Github user jinxing64 commented on a diff in the pull request:

    https://github.com/apache/spark/pull/16867#discussion_r104344274
  
    --- Diff: 
core/src/main/scala/org/apache/spark/util/collection/MedianHeap.scala ---
    @@ -0,0 +1,94 @@
    +/*
    + * 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.util.collection
    +
    +import scala.collection.mutable
    +
    +/**
    + * MedianHeap stores numbers and returns the median by O(1) time 
complexity.
    + * The basic idea is to maintain two heaps: a maxHeap and a minHeap. The 
maxHeap stores
    + * the smaller half of all numbers while the minHeap stores the larger 
half.  The sizes
    + * of two heaps need to be balanced each time when a new number is 
inserted so that their
    + * sizes will not be different by more than 1. Therefore each time when 
findMedian() is
    + * called we check if two heaps have the same size. If they do, we should 
return the
    + * average of the two top values of heaps. Otherwise we return the top of 
the heap which
    + * has one more element.
    + */
    +
    +private[spark]
    +class MedianHeap(implicit val ord: Ordering[Double]) {
    +
    +  // Stores all the numbers less than the current median in a maxHeap,
    +  // i.e median is the maximum, at the root
    +  val maxHeap = 
mutable.PriorityQueue.empty[Double](implicitly[Ordering[Double]])
    +
    +  // Stores all the numbers greater than the current median in a minHeap,
    +  // i.e median is the minimum, at the root
    +  val minHeap = 
mutable.PriorityQueue.empty[Double](implicitly[Ordering[Double]].reverse)
    +
    +  // Returns if there is no element in MedianHeap.
    +  def isEmpty(): Boolean = {
    +    maxHeap.isEmpty && minHeap.isEmpty
    +  }
    +
    +  // Size of MedianHeap.
    +  def size(): Int = {
    +    maxHeap.size + minHeap.size
    +  }
    +
    +  // Insert a new number into MedianHeap.
    +  def insert(x: Double): Unit = {
    +    // If both heaps are empty, we arbitrarily insert it into a heap, 
let's say, the minHeap.
    +    if (isEmpty) {
    +      minHeap.enqueue(x)
    +    } else {
    +      // If the number is larger than current median, it should be 
inserted into minHeap,
    +      // otherwise maxHeap.
    +      if (x > findMedian) {
    +        minHeap.enqueue(x)
    +      } else {
    +        maxHeap.enqueue(x)
    +      }
    +    }
    +    rebalance()
    +  }
    +
    +  // Re-balance the heaps.
    +  private[this] def rebalance(): Unit = {
    +    if (minHeap.size - maxHeap.size > 1) {
    +      maxHeap.enqueue(minHeap.dequeue())
    +    }
    +    if (maxHeap.size - minHeap.size > 1) {
    +      minHeap.enqueue(maxHeap.dequeue)
    +    }
    +  }
    +
    +  // Returns the median of the numbers.
    +  def findMedian(): Double = {
    +    if (isEmpty) {
    +      throw new NoSuchElementException("MedianHeap is empty.")
    +    }
    +    if (minHeap.size == maxHeap.size) {
    +      (minHeap.head + maxHeap.head) / 2.0
    --- End diff --
    
    I think average value is the definition of 'median' when there are even 
numbers. Maybe it's better to keep it as `(minHeap.head + maxHeap.head) / 2.0` ?


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