Find Median from Data Stream

Numbers keep coming, return the median of numbers at every time a new number added.

Example

Example 1

Input: [1,2,3,4,5]
Output: [1,1,2,2,3]
Explanation:
The medium of [1] and [1,2] is 1.
The medium of [1,2,3] and [1,2,3,4] is 2.
The medium of [1,2,3,4,5] is 3.
           

Example 2

Input: [4,5,1,3,2,6,0]
Output: [4,4,4,3,3,3,3]
Explanation:
The medium of [4], [4,5], [4,5,1] is 4.
The medium of [4,5,1,3], [4,5,1,3,2], [4,5,1,3,2,6] and [4,5,1,3,2,6,0] is 3.
           

Challenge

Total run time in O(nlogn).

Clarification

What's the definition of Median?

• The 

  median

   is not equal to 

  median

   in math.
• Median is the number that in the middle of a sorted array. If there are n numbers in a sorted array A, the median is A[(n - 1) / 2]A[(n−1)/2].
• For example, if 

  A=[1,2,3]

  , median is 

  2

  . If 

  A=[1,19]

  , median is 

  1

  .

思路：用兩個堆來維持關系，左邊用最大堆，右邊用最小堆，如果num[i] 比最大堆的堆頂小，加入最大堆，否則加入最小堆，然後再調整數目，始終保證最大堆比最小堆數目相等，或者隻大于1；

class MedianFinder {

    private PriorityQueue<Integer> maxheap;
    private PriorityQueue<Integer> minheap;
    /** initialize your data structure here. */
    public MedianFinder() {
        maxheap = new PriorityQueue<Integer>((a, b) -> (b - a));
        minheap = new PriorityQueue<Integer>();
    }
    
    public void addNum(int num) {
        if(maxheap.isEmpty() || num < maxheap.peek()) {
            maxheap.add(num);
        } else {
            minheap.add(num);
        }
        balance();
    }
    
    private void balance() {
        while(maxheap.size() < minheap.size()) {
            maxheap.add(minheap.poll());
        }
        while(minheap.size() < maxheap.size() - 1) {
            minheap.add(maxheap.poll());
        }
    }
    
    public double findMedian() {
        if(maxheap.size() == minheap.size()) {
            return 0.5 * ((double)maxheap.peek() + (double)minheap.peek());
        } else {
            return (double)maxheap.peek();
        }
    }
}

/**
 * Your MedianFinder object will be instantiated and called as such:
 * MedianFinder obj = new MedianFinder();
 * obj.addNum(num);
 * double param_2 = obj.findMedian();
 */