我是靠谱客的博主 英勇寒风,最近开发中收集的这篇文章主要介绍4.2 Hadoop-协同过滤算法,觉得挺不错的,现在分享给大家,希望可以做个参考。

概述

协同过滤常常被用于分辨某位特定顾客可能感兴趣的东西,这些结论来自于对其他相似顾客对哪些产品感兴趣的分析。协同过滤以其出色的速度和健壮性,在全球互联网领域炙手可热
基于用户的协同过滤算法UserCF
基于用户的协同过滤,通过不同用户对物品的评分来评测用户之间的相似性,基于用户之间的相似性做出推荐。简单来讲就是:给用户推荐和他兴趣相似的其他用户喜欢的物品

基于物品的协同过滤算法ItemCF
基于item的协同过滤,通过用户对不同item的评分来评测item之间的相似性,基于item之间的相似性做出推荐。简单来讲就是:给用户推荐和他之前喜欢的物品相似的物品

注:基于物品的协同过滤算法,是目前商用最广泛的推荐算法
案例:天池大数据竞赛

提供的数据量,涉及千万级天猫用户,万级天猫品牌,时间跨度4个月的行为记录。 
     提供的训练数据在天池集群的表t_alibaba_bigdata_user_brand_total_1中,字段分别为:user_id,brand_id, type, visit_datetime。如图所示

用户4种行为类型(Type)对应代码分别为: 
     点击:0;购买:1;收藏:2;购物车:3

代码步骤:
  1. 去重
  2. 获取所有用户的喜欢矩阵:
    1.  
 
I1
I2
I3
U1
   
U2
   
  1. 获得所有物品之间的同现矩阵
  2. 两个矩阵相乘得到三维矩阵
  3. 三维矩阵的数据相加获得所有用户对所有物品的推荐值(二维矩阵)
  4. 按照推荐值降序排序。
工程结构:

Step1:
package com.laoxiao.mr.tianchi;



import java.io.IOException;

import java.util.Map;

import org.apache.hadoop.conf.Configuration;

import org.apache.hadoop.fs.FileSystem;

import org.apache.hadoop.fs.Path;

import org.apache.hadoop.io.IntWritable;

import org.apache.hadoop.io.LongWritable;

import org.apache.hadoop.io.NullWritable;

import org.apache.hadoop.io.Text;

import org.apache.hadoop.mapreduce.Job;

import org.apache.hadoop.mapreduce.Mapper;

import org.apache.hadoop.mapreduce.Reducer;

import org.apache.hadoop.mapreduce.lib.input.FileInputFormat;

import org.apache.hadoop.mapreduce.lib.output.FileOutputFormat;



/**

 * 去重复

 * @author root

 *

 */

public class Step1 {



 

 public static boolean run(Configuration config,Map<String, String> paths){

  try {

   FileSystem fs =FileSystem.get(config);

   Job job =Job.getInstance(config);

   job.setJobName("step1");

   job.setJarByClass(Step1.class);

   job.setMapperClass(Step1_Mapper.class);

   job.setReducerClass(Step1_Reducer.class);

//

   job.setMapOutputKeyClass(Text.class);

   job.setMapOutputValueClass(NullWritable.class);

   

   

   

   FileInputFormat.addInputPath(job, new Path(paths.get("Step1Input")));

   Path outpath=new Path(paths.get("Step1Output"));

   if(fs.exists(outpath)){

    fs.delete(outpath,true);

   }

   FileOutputFormat.setOutputPath(job, outpath);

   

   boolean f= job.waitForCompletion(true);

   return f;

  } catch (Exception e) {

   e.printStackTrace();

  }

  return false;

 }

 

  static class Step1_Mapper extends Mapper<LongWritable, Text, Text, NullWritable>{



  protected void map(LongWritable key, Text value,

    Context context)

    throws IOException, InterruptedException {

   if(key.get()!=0){

    context.write(value, NullWritable.get());

   }

  }

 }

 

 

  static class Step1_Reducer extends Reducer<Text, IntWritable, Text, NullWritable>{



   protected void reduce(Text key, Iterable<IntWritable> i,

     Context context)

     throws IOException, InterruptedException {

    context.write(key,NullWritable.get());

