spark高级排序彻底解秘

Posted 2020-08-11 大数据和人工智能躺过的坑

　　

　　排序，真的非常重要！

RDD.scala（源码）

　　在其，没有罗列排序，不是说它不重要！

 

 

本博文的主要内容有:

　　1、基础排序算法实战

　　2、二次排序算法实战

　　3、更高级别排序算法

　　4、排序算法内幕解密

 

 

 

 

 

 

 

1、基础排序算法实战

　　启动hdfs集群

spark@SparkSingleNode:/usr/local/hadoop/hadoop-2.6.0$ sbin/start-dfs.sh

 

 

 

 

 

 

 

 

 

　　启动spark集群

 

spark@SparkSingleNode:/usr/local/spark/spark-1.5.2-bin-hadoop2.6$ sbin/start-all.sh

 

 

 

 

 

 

　　启动spark-shell

spark@SparkSingleNode:/usr/local/spark/spark-1.5.2-bin-hadoop2.6/bin$ ./spark-shell --master spark://SparkSingleNode:7077 --executor-memory 1g

 

 

scala> sc.setLogLevel("WARN")    //过滤日志提醒

scala> sc.textFile("/README.md").flatMap(_.split(" ")).map(word =>(word,1)).reduceByKey(_+_,1).map(pair => (pair._2,pair._1)).sortByKey(false).map(pair => (pair._2,pair._1)).collect

 

 

 

 

scala> sc.textFile("/README.md").flatMap(_.split(" ")).map(word =>(word,1)).reduceByKey(_+_,1).map(pair => (pair._2,pair._1)).sortByKey(false).map(pair => (pair._2,pair._1)).collect
res2: Array[(String, Int)] = Array(("",67), (the,21), (Spark,14), (to,14), (for,12), (a,10), (and,10), (##,8), (run,7), (is,6), (on,6), (can,6), (of,5), (also,5), (in,5), (if,4), (or,4), (Hadoop,4), (with,4), (you,4), (build,3), (including,3), (Please,3), (use,3), (particular,3), (documentation,3), (example,3), (an,3), (You,3), (building,3), (that,3), (guidance,3), (For,2), (This,2), (Hive,2), (To,2), (SparkPi,2), (refer,2), (Interactive,2), (be,2), (./bin/run-example,2), (1000:,2), (tests,2), (examples,2), (at,2), (using,2), (Shell,2), (class,2), (`examples`,2), (set,2), (Hadoop,,2), (cluster,2), (supports,2), (Python,2), (general,2), (locally,2), (following,2), (which,2), (should,2), ([project,2), (do,2), (how,2), (It,2), (Scala,2), (detailed,2), (return,2), (one,2), (Python,,2), (SQL...
scala>

 　　则，可看出，是sortByKey(false)是按key排序且降序.

 

 

 

sortByKey源码

/**
 * Sort the RDD by key, so that each partition contains a sorted range of the elements. Calling
 * `collect` or `save` on the resulting RDD will return or output an ordered list of records
 * (in the `save` case, they will be written to multiple `part-X` files in the filesystem, in
 * order of the keys).
 */
// TODO: this currently doesn\'t work on P other than Tuple2!
def sortByKey(ascending: Boolean = true, numPartitions: Int = self.partitions.length)
    : RDD[(K, V)] = self.withScope
{
  val part = new RangePartitioner(numPartitions, self, ascending)
  new ShuffledRDD[K, V, V](self, part)
    .setKeyOrdering(if (ascending) ordering else ordering.reverse)
}

 

　　由此，可看出，一旦排序，则产生ShuffledRDD。

 

　　为什么我的是没显示出来？

　　rangPartition是怎么排序的呢？

好的，基础排序算法实战至此。

 

 

 

 

 

 

2、二次排序算法实战

　　所谓，二次排序，就是指排序的时候考虑两个维度。

 　　如，在第一列，按照降序排，第一列的key相同，那么，再怎么排呢？则，考虑第二列，按照降序排。即，用到了二次排序。

 

准备

【数据文件Input】

 2 3
 4 1
 3 2
 4 3
 8 7
 2 1

 

【运行结果Output】

 2 1
 2 3
 3 2
 4 1
 4 3
 8 7

　　如果是去大公司的话，则要掌握，5个维度，甚至8个维度，而不是才2个维度而已。加油！zhouls。

 

