基于springboot的电影售票及管理系统，设计一个协同过滤算法。根据用户购买的电影票类型进行推荐。后端使用的是springboot和mybatisplus。1：说明算法思路:。2：写出算法的详细代码，以及代码的注解。3：需要写清楚controler，service,dao,mappeer,impl中的代码

1. 算法思路：

协同过滤算法是一种推荐系统算法。其核心思想是根据用户的历史行为，如购买、评分等，找到与其兴趣相似的其他用户，然后将这些用户喜欢的物品推荐给该用户。

在本场景中，我们可以根据用户购买的电影票类型进行推荐。具体而言，我们可以先统计每个用户购买的电影票类型，并建立一个用户-电影票类型的矩阵。然后，对于一个用户，我们可以找到与其购买电影票类型相似的其他用户，并将这些用户购买的电影票类型推荐给该用户。

在找到与其购买电影票类型相似的其他用户的过程中，可以使用皮尔逊相关系数等相似度算法进行计算。同时，为了避免推荐重复的电影票类型，可以设定一个阈值，只推荐相似度高于该阈值的电影票类型。

2. 算法详细代码及注解：

// 计算两个用户之间的皮尔逊相关系数
public double pearsonCorrelation(Map<Integer, Double> user1, Map<Integer, Double> user2) {
    double sum1 = 0, sum2 = 0;
    double sum1Sq = 0, sum2Sq = 0, pSum = 0;
    int n = 0;
    for (Map.Entry<Integer, Double> entry : user1.entrySet()) {
        Integer itemId = entry.getKey();
        Double rating1 = entry.getValue();
        if (user2.containsKey(itemId)) {
            Double rating2 = user2.get(itemId);
            sum1 += rating1;
            sum2 += rating2;
            sum1Sq += Math.pow(rating1, 2);
            sum2Sq += Math.pow(rating2, 2);
            pSum += rating1 * rating2;
            n++;
        }
    }
    if (n == 0) {
        return 0;
    }
    double num = pSum - (sum1 * sum2 / n);
    double den = Math.sqrt((sum1Sq - Math.pow(sum1, 2) / n) * (sum2Sq - Math.pow(sum2, 2) / n));
    if (den == 0) {
        return 0;
    }
    return num / den;
}

// 根据用户购买的电影票类型进行推荐
public List<Integer> recommendMovies(Map<Integer, Map<Integer, Double>> userItemRatings, int userId, double threshold) {
    Map<Integer, Double> userRatings = userItemRatings.get(userId);

    // 计算用户与其他用户之间的皮尔逊相关系数
    Map<Integer, Double> simScores = new HashMap<>();
    for (Map.Entry<Integer, Map<Integer, Double>> entry : userItemRatings.entrySet()) {
        int otherUserId = entry.getKey();
        if (otherUserId != userId) {
            Map<Integer, Double> otherUserRatings = entry.getValue();
            double simScore = pearsonCorrelation(userRatings, otherUserRatings);
            if (simScore > threshold) {
                simScores.put(otherUserId, simScore);
            }
        }
    }

    // 找到与用户相似度最高的其他用户
    int mostSimilarUserId = 0;
    double maxSimScore = 0;
    for (Map.Entry<Integer, Double> entry : simScores.entrySet()) {
        int otherUserId = entry.getKey();
        double simScore = entry.getValue();
        if (simScore > maxSimScore) {
            mostSimilarUserId = otherUserId;
            maxSimScore = simScore;
        }
    }

    // 获取与用户相似度最高的其他用户购买的电影票类型
    List<Integer> recommendedMovies = new ArrayList<>();
    if (mostSimilarUserId > 0) {
        Map<Integer, Double> mostSimilarUserRatings = userItemRatings.get(mostSimilarUserId);
        for (Map.Entry<Integer, Double> entry : mostSimilarUserRatings.entrySet()) {
            Integer itemId = entry.getKey();
            Double rating = entry.getValue();
            if (!userRatings.containsKey(itemId) && rating > 0) {
                recommendedMovies.add(itemId);
            }
        }
    }

    return recommendedMovies;
}

3. 控制器、服务、DAO、Mapper、Impl中的代码：

Controller：

@RestController
@RequestMapping("/movie")
public class MovieController {
    @Autowired
    private MovieService movieService;

    @GetMapping("/recommendations")
    public List<Movie> getRecommendations(@RequestParam("userId") int userId) {
        return movieService.getRecommendations(userId);
    }
}

Service：

@Service
public class MovieServiceImpl implements MovieService {
    @Autowired
    private MovieMapper movieMapper;

    @Autowired
    private UserMapper userMapper;

    @Override
    public List<Movie> getRecommendations(int userId) {
        List<Movie> allMovies = movieMapper.selectAll();
        List<Movie> recommendedMovies = new ArrayList<>();

        // 构建用户-电影票类型矩阵
        Map<Integer, Map<Integer, Double>> userItemRatings = new HashMap<>();
        List<User> users = userMapper.selectAll();
        for (User user : users) {
            List<Ticket> tickets = user.getTickets();
            Map<Integer, Double> itemRatings = new HashMap<>();
            for (Ticket ticket : tickets) {
                int movieType = ticket.getMovieType();
                itemRatings.put(movieType, 1.0);
            }
            userItemRatings.put(user.getId(), itemRatings);
        }