   }

  }

}
Step2:
package com.laoxiao.mr.tianchi;



import java.io.IOException;

import java.util.HashMap;

import java.util.Map;

import java.util.Map.Entry;

import org.apache.hadoop.conf.Configuration;

import org.apache.hadoop.fs.FileSystem;

import org.apache.hadoop.fs.Path;

import org.apache.hadoop.io.LongWritable;

import org.apache.hadoop.io.Text;

import org.apache.hadoop.mapreduce.Job;

import org.apache.hadoop.mapreduce.Mapper;

import org.apache.hadoop.mapreduce.Reducer;

import org.apache.hadoop.mapreduce.lib.input.FileInputFormat;

import org.apache.hadoop.mapreduce.lib.output.FileOutputFormat;



/**

 * 按用户分组,计算所有物品出现的组合列表,得到用户对物品的喜爱度得分矩阵

u13 i160:1,

u14 i25:1,i223:1,

u16 i252:1,

u21 i266:1,

u24 i64:1,i218:1,i185:1,

u26 i276:1,i201:1,i348:1,i321:1,i136:1,

 * @author root

 *

 */

public class Step2 {



 

 public static boolean run(Configuration config,Map<String, String> paths){

  try {

   FileSystem fs =FileSystem.get(config);

   Job job =Job.getInstance(config);

   job.setJobName("step2");

   job.setJarByClass(StartRun.class);

   job.setMapperClass(Step2_Mapper.class);

   job.setReducerClass(Step2_Reducer.class);

//

   job.setMapOutputKeyClass(Text.class);

   job.setMapOutputValueClass(Text.class);

   

   

   

   FileInputFormat.addInputPath(job, new Path(paths.get("Step2Input")));

   Path outpath=new Path(paths.get("Step2Output"));

   if(fs.exists(outpath)){

    fs.delete(outpath,true);

   }

   FileOutputFormat.setOutputPath(job, outpath);

   

   boolean f= job.waitForCompletion(true);

   return f;

  } catch (Exception e) {

   e.printStackTrace();

  }

  return false;

 }

 

  static class Step2_Mapper extends Mapper<LongWritable, Text, Text, Text>{



   //如果使用:用户+物品,同时作为输出key,更优

  protected void map(LongWritable key, Text value,

    Context context)

    throws IOException, InterruptedException {

   String[] tokens=value.toString().split(",");

   String item=tokens[0];

   String user=tokens[1];

   String action =tokens[2];

   Text k= new Text(user);

   Integer rv =StartRun.R.get(action);

// if(rv!=null){

   Text v =new Text(item+":"+ rv.intValue());

   context.write(k, v);

  }

 }

 

 

  static class Step2_Reducer extends Reducer<Text, Text, Text, Text>{



   protected void reduce(Text key, Iterable<Text> i,

     Context context)

     throws IOException, InterruptedException {

    Map<String, Integer> r =new HashMap<String, Integer>();

   

    for(Text value :i){

     String[] vs =value.toString().split(":");

     String item=vs[0];

     Integer action=Integer.parseInt(vs[1]);

     action = ((Integer) (r.get(item)==null? 0:r.get(item))).intValue() + action;

     r.put(item,action);

    }

    StringBuffer sb =new StringBuffer();

    for(Entry<String, Integer> entry :r.entrySet() ){

     sb.append(entry.getKey()+":"+entry.getValue().intValue()+",");

    }

   

    context.write(key,new Text(sb.toString()));

   }

  }

}
Step3:
package com.laoxiao.mr.tianchi;



import java.io.IOException;

import java.util.Map;

import org.apache.hadoop.conf.Configuration;

import org.apache.hadoop.fs.FileSystem;

import org.apache.hadoop.fs.Path;

import org.apache.hadoop.io.IntWritable;

import org.apache.hadoop.io.LongWritable;

import org.apache.hadoop.io.Text;

import org.apache.hadoop.mapreduce.Job;

import org.apache.hadoop.mapreduce.Mapper;

import org.apache.hadoop.mapreduce.Reducer;

import org.apache.hadoop.mapreduce.lib.input.FileInputFormat;

import org.apache.hadoop.mapreduce.lib.output.FileOutputFormat;

/**

 * 对物品组合列表进行计数,建立物品的同现矩阵

i100:i100 3

i100:i105 1

i100:i106 1

i100:i109 1

i100:i114 1

i100:i124 1

 * @author root

 *

 */

public class Step3 {

  private final static Text K = new Text();

     private final static IntWritable V = new IntWritable(1);

