the specific role of the user:

if (user instanceof Administrator admin) {
    // Here we can access the properties and methods of the admin user.
    admin.addNewUser();
} else if (user instanceof RegularUser regUser) {
    // Here we can only access the properties and methods of a regular user.
    regUser.editProfile();
}

In the above code, the scope of the pattern variable admin is limited to the if statement where the instanceof condition is true. This means that we can only access the properties and methods of the admin user within that statement.

Similarly, the scope of a pattern variable can extend beyond the statement where it was introduced. Let's say we have a function that checks if a given shape is a rectangle and if it is big enough. In this case, the scope of the pattern variable r would extend beyond the if statement where it was introduced:

public static boolean bigEnoughRect(Shape s) {
    if (!(s instanceof Rectangle r)) {
        // Here the pattern variable 'r' cannot be used as the instance of Rectangle is false.
        return false;
    }
    // However, we can access the properties and methods of the rectangle 'r' here.
    return r.length() > 5; 
}

Pattern variables can also be used in the expressions of if statements. This allows us to access the pattern variable only if the conditional statement is true. In the following example, we use the pattern variable r to check if a rectangle's length is greater than 5 using the conditional-AND operator:

if (shape instanceof Rectangle r && r.length() > 5) {
    // Here we can use the pattern variable 'r' to access the properties of a rectangle only if the instance of Rectangle is true.
    System.out.println("This rectangle is big enough!");
}

However, we cannot use the instanceof operator in a conditional statement to pattern match, as it checks for a different type of scope. In the following example, the program will throw an error because the scope of the pattern variable r cannot be accessed if the instanceof Rectangle is false:

if (shape instanceof Rectangle r || r.length() > 0) { // error
    // Here we cannot use the pattern variable 'r' as it may or may not exist depending on the instance of Rectangle.
    System.out.println("This is a rectangle with a length greater than 0");
}

In conclusion, the scope of a pattern variable is essential in determining where we can access and use it within our code. By understanding its scope, we can efficiently use pattern variables to match data structures and write efficient and error-free code.