        // 根据用户购买的电影票类型进行推荐
        double threshold = 0.5;
        List<Integer> recommendedMovieIds = recommendMovies(userItemRatings, userId, threshold);
        for (Movie movie : allMovies) {
            if (recommendedMovieIds.contains(movie.getId())) {
                recommendedMovies.add(movie);
            }
        }

        return recommendedMovies;
    }
}

DAO：

@Mapper
public interface MovieMapper extends BaseMapper<Movie> {
}

@Mapper
public interface UserMapper extends BaseMapper<User> {
}

Mapper：

<mapper namespace="com.example.mapper.MovieMapper">
    <resultMap id="BaseResultMap" type="com.example.entity.Movie">
        <id column="id" jdbcType="INTEGER" property="id" />
        <result column="name" jdbcType="VARCHAR" property="name" />
        <result column="type" jdbcType="INTEGER" property="type" />
        <result column="description" jdbcType="VARCHAR" property="description" />
    </resultMap>
    
    <select id="selectAll" resultMap="BaseResultMap">
        select * from movie
    </select>
</mapper>

<mapper namespace="com.example.mapper.UserMapper">
    <resultMap id="BaseResultMap" type="com.example.entity.User">
        <id column="id" jdbcType="INTEGER" property="id" />
        <result column="name" jdbcType="VARCHAR" property="name" />
        <collection property="tickets" ofType="com.example.entity.Ticket">
            <id column="id" jdbcType="INTEGER" property="id" />
            <result column="user_id" jdbcType="INTEGER" property="userId" />
            <result column="movie_type" jdbcType="INTEGER" property="movieType" />
        </collection>
    </resultMap>
    
    <select id="selectAll" resultMap="BaseResultMap">
        select *
        from user u
        left join ticket t on u.id = t.user_id
    </select>
</mapper>

Impl：

@Service
public class MovieServiceImpl implements MovieService {
    @Autowired
    private MovieMapper movieMapper;

    @Autowired
    private UserMapper userMapper;

    @Override
    public List<Movie> getRecommendations(int userId) {
        List<Movie> allMovies = movieMapper.selectAll();
        List<Movie> recommendedMovies = new ArrayList<>();

        // 构建用户-电影票类型矩阵
        Map<Integer, Map<Integer, Double>> userItemRatings = new HashMap<>();
        List<User> users = userMapper.selectAll();
        for (User user : users) {
            List<Ticket> tickets = user.getTickets();
            Map<Integer, Double> itemRatings = new HashMap<>();
            for (Ticket ticket : tickets) {
                int movieType = ticket.getMovieType();
                itemRatings.put(movieType, 1.0);
            }
            userItemRatings.put(user.getId(), itemRatings);
        }

        // 根据用户购买的电影票类型进行推荐
        double threshold = 0.5;
        List<Integer> recommendedMovieIds = recommendMovies(userItemRatings, userId, threshold);
        for (Movie movie : allMovies) {
            if (recommendedMovieIds.contains(movie.getId())) {
                recommendedMovies.add(movie);
            }
        }

        return recommendedMovies;
    }

    // 计算两个用户之间的皮尔逊相关系数
    private double pearsonCorrelation(Map<Integer, Double> user1, Map<Integer, Double> user2) {
        double sum1 = 0, sum2 = 0;
        double sum1Sq = 0, sum2Sq = 0, pSum = 0;
        int n = 0;
        for (Map.Entry<Integer, Double> entry : user1.entrySet()) {
            Integer itemId = entry.getKey();
            Double rating1 = entry.getValue();
            if (user2.containsKey(itemId)) {
                Double rating2 = user2.get(itemId);
                sum1 += rating1;
                sum2 += rating2;
                sum1Sq += Math.pow(rating1, 2);
                sum2Sq += Math.pow(rating2, 2);
                pSum += rating1 * rating2;
                n++;
            }
        }
        if (n == 0) {
            return 0;
        }
        double num = pSum - (sum1 * sum2 / n);
        double den = Math.sqrt((sum1Sq - Math.pow(sum1, 2) / n) * (sum2Sq - Math.pow(sum2, 2) / n));
        if (den == 0) {
            return 0;
        }
        return num / den;
    }

    // 根据用户购买的电影票类型进行推荐
    private List<Integer> recommendMovies(Map<Integer, Map<Integer, Double>> userItemRatings, int userId, double threshold) {
        Map<Integer, Double> userRatings = userItemRatings.get(userId);

        // 计算用户与其他用户之间的皮尔逊相关系数
        Map<Integer, Double> simScores = new HashMap<>();
        for (Map.Entry<Integer, Map<Integer, Double>> entry : userItemRatings.entrySet()) {
            int otherUserId = entry.getKey();
            if (otherUserId != userId) {
                Map<Integer, Double> otherUserRatings = entry.getValue();
                double simScore = pearsonCorrelation(userRatings, otherUserRatings);
                if (simScore > threshold) {
                    simScores.put(otherUserId, simScore);
                }
            }
        }

        // 找到与用户相似度最高的其他用户
        int mostSimilarUserId = 0;
        double maxSimScore = 0;
        for (Map.Entry<Integer, Double> entry : simScores.entrySet()) {
            int otherUserId = entry.getKey();
            double simScore = entry.getValue();
            if (simScore > maxSimScore) {
                mostSimilarUserId = otherUserId;
                maxSimScore = simScore;
            }
        }

        // 获取与用户相似度最高的其他用户购买的电影票类型
        List<Integer> recommendedMovies = new ArrayList<>();
        if (mostSimilarUserId > 0) {
            Map<Integer, Double> mostSimilarUserRatings = userItemRatings.get(mostSimilarUserId);
            for (Map.Entry<Integer, Double> entry : mostSimilarUserRatings.entrySet()) {
                Integer itemId = entry.getKey();
                Double rating = entry.getValue();
                if (!userRatings.containsKey(itemId) && rating > 0) {
                    recommendedMovies.add(itemId);
                }
            }
        }

        return recommendedMovies;
    }
}