 

 　　这里，就用，Scala IDE for Eclipse，来写，

Scala IDE for Eclipse的下载、安装和WordCount的初步使用（本地模式和集群模式）

　　

 

 

　　SecondarySortKey.java

package com.zhouls.spark.SparkApps.cores;

import java.io.Serializable;
import scala.math.Ordered;


public class SecondarySortKey implements Ordered<SecondarySortKey>,Serializable{
　　private int first;
　　private int second;


　　@Override
　　public boolean $greater(SecondarySortKey arg0) {
　　// TODO Auto-generated method stub
　　　　return false;
　　}


　　@Override
　　public boolean $greater$eq(SecondarySortKey arg0) {
　　// TODO Auto-generated method stub
　　return false;
　　}


　　@Override
　　public boolean $less(SecondarySortKey arg0) {
　　// TODO Auto-generated method stub
　　return false;
　　}


　　@Override
　　public boolean $less$eq(SecondarySortKey arg0) {
　　// TODO Auto-generated method stub
　　return false;
　　}


　　@Override
　　public int compare(SecondarySortKey arg0) {
　　// TODO Auto-generated method stub
　　return 0;
　　}


　　@Override
　　public int compareTo(SecondarySortKey arg0) {
　　// TODO Auto-generated method stub
　　return 0;
　　}
}

 

 

 

　　在这里，学下技巧。

　　然后，修改成我们自己想要的。

 

 

 

 

最终的SecondarySortKey.java如下:

package com.zhouls.spark.SparkApps.cores;

import java.io.Serializable;
import scala.math.Ordered;


public class SecondarySortKey implements Ordered<SecondarySortKey>,Serializable{
　　private int first;
　　private int second;

　　//二次排序的公开构造器
　　public SecondarySortKey(int first,int second){
　　this.first=first;
　　this.second=second;
　　}

　　public boolean $greater(SecondarySortKey other) {
　　　　if(this.first>other.getFirst()){
　　　　　　return true;
　　　　}else if(this.first==other.getFirst()&&this.second>other.getSecond()){
　　　　　　return true;
　　}
　　　　　　return false;
　　}

　　public boolean $greater$eq(SecondarySortKey other) {
　　　　if(this.$greater(other)){
　　　　　　return true;
　　　　}else if(this.first==other.getFirst()&&this.second==other.getSecond()){
　　　　　　return true;
　　　　}
　　　　　　return false;
　　}

　　public boolean $less(SecondarySortKey other) {
　　　　if(this.first<other.getFirst()){
　　　　　　return true;
　　　　}else if(this.first==other.getFirst()&&this.second<other.getSecond()){
　　　　　　return true;
　　　　}
　　　　　　return false;
　　}

　　public boolean $less$eq(SecondarySortKey other) {
　　　　if(this.$less(other)){
　　　　　　return true;
　　}else if(this.first==other.getFirst()&&this.second==other.getSecond()){
　　　　　　return true;
　　}
　　　　　　return false;
　　}

　　public int compare(SecondarySortKey other) {
　　　　if(this.first-other.getFirst() !=0){
　　　　　　return this.first-other.getFirst();
　　}else{
　　　　　　return this.second-other.getSecond();
　　　　}
　　}

　　public int compareTo(SecondarySortKey other) {
　　　　if(this.first-other.getFirst() !=0){
　　　　　　return this.first-other.getFirst();
　　}else{
　　　　return this.second-other.getSecond();
　　　　}
　　}

　　public int hashCode() {
　　　　final int prime = 31;
　　　　int result = 1;
　　　　result = prime * result + first;
　　　　result = prime * result + second;
　　　　return result;
　　}

　　public boolean equals(Object obj) {
　　　　if (this == obj)
　　　　return true;
　　　　if (obj == null)
　　　　return false;
　　　　if (getClass() != obj.getClass())
　　　　return false;
　　　　SecondarySortKey other = (SecondarySortKey) obj;
　　　　if (first != other.first)
　　　　return false;
　　　　if (second != other.second)
　　　　return false;
　　　　return true;
　　}

　　public int getFirst() {
　　　　return first;
　　}

　　public void setFirst(int first) {
　　　　this.first = first;
　　}

　　public int getSecond() {
　　　　return second;
　　}

　　public void setSecond(int second) {
　　　　this.second = second;
　　}
}

 

