FindMedianFromDataStream.java

package com.stevesun.solutions;

import java.util.*;

/**
 * Median is the middle value in an ordered integer list. If the size of the list is even, there is no middle value. So the median is the mean of the two middle value.

 Examples:
 [2,3,4] , the median is 3

 [2,3], the median is (2 + 3) / 2 = 2.5

 Design a data structure that supports the following two operations:

 void addNum(int num) - Add a integer number from the data stream to the data structure.
 double findMedian() - Return the median of all elements so far.
 For example:

 addNum(1)
 addNum(2)
 findMedian() -> 1.5
 addNum(3)
 findMedian() -> 2
 */
public class FindMedianFromDataStream {
}

class MedianFinder {
    //Thanks to Stefan's post: https://discuss.leetcode.com/topic/27521/short-simple-java-c-python-o-log-n-o-1
    /**
     * The idea is for sure to use two heaps, one is max heap, one is min heap, we always let the max heap be one element
     * bigger than min heap if the total number of elements is not even.
     * we could always get the median in O(1) time.
     * 1. use Long type to avoid overflow
     * 2. negate the numbers for small heap to save the effort for writing a reverse comparator, brilliant!*/
    private Queue<Long> large = new PriorityQueue<Long>();
    private Queue<Long> small = new PriorityQueue<Long>();

    // Adds a number into the data structure.
    public void addNum(int num) {
        large.offer((long) num);
        small.offer(-large.poll());
        if(large.size() < small.size()) large.offer(-small.poll());
    }

    // Returns the median of current data stream
    public double findMedian() {
        if(large.size() > small.size()) return large.peek();
        return (large.peek()-small.peek())/2.0;
    }

};

// Your MedianFinder object will be instantiated and called as such:
// MedianFinder mf = new MedianFinder();
// mf.addNum(1);
// mf.findMedian();