 

 public static boolean run(Configuration config,Map<String, String> paths){

  try {

   FileSystem fs =FileSystem.get(config);

   Job job =Job.getInstance(config);

   job.setJobName("step3");

   job.setJarByClass(StartRun.class);

   job.setMapperClass(Step3_Mapper.class);

   job.setReducerClass(Step3_Reducer.class);

   job.setCombinerClass(Step3_Reducer.class);

//

   job.setMapOutputKeyClass(Text.class);

   job.setMapOutputValueClass(IntWritable.class);

   

   

   

   FileInputFormat.addInputPath(job, new Path(paths.get("Step3Input")));

   Path outpath=new Path(paths.get("Step3Output"));

   if(fs.exists(outpath)){

    fs.delete(outpath,true);

   }

   FileOutputFormat.setOutputPath(job, outpath);

   

   boolean f= job.waitForCompletion(true);

   return f;

  } catch (Exception e) {

   e.printStackTrace();

  }

  return false;

 }

 

  static class Step3_Mapper extends Mapper<LongWritable, Text, Text, IntWritable>{



  protected void map(LongWritable key, Text value,

    Context context)

    throws IOException, InterruptedException {

   String[] tokens=value.toString().split("t");

   String[] items =tokens[1].split(",");

   for (int i = 0; i < items.length; i++) {

    String itemA = items[i].split(":")[0];

    for (int j = 0; j < items.length; j++) {

     String itemB = items[j].split(":")[0];

     K.set(itemA+":"+itemB);

     context.write(K, V);

    }

   }

   

  }

 }

 

 

 

  static class Step3_Reducer extends Reducer<Text, IntWritable, Text, IntWritable>{



   protected void reduce(Text key, Iterable<IntWritable> i,

     Context context)

     throws IOException, InterruptedException {

    int sum =0;

    for(IntWritable v :i ){

     sum =sum+v.get();

    }

    V.set(sum);

    context.write(key, V);

   }

  }

 

}
Step4:
package com.laoxiao.mr.tianchi;



import java.io.IOException;

import java.util.HashMap;

import java.util.Iterator;

import java.util.Map;

import java.util.regex.Pattern;



import org.apache.hadoop.conf.Configuration;

import org.apache.hadoop.fs.FileSystem;

import org.apache.hadoop.fs.Path;

import org.apache.hadoop.io.LongWritable;

import org.apache.hadoop.io.Text;

import org.apache.hadoop.mapreduce.Job;

import org.apache.hadoop.mapreduce.Mapper;

import org.apache.hadoop.mapreduce.Reducer;

import org.apache.hadoop.mapreduce.lib.input.FileInputFormat;

import org.apache.hadoop.mapreduce.lib.input.FileSplit;

import org.apache.hadoop.mapreduce.lib.output.FileOutputFormat;

/**

 *

 * 把同现矩阵和得分矩阵相乘

 * @author root

 *

 */

public class Step4 {



 public static boolean run(Configuration config, Map<String, String> paths) {

  try {

   FileSystem fs = FileSystem.get(config);

   Job job = Job.getInstance(config);

   job.setJobName("step4");

   job.setJarByClass(StartRun.class);

   job.setMapperClass(Step4_Mapper.class);

   job.setReducerClass(Step4_Reducer.class);

   job.setMapOutputKeyClass(Text.class);

   job.setMapOutputValueClass(Text.class);



   // FileInputFormat.addInputPath(job, new

   // Path(paths.get("Step4Input")));

   FileInputFormat.setInputPaths(job,

     new Path[] { new Path(paths.get("Step4Input1")),

       new Path(paths.get("Step4Input2")) });

   Path outpath = new Path(paths.get("Step4Output"));

   if (fs.exists(outpath)) {

    fs.delete(outpath, true);

   }

   FileOutputFormat.setOutputPath(job, outpath);



   boolean f = job.waitForCompletion(true);

   return f;

  } catch (Exception e) {

   e.printStackTrace();

  }

  return false;

 }



 static class Step4_Mapper extends Mapper<LongWritable, Text, Text, Text> {

  private String flag;// A同现矩阵 or B得分矩阵



  //每个maptask,初始化时调用一次

  protected void setup(Context context) throws IOException,

    InterruptedException {

   FileSplit split = (FileSplit) context.getInputSplit();

   flag = split.getPath().getParent().getName();// 判断读的数据集



   System.out.println(flag + "**********************");