 

 

 

 

 

 

 

 

 

 

SecondarySortApp.java的完整代码：

package com.zhouls.spark.SparkApps.cores;

import org.apache.spark.SparkConf;
import org.apache.spark.api.java.JavaPairRDD;
import org.apache.spark.api.java.JavaRDD;
import org.apache.spark.api.java.JavaSparkContext;
import org.apache.spark.api.java.function.Function;
import org.apache.spark.api.java.function.PairFunction;
import org.apache.spark.api.java.function.VoidFunction;

import scala.Tuple2;

/*
* 二次排序，具体的实现步骤：
* 第一步：安装Ordered和Serrializable接口实现自定义排序的key
* 第二步:将要进行二次排序的文件加载进来<key,value>类型的RDD
* 第三步：使用sortByKey基于自定义的Key进行二次排序
* 第四步：去除掉排序的Key,只保留排序的结果
*/
public class SecondarySortApp {
public static void main(String[] args) {
SparkConf conf=new SparkConf().setAppName("SecondarySortApp").setMaster("local");
JavaSparkContext sc=new JavaSparkContext(conf);//其底层实际上就是Scala的SparkContext
JavaRDD<String> lines = sc.textFile("D://SoftWare//spark-1.5.2-bin-hadoop2.6//helloSpark.txt"); 
JavaPairRDD<SecondarySortKey, String> pairs = lines.mapToPair(new PairFunction<String, SecondarySortKey, String>() {

private static final long serialVersionUID = 1L;

@Override
public Tuple2<SecondarySortKey, String> call(String line) throws Exception {
String[] splited = line.split(" ");
SecondarySortKey key =new SecondarySortKey(Integer.valueOf(splited[0]),Integer.valueOf(splited[1]));
return new Tuple2<SecondarySortKey,String>(key,line);
}
});

JavaPairRDD<SecondarySortKey, String> sorted = pairs.sortByKey();

//过滤掉排序后自定的Key，保留排序的结果
JavaRDD<String> SecondaySorted=sorted.map(new Function<Tuple2<SecondarySortKey,String>, String>() {

private static final long serialVersionUID = 1L;

@Override
public String call(Tuple2<SecondarySortKey, String> sortedContent) throws Exception {

System.out.println("sortedContent._1 "+(sortedContent._1).toString());
System.out.println("sortedContent._2 "+sortedContent._2);

return sortedContent._2;
}
});
SecondaySorted.foreach(new VoidFunction<String>() {

@Override
public void call(String sorted) throws Exception {
System.out.println(sorted);
}
});

}
}

 

 

 

 

 

 

 　　Scala

 

 

package com.zhouls.spark.cores

/**
  * Created by Administrator on 2016/9/30.
  */
class SecondarySortKey(val first:Int,val second:Int) extends Ordered[SecondarySortKey] with Serializable {
    def compare(that: SecondarySortKey): Int = {
        if(this.first-that.first!=0){
          return this.first-that.first
        }else{
          return this.second-that.second
        }
    }
}

 

 

package com.zhouls.spark.cores
import org.apache.spark.{SparkConf, SparkContext}
/**
  * Created by Administrator on 2016/9/30.
  * 二次排序：具体的实现步骤：
  * 第一步：按照Ordered和Serrializable接口实现自定义排序的Key
  * 第二步：将要进行二次排序的文件加载进来< key,value> 类型的RDD
  * 第三步：使用sortByKey基于自定义的Key进行二次排序
  * 第四步：去除掉排序的Key,只保留排序的结果
  */
object SecondarySortApp {
  def main (args: Array[String]) {
    val conf=new SparkConf().setAppName("SecondarySortApp").setMaster("local")//创建SparkConf,初始化程序的配置
    val sc = new SparkContext(conf)//创建SparkContext，这是第一个RDD创建的唯一入口，也是Driver的灵魂，是通往集群的唯一通道

    val lines = sc.textFile("D:\\\\SoftWare\\\\spark-1.5.2-bin-hadoop2.6\\\\helloSpark.txt")//读取文件
//    val results = lines.map(line=>(new SecondarySortKey(line.split(" ")(0).toInt , line.split(" ")(1).toInt), line)).sortByKey().map(pair => pair._2)
    val pairWithSortKey =  lines.map (line=> (
      new SecondarySortKey(line.split(" ")(0).toInt ,line.split(" ")(1).toInt), line
      ))
    val sorted = pairWithSortKey.sortByKey()
    val sortedResult = sorted.map(sortedLine => sortedLine._2)
    sortedResult.collect.foreach(println)
  }

