SomeApp.java

import com.mongodb.*;

import java.net.UnknownHostException;
import java.util.Optional;
import java.util.stream.Stream;

public class SomeApp {
    public static void main(String[] args) throws UnknownHostException {
        MongoClient client = new MongoClient();
        DB db = client.getDB("school");
        DBCollection students = db.getCollection("students");

        assert(students.count()==200);

        System.out.println(students.findOne());
        students.find()
                .forEach(student -> {
                            Optional<Object> min = ((BasicDBList) student.get("scores"))
                                    .stream()
                                    .filter(filterScoreType)
                                    .min(scoreComparator);
                            students.update(student, new BasicDBObject("$pull", new BasicDBObject("scores", min.get())));
                        });
        System.out.println(students.findOne());
    }

    private static Predicate<Object> filterScoreType = t -> ((BasicDBObject) t).getString("type").equals("homework");
    private static Comparator<Object> scoreComparator = 
            (o1, o2) -> Double.compare(((BasicDBObject) o1).getDouble("score"), ((BasicDBObject) o2).getDouble("score"));
}