  }



  protected void map(LongWritable key, Text value, Context context)

    throws IOException, InterruptedException {

   String[] tokens = Pattern.compile("[t,]").split(value.toString());



   if (flag.equals("step3")) {// 同现矩阵

    String[] v1 = tokens[0].split(":");

    String itemID1 = v1[0];

    String itemID2 = v1[1];

    String num = tokens[1];



    Text k = new Text(itemID2);// 以前一个物品为key 比如i100

    Text v = new Text("A:" + itemID1 + "," + num);// A:i109,1



    context.write(k, v);



   } else if (flag.equals("step2")) {// 用户对物品喜爱得分矩阵

    String userID = tokens[0];

    for (int i = 1; i < tokens.length; i++) {

     String[] vector = tokens[i].split(":");

     String itemID = vector[0];// 物品id

     String pref = vector[1];// 喜爱分数



     Text k = new Text(itemID); // 以物品为key 比如:i100

     Text v = new Text("B:" + userID + "," + pref); // B:u401,2



     context.write(k, v);

    }

   }

  }

 }



 static class Step4_Reducer extends Reducer<Text, Text, Text, Text> {

  protected void reduce(Text key, Iterable<Text> values, Context context)

    throws IOException, InterruptedException {

   // A同现矩阵 or B得分矩阵

   //某一个物品,针对它和其他所有物品的同现次数,都在mapA集合中

   Map<String, Integer> mapA = new HashMap<String, Integer>();// 和该物品(key中的itemID)同现的其他物品的同现集合// 。其他物品ID为map的key,同现数字为值

   Map<String, Integer> mapB = new HashMap<String, Integer>();// 该物品(key中的itemID),所有用户的推荐权重分数。



   for (Text line : values) {

    String val = line.toString();

    if (val.startsWith("A:")) {// 表示物品同现数字

     String[] kv = Pattern.compile("[t,]").split(

       val.substring(2));

     try {

      mapA.put(kv[0], Integer.parseInt(kv[1]));

     } catch (Exception e) {

      e.printStackTrace();

     }



    } else if (val.startsWith("B:")) {

     String[] kv = Pattern.compile("[t,]").split(

       val.substring(2));

     try {

      mapB.put(kv[0], Integer.parseInt(kv[1]));

     } catch (Exception e) {

      e.printStackTrace();

     }

    }

   }



   double result = 0;

   Iterator<String> iter = mapA.keySet().iterator();

   while (iter.hasNext()) {

    String mapk = iter.next();// itemID



    int num = mapA.get(mapk).intValue();

    Iterator<String> iterb = mapB.keySet().iterator();

    while (iterb.hasNext()) {

     String mapkb = iterb.next();// userID

     int pref = mapB.get(mapkb).intValue();

     result = num * pref;// 矩阵乘法相乘计算



     Text k = new Text(mapkb);

     Text v = new Text(mapk + "," + result);

     context.write(k, v);

    }

   }

  }

 }

}
Step5:
package com.laoxiao.mr.tianchi;



import java.io.IOException;

import java.util.HashMap;

import java.util.Iterator;

import java.util.Map;

import java.util.regex.Pattern;



import org.apache.hadoop.conf.Configuration;

import org.apache.hadoop.fs.FileSystem;

import org.apache.hadoop.fs.Path;

import org.apache.hadoop.io.LongWritable;

import org.apache.hadoop.io.Text;

import org.apache.hadoop.mapreduce.Job;

import org.apache.hadoop.mapreduce.Mapper;

import org.apache.hadoop.mapreduce.Reducer;

import org.apache.hadoop.mapreduce.lib.input.FileInputFormat;

import org.apache.hadoop.mapreduce.lib.output.FileOutputFormat;

/**

 *

 * 把相乘之后的矩阵相加获得结果矩阵

 *

 * @author root

 *

 */

public class Step5 {

 private final static Text K = new Text();

 private final static Text V = new Text();



 public static boolean run(Configuration config, Map<String, String> paths) {

  try {

   FileSystem fs = FileSystem.get(config);