}

 

 

 

 

 

 

 

 

作业：

1：Scala实现二次排序

SecondarySortKey.scala的完整代码：

class SecondarySortKey(val first:Int,val second:Int) extends Ordered[SecondarySortKey] with Serializable{
  override def compare(that: SecondarySortKey): Int = {
    if(this.first-that.first!=0){
      return this.first-that.first
    }else{
      return this.second-that.second
    }
  }
}

 

object SecondarySortKey extends scala.AnyRef with Serializable{
  def apply(first:Int,second:Int): SecondarySortKey ={
    new SecondarySortKey(first,second)
  }
}

 

 

SecondarySortApp.scala的完整代码：

object SecondarySortApp {
  def main (args: Array[String]) {
    val conf=new SparkConf().setAppName("SecondarySortApp").setMaster("local")
    val sc=new SparkContext(conf)
    val lines=sc.textFile("D:\\\\SoftWare\\\\spark-1.5.2-bin-hadoop2.6\\\\helloSpark.txt")
    //val results=lines.map(line=>(new SecondarySortKey(line.split(" ")(0).toInt,line.split(" ")(1).toInt),line)).sortByKey().map(pair=>pair._2)
    val results=lines.map(line=>(SecondarySortKey.apply(line.split(" ")(0).toInt,line.split(" ")(1).toInt),line)).sortByKey().map(pair=>pair._2)
    results.collect.foreach(println)
  }
}

 

 

 

 

2：RangePartitioner的源码阅读：

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *    http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

package org.apache.spark

import java.io.{IOException, ObjectInputStream, ObjectOutputStream}

import scala.collection.mutable
import scala.collection.mutable.ArrayBuffer
import scala.reflect.{ClassTag, classTag}
import scala.util.hashing.byteswap32

import org.apache.spark.rdd.{PartitionPruningRDD, RDD}
import org.apache.spark.serializer.JavaSerializer
import org.apache.spark.util.{CollectionsUtils, Utils}
import org.apache.spark.util.random.{XORShiftRandom, SamplingUtils}

/**
 * An object that defines how the elements in a key-value pair RDD are partitioned by key.
 * Maps each key to a partition ID, from 0 to `numPartitions - 1`.
 */
abstract class Partitioner extends Serializable {
  def numPartitions: Int
  def getPartition(key: Any): Int
}

object Partitioner {
  /**
   * Choose a partitioner to use for a cogroup-like operation between a number of RDDs.
   *
   * If any of the RDDs already has a partitioner, choose that one.
   *
   * Otherwise, we use a default HashPartitioner. For the number of partitions, if
   * spark.default.parallelism is set, then we\'ll use the value from SparkContext
   * defaultParallelism, otherwise we\'ll use the max number of upstream partitions.
   *
   * Unless spark.default.parallelism is set, the number of partitions will be the
   * same as the number of partitions in the largest upstream RDD, as this should
   * be least likely to cause out-of-memory errors.
   *
   * We use two method parameters (rdd, others) to enforce callers passing at least 1 RDD.
   */
  def defaultPartitioner(rdd: RDD[_], others: RDD[_]*): Partitioner = {
    val bySize = (Seq(rdd) ++ others).sortBy(_.partitions.size).reverse
    for (r <- bySize if r.partitioner.isDefined && r.partitioner.get.numPartitions > 0) {
      return r.partitioner.get
    }
    if (rdd.context.conf.contains("spark.default.parallelism")) {
      new HashPartitioner(rdd.context.defaultParallelism)
    } else {
      new HashPartitioner(bySize.head.partitions.size)
    }
  }
}

/**
 * A [[org.apache.spark.Partitioner]] that implements hash-based partitioning using
 * Java\'s `Object.hashCode`.
 *
 * Java arrays have hashCodes that are based on the arrays\' identities rather than their contents,
 * so attempting to partition an RDD[Array[_]] or RDD[(Array[_], _)] using a HashPartitioner will
 * produce an unexpected or incorrect result.
 */
class HashPartitioner(partitions: Int) extends Partitioner {
  require(partitions >= 0, s"Number of partitions ($partitions) cannot be negative.")

