LeetCode295 从数据流中寻找中位数

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.

For example,
[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.

Example:

addNum(1)
addNum(2)
findMedian() -> 1.5
addNum(3)
findMedian() -> 2

Follow up:

If all integer numbers from the stream are between 0 and 100, how would you optimize it?
If 99% of all integer numbers from the stream are between 0 and 100, how would you optimize it?
设置一个大顶堆，一个小顶堆。大顶堆存放一半比较小的数，小顶堆存放一半比较大的数。使得大顶堆的size比小顶堆多1或者相等。

class MedianFinder {
    PriorityQueue maxHeap;
    PriorityQueue minHeap;
    /** initialize your data structure here. */
    public MedianFinder() {
        this.minHeap = new PriorityQueue();
        this.maxHeap = new PriorityQueue(Collections.reverseOrder());
    }
    
    public void addNum(int num) {
        maxHeap.add(num);
        minHeap.add(maxHeap.poll());
        if(maxHeap.size() < minHeap.size()){
            maxHeap.add(minHeap.poll());
        }
    }
    
    public double findMedian() {
        if(maxHeap.size() == minHeap.size()) return 0.5 * (maxHeap.peek() + minHeap.peek());
        return maxHeap.peek();
    }
}