   Job job = Job.getInstance(config);

   job.setJobName("step5");

   job.setJarByClass(StartRun.class);

   job.setMapperClass(Step5_Mapper.class);

   job.setReducerClass(Step5_Reducer.class);

   job.setMapOutputKeyClass(Text.class);

   job.setMapOutputValueClass(Text.class);



   FileInputFormat

     .addInputPath(job, new Path(paths.get("Step5Input")));

   Path outpath = new Path(paths.get("Step5Output"));

   if (fs.exists(outpath)) {

    fs.delete(outpath, true);

   }

   FileOutputFormat.setOutputPath(job, outpath);



   boolean f = job.waitForCompletion(true);

   return f;

  } catch (Exception e) {

   e.printStackTrace();

  }

  return false;

 }



 static class Step5_Mapper extends Mapper<LongWritable, Text, Text, Text> {



  /**

   * 原封不动输出

   */

  protected void map(LongWritable key, Text value, Context context)

    throws IOException, InterruptedException {

   String[] tokens = Pattern.compile("[t,]").split(value.toString());

   Text k = new Text(tokens[0]);// 用户为key

   Text v = new Text(tokens[1] + "," + tokens[2]);

   context.write(k, v);

  }

 }



 static class Step5_Reducer extends Reducer<Text, Text, Text, Text> {

  protected void reduce(Text key, Iterable<Text> values, Context context)

    throws IOException, InterruptedException {

   Map<String, Double> map = new HashMap<String, Double>();// 结果



   for (Text line : values) {// i9,4.0

    String[] tokens = line.toString().split(",");

    String itemID = tokens[0];

    Double score = Double.parseDouble(tokens[1]);



    if (map.containsKey(itemID)) {

     map.put(itemID, map.get(itemID) + score);// 矩阵乘法求和计算

    } else {

     map.put(itemID, score);

    }

   }



   Iterator<String> iter = map.keySet().iterator();

   while (iter.hasNext()) {

    String itemID = iter.next();

    double score = map.get(itemID);

    Text v = new Text(itemID + "," + score);

    context.write(key, v);

   }

  }



 }

}
Step6:
package com.laoxiao.mr.tianchi;



import java.io.DataInput;

import java.io.DataOutput;

import java.io.IOException;

import java.util.Map;

import java.util.regex.Pattern;

import org.apache.hadoop.conf.Configuration;

import org.apache.hadoop.fs.FileSystem;

import org.apache.hadoop.fs.Path;

import org.apache.hadoop.io.LongWritable;

import org.apache.hadoop.io.Text;

import org.apache.hadoop.io.WritableComparable;

import org.apache.hadoop.io.WritableComparator;

import org.apache.hadoop.mapreduce.Job;

import org.apache.hadoop.mapreduce.Mapper;

import org.apache.hadoop.mapreduce.Reducer;

import org.apache.hadoop.mapreduce.lib.input.FileInputFormat;

import org.apache.hadoop.mapreduce.lib.output.FileOutputFormat;



/**

 *

 * 按照推荐得分降序排序,每个用户列出10个推荐物品

 *

 * @author root

 *

 */

public class Step6 {

 private final static Text K = new Text();

 private final static Text V = new Text();



 public static boolean run(Configuration config, Map<String, String> paths) {

  try {

   FileSystem fs = FileSystem.get(config);

   Job job = Job.getInstance(config);

   job.setJobName("step6");

   job.setJarByClass(StartRun.class);

   job.setMapperClass(Step6_Mapper.class);

   job.setReducerClass(Step6_Reducer.class);

   job.setSortComparatorClass(NumSort.class);

   job.setGroupingComparatorClass(UserGroup.class);

   job.setMapOutputKeyClass(PairWritable.class);

   job.setMapOutputValueClass(Text.class);



   FileInputFormat

     .addInputPath(job, new Path(paths.get("Step6Input")));

   Path outpath = new Path(paths.get("Step6Output"));

   if (fs.exists(outpath)) {

    fs.delete(outpath, true);

   }

   FileOutputFormat.setOutputPath(job, outpath);



   boolean f = job.waitForCompletion(true);

   return f;

  } catch (Exception e) {

   e.printStackTrace();

  }

  return false;

 }



 static class Step6_Mapper extends Mapper<LongWritable, Text, PairWritable, Text> {



  protected void map(LongWritable key, Text value, Context context)

    throws IOException, InterruptedException {

   String[] tokens = Pattern.compile("[t,]").split(value.toString());