  def numPartitions: Int = partitions

  def getPartition(key: Any): Int = key match {
    case null => 0
    case _ => Utils.nonNegativeMod(key.hashCode, numPartitions)
  }

  override def equals(other: Any): Boolean = other match {
    case h: HashPartitioner =>
      h.numPartitions == numPartitions
    case _ =>
      false
  }

  override def hashCode: Int = numPartitions
}

/**
 * A [[org.apache.spark.Partitioner]] that partitions sortable records by range into roughly
 * equal ranges. The ranges are determined by sampling the content of the RDD passed in.
 *
 * Note that the actual number of partitions created by the RangePartitioner might not be the same
 * as the `partitions` parameter, in the case where the number of sampled records is less than
 * the value of `partitions`.
 */
class RangePartitioner[K : Ordering : ClassTag, V](
    @transient partitions: Int,
    @transient rdd: RDD[_ <: Product2[K, V]],
    private var ascending: Boolean = true)
  extends Partitioner {

  // We allow partitions = 0, which happens when sorting an empty RDD under the default settings.
  require(partitions >= 0, s"Number of partitions cannot be negative but found $partitions.")

  private var ordering = implicitly[Ordering[K]]

  // An array of upper bounds for the first (partitions - 1) partitions
  private var rangeBounds: Array[K] = {
    if (partitions <= 1) {
      Array.empty
    } else {
      // This is the sample size we need to have roughly balanced output partitions, capped at 1M.
      val sampleSize = math.min(20.0 * partitions, 1e6)
      // Assume the input partitions are roughly balanced and over-sample a little bit.
      val sampleSizePerPartition = math.ceil(3.0 * sampleSize / rdd.partitions.size).toInt
      val (numItems, sketched) = RangePartitioner.sketch(rdd.map(_._1), sampleSizePerPartition)
      if (numItems == 0L) {
        Array.empty
      } else {
        // If a partition contains much more than the average number of items, we re-sample from it
        // to ensure that enough items are collected from that partition.
        val fraction = math.min(sampleSize / math.max(numItems, 1L), 1.0)
        val candidates = ArrayBuffer.empty[(K, Float)]
        val imbalancedPartitions = mutable.Set.empty[Int]
        sketched.foreach { case (idx, n, sample) =>
          if (fraction * n > sampleSizePerPartition) {
            imbalancedPartitions += idx
          } else {
            // The weight is 1 over the sampling probability.
            val weight = (n.toDouble / sample.size).toFloat
            for (key <- sample) {
              candidates += ((key, weight))
            }
          }
        }
        if (imbalancedPartitions.nonEmpty) {
          // Re-sample imbalanced partitions with the desired sampling probability.
          val imbalanced = new PartitionPruningRDD(rdd.map(_._1), imbalancedPartitions.contains)
          val seed = byteswap32(-rdd.id - 1)
          val reSampled = imbalanced.sample(withReplacement = false, fraction, seed).collect()
          val weight = (1.0 / fraction).toFloat
          candidates ++= reSampled.map(x => (x, weight))
        }
        RangePartitioner.determineBounds(candidates, partitions)
      }
    }
  }

  def numPartitions: Int = rangeBounds.length + 1

  private var binarySearch: ((Array[K], K) => Int) = CollectionsUtils.makeBinarySearch[K]

  def getPartition(key: Any): Int = {
    val k = key.asInstanceOf[K]
    var partition = 0
    if (rangeBounds.length <= 128) {
      // If we have less than 128 partitions naive search
      while (partition < rangeBounds.length && ordering.gt(k, rangeBounds(partition))) {
        partition += 1
      }
    } else {
      // Determine which binary search method to use only once.
      partition = binarySearch(rangeBounds, k)
      // binarySearch either returns the match location or -[insertion point]-1
      if (partition < 0) {
        partition = -partition-1
      }
      if (partition > rangeBounds.length) {
        partition = rangeBounds.length
      }
    }
    if (ascending) {
      partition
    } else {
      rangeBounds.length - partition
    }
  }

  override def equals(other: Any): Boolean = other match {
    case r: RangePartitioner[_, _] =>
      r.rangeBounds.sameElements(rangeBounds) && r.ascending == ascending
    case _ =>
      false
  }

  override def hashCode(): Int = {
    val prime = 31
    var result = 1
    var i = 0
    while (i < rangeBounds.length) {
      result = prime * result + rangeBounds(i).hashCode
      i += 1
    }
    result = prime * result + ascending.hashCode
    result
  }

