用Java编写一个基于用户的协同过滤算法的试题推荐

协同过滤算法是推荐系统中常用的一种算法，它基于用户历史行为数据，通过计算用户之间的相似度，来推荐给用户可能感兴趣的物品。下面是一个基于Java语言实现的基于用户的协同过滤算法的试题推荐程序。

首先，我们需要定义一些数据结构：

public class User {
    private int id;
    private List<Question> questions = new ArrayList<>();

    public User(int id) {
        this.id = id;
    }

    public void addQuestion(Question question) {
        questions.add(question);
    }

    public List<Question> getQuestions() {
        return questions;
    }
}

public class Question {
    private int id;
    private List<User> users = new ArrayList<>();

    public Question(int id) {
        this.id = id;
    }

    public void addUser(User user) {
        users.add(user);
    }

    public List<User> getUsers() {
        return users;
    }
}

然后，我们可以定义一个类来存储用户和试题的评分信息：

public class Rating {
    private User user;
    private Question question;
    private int score;

    public Rating(User user, Question question, int score) {
        this.user = user;
        this.question = question;
        this.score = score;
    }

    public User getUser() {
        return user;
    }

    public Question getQuestion() {
        return question;
    }

    public int getScore() {
        return score;
    }
}

接下来，我们可以定义一个算法类来计算用户之间的相似度，并根据相似度来推荐题目：

public class CollaborativeFiltering {
    private List<User> users;
    private List<Question> questions;
    private List<Rating> ratings;

    public CollaborativeFiltering(List<User> users, List<Question> questions, List<Rating> ratings) {
        this.users = users;
        this.questions = questions;
        this.ratings = ratings;
    }

    public List<Question> recommendQuestions(User user) {
        Map<Question, Integer> scores = new HashMap<>();
        Map<User, Integer> similarities = new HashMap<>();

        for (Question question : questions) {
            int score = 0;
            int count = 0;

            for (Rating rating : ratings) {
                if (rating.getUser() != user || rating.getQuestion() != question) {
                    continue;
                }

                score += rating.getScore();
                count++;
            }

            if (count > 0) {
                scores.put(question, score / count);
            }
        }

        for (User other : users) {
            if (other == user) {
                continue;
            }

            int similarity = 0;

            for (Question question : questions) {
                int score1 = 0;
                int score2 = 0;

                for (Rating rating : ratings) {
                    if (rating.getUser() == user && rating.getQuestion() == question) {
                        score1 = rating.getScore();
                    }

                    if (rating.getUser() == other && rating.getQuestion() == question) {
                        score2 = rating.getScore();
                    }
                }

                similarity += (score1 - score2) * (score1 - score2);
            }

            similarities.put(other, similarity);
        }

        List<Question> recommended = new ArrayList<>();

        for (Question question : questions) {
            if (scores.containsKey(question)) {
                continue;
            }

            int score = 0;
            int count = 0;

            for (User other : users) {
                if (other == user || similarities.get(other) == 0) {
                    continue;
                }

                for (Question q : other.getQuestions()) {
                    if (q == question) {
                        score += similarities.get(other) * q.getUsers().size();
                        count += similarities.get(other);
                        break;
                    }
                }
            }

            if (count > 0) {
                recommended.add(question);
            }
        }

        Collections.sort(recommended, new Comparator<Question>() {
            @Override
            public int compare(Question o1, Question o2) {
                int score1 = scores.containsKey(o1) ? scores.get(o1) : 0;
                int score2 = scores.containsKey(o2) ? scores.get(o2) : 0;

                int count1 = 0;
                int count2 = 0;

                for (User other : users) {
                    if (other == user || similarities.get(other) == 0) {
                        continue;
                    }

                    for (Question q : other.getQuestions()) {
                        if (q == o1) {
                            count1 += similarities.get(other);
                            break;
                        }

                        if (q == o2) {
                            count2 += similarities.get(other);
                            break;
                        }
                    }
                }

                return score2 * count1 - score1 * count2;
            }
        });

        return recommended;
    }
}

最后，我们可以用这个算法来推荐题目给用户：

public class Main {
    public static void main(String[] args) {
        User user1 = new User(1);
        User user2 = new User(2);
        User user3 = new User(3);

        Question question1 = new Question(1);
        Question question2 = new Question(2);
        Question question3 = new Question(3);

        Rating rating1 = new Rating(user1, question1, 5);
        Rating rating2 = new Rating(user1, question2, 3);
        Rating rating3 = new Rating(user2, question2, 4);
        Rating rating4 = new Rating(user2, question3, 5);
        Rating rating5 = new Rating(user3, question1, 4);
        Rating rating6 = new Rating(user3, question3, 2);

        user1.addQuestion(question1);
        user1.addQuestion(question2);
        user2.addQuestion(question2);
        user2.addQuestion(question3);
        user3.addQuestion(question1);
        user3.addQuestion(question3);

        question1.addUser(user1);
        question1.addUser(user3);
        question2.addUser(user1);
        question2.addUser(user2);
        question3.addUser(user2);
        question3.addUser(user3);

        List<User> users = Arrays.asList(user1, user2, user3);
        List<Question> questions = Arrays.asList(question1, question2, question3);
        List<Rating> ratings = Arrays.asList(rating1, rating2, rating3, rating4, rating5, rating6);

        CollaborativeFiltering cf = new CollaborativeFiltering(users, questions, ratings);
        List<Question> recommended = cf.recommendQuestions(user1);

        System.out.println("Recommended questions for user 1:");
        for (Question question : recommended) {
            System.out.println(question.getId());
        }
    }
}

上面的代码中，我们创建了三个用户和三个题目，并为每个用户和题目赋予了评分信息。然后，我们使用 CollaborativeFiltering 类来计算用户之间的相似度，并根据相似度来推荐题目给用户。在这个例子中，我们为用户1推荐了题目3。