   String u = tokens[0];

   String item = tokens[1];

   String num = tokens[2];

   PairWritable k =new PairWritable();

   k.setUid(u);

   k.setNum(Double.parseDouble(num));

   V.set(item+":"+num);

   context.write(k, V);



  }

 }



 static class Step6_Reducer extends Reducer<PairWritable, Text, Text, Text> {

  protected void reduce(PairWritable key, Iterable<Text> values, Context context)

    throws IOException, InterruptedException {

   int i=0;

   StringBuffer sb =new StringBuffer();

   for(Text v :values){//输出前10个推荐物品

    if(i==10)

     break;

    sb.append(v.toString()+",");

    i++;

   }

   K.set(key.getUid());

   V.set(sb.toString());

   context.write(K, V);

  }



 }

 

 static class PairWritable implements WritableComparable<PairWritable>{



// private String itemId;

  private String uid;

  private double num;

  public void write(DataOutput out) throws IOException {

   out.writeUTF(uid);

// out.writeUTF(itemId);

   out.writeDouble(num);

  }



  public void readFields(DataInput in) throws IOException {

   this.uid=in.readUTF();

// this.itemId=in.readUTF();

   this.num=in.readDouble();

  }



  public int compareTo(PairWritable o) {

   int r =this.uid.compareTo(o.getUid());

   if(r==0){

    return Double.compare(this.num, o.getNum());

   }

   return r;

  }



  public String getUid() {

   return uid;

  }



  public void setUid(String uid) {

   this.uid = uid;

  }



  public double getNum() {

   return num;

  }



  public void setNum(double num) {

   this.num = num;

  }

 

 }

 

 static class NumSort extends WritableComparator{

  public NumSort(){

   super(PairWritable.class,true);

  }

 

  public int compare(WritableComparable a, WritableComparable b) {

   PairWritable o1 =(PairWritable) a;

   PairWritable o2 =(PairWritable) b;

   

   int r =o1.getUid().compareTo(o2.getUid());

   if(r==0){

    return -Double.compare(o1.getNum(), o2.getNum());

   }

   return r;

  }

 }

 

 static class UserGroup extends WritableComparator{

  public UserGroup(){

   super(PairWritable.class,true);

  }

 

  public int compare(WritableComparable a, WritableComparable b) {

   PairWritable o1 =(PairWritable) a;

   PairWritable o2 =(PairWritable) b;

   return o1.getUid().compareTo(o2.getUid());

  }

 }

}
StartRun:
package com.laoxiao.mr.tianchi;



import java.util.HashMap;

import java.util.Map;



import org.apache.hadoop.conf.Configuration;



public class StartRun {



 public static void main(String[] args) {

  Configuration config = new Configuration();

  config.set("fs.defaultFS", "hdfs://node1:9000");

// config.set("yarn.resourcemanager.hostname", "node5");

  //所有mr的输入和输出目录定义在map集合中

  Map<String, String> paths = new HashMap<String, String>();

  paths.put("Step1Input", "/usr/input/(sample)sam_tianchi_2014002_rec_tmall_log.csv");

  paths.put("Step1Output", "/output/step1");

  paths.put("Step2Input", paths.get("Step1Output"));

  paths.put("Step2Output", "/output/step2");

  paths.put("Step3Input", paths.get("Step2Output"));

  paths.put("Step3Output", "/output/step3");

  paths.put("Step4Input1", paths.get("Step2Output"));

  paths.put("Step4Input2", paths.get("Step3Output"));

  paths.put("Step4Output", "/output/step4");

  paths.put("Step5Input", paths.get("Step4Output"));

  paths.put("Step5Output", "/output/step5");

  paths.put("Step6Input", paths.get("Step5Output"));

  paths.put("Step6Output", "/output/step6");



  Step1.run(config, paths);

  Step2.run(config, paths);

  Step3.run(config, paths);

  Step4.run(config, paths);

  Step5.run(config, paths);

  Step6.run(config, paths);

 }



 public static Map<String, Integer> R = new HashMap<String, Integer>();

 static {

  R.put("click", 1);

  R.put("collect", 2);

  R.put("cart", 3);

  R.put("alipay", 4);

 }

}

最后

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