  @throws(classOf[IOException])
  private def writeObject(out: ObjectOutputStream): Unit = Utils.tryOrIOException {
    val sfactory = SparkEnv.get.serializer
    sfactory match {
      case js: JavaSerializer => out.defaultWriteObject()
      case _ =>
        out.writeBoolean(ascending)
        out.writeObject(ordering)
        out.writeObject(binarySearch)

        val ser = sfactory.newInstance()
        Utils.serializeViaNestedStream(out, ser) { stream =>
          stream.writeObject(scala.reflect.classTag[Array[K]])
          stream.writeObject(rangeBounds)
        }
    }
  }

  @throws(classOf[IOException])
  private def readObject(in: ObjectInputStream): Unit = Utils.tryOrIOException {
    val sfactory = SparkEnv.get.serializer
    sfactory match {
      case js: JavaSerializer => in.defaultReadObject()
      case _ =>
        ascending = in.readBoolean()
        ordering = in.readObject().asInstanceOf[Ordering[K]]
        binarySearch = in.readObject().asInstanceOf[(Array[K], K) => Int]

        val ser = sfactory.newInstance()
        Utils.deserializeViaNestedStream(in, ser) { ds =>
          implicit val classTag = ds.readObject[ClassTag[Array[K]]]()
          rangeBounds = ds.readObject[Array[K]]()
        }
    }
  }
}

private[spark] object RangePartitioner {

  /**
   * Sketches the input RDD via reservoir sampling on each partition.
   *
   * @param rdd the input RDD to sketch
   * @param sampleSizePerPartition max sample size per partition
   * @return (total number of items, an array of (partitionId, number of items, sample))
   */
  def sketch[K : ClassTag](
      rdd: RDD[K],
      sampleSizePerPartition: Int): (Long, Array[(Int, Int, Array[K])]) = {
    val shift = rdd.id
    // val classTagK = classTag[K] // to avoid serializing the entire partitioner object
    val sketched = rdd.mapPartitionsWithIndex { (idx, iter) =>
      val seed = byteswap32(idx ^ (shift << 16))
      val (sample, n) = SamplingUtils.reservoirSampleAndCount(
        iter, sampleSizePerPartition, seed)
      Iterator((idx, n, sample))
    }.collect()
    val numItems = sketched.map(_._2.toLong).sum
    (numItems, sketched)
  }

  /**
   * Determines the bounds for range partitioning from candidates with weights indicating how many
   * items each represents. Usually this is 1 over the probability used to sample this candidate.
   *
   * @param candidates unordered candidates with weights
   * @param partitions number of partitions
   * @return selected bounds
   */
  def determineBounds[K : Ordering : ClassTag](
      candidates: ArrayBuffer[(K, Float)],
      partitions: Int): Array[K] = {
    val ordering = implicitly[Ordering[K]]
    val ordered = candidates.sortBy(_._1)
    val numCandidates = ordered.size
    val sumWeights = ordered.map(_._2.toDouble).sum
    val step = sumWeights / partitions
    var cumWeight = 0.0
    var target = step
    val bounds = ArrayBuffer.empty[K]
    var i = 0
    var j = 0
    var previousBound = Option.empty[K]
    while ((i < numCandidates) && (j < partitions - 1)) {
      val (key, weight) = ordered(i)
      cumWeight += weight
      if (cumWeight > target) {
        // Skip duplicate values.
        if (previousBound.isEmpty || ordering.gt(key, previousBound.get)) {
          bounds += key
          target += step
          j += 1
          previousBound = Some(key)
        }
      }
      i += 1
    }
    bounds.toArray
  }
}

 

 

 

 

 

参考 ：

http://blog.sina.com.cn/s/blog_4a7854d90102ws97.html

http://blog.csdn.net/duan_zhihua/article/details/50761582