題目連結：劍指 Offer 41. 資料流中的中位數

思路：極大堆、極小堆。因為輸入是資料流不是陣列，說明輸入的資料是不確定的。一般來說先排序，然後返回中間數，但每查詢一次就要排序，時間複雜度較高。所以想能不能每次查詢都可以直接獲取到中間數，而不是對輸入的資料排序取中間數。那麼，我們就把輸入的資料分為兩堆，每次輸入資料都只會進入兩個堆中的一個，而兩個堆的中間分界線就是中位數。

程式碼：

class MedianFinder {
    PriorityQueue<Integer> maxHeap, minHeap;

    /** initialize your data structure here. 
 
*/
    public MedianFinder() {
        maxHeap = new PriorityQueue<>((a, b) -> b - a);
        minHeap = new PriorityQueue<>((a, b) -> a - b);
    }
    
    public void addNum(int num) {
        if(maxHeap.isEmpty()){
            maxHeap.offer(num);
            return ;
        }
        
 
if(num <= maxHeap.peek()){
            maxHeap.offer(num);
        }else{
            minHeap.offer(num);
        }
        this.adjust();
    }
    
    public double findMedian() {
        return maxHeap.size()==minHeap.size()?(double)(maxHeap.peek()+minHeap.peek())/2:maxHeap.size() > minHeap.size()?maxHeap.peek():minHeap.peek();
    }

    
 
private void adjust(){
        if(maxHeap.size() - minHeap.size() < 2 && maxHeap.size() - minHeap.size() > -2){
            return ;
        }
        if(maxHeap.size() - minHeap.size() >= 2){
            minHeap.offer(maxHeap.poll());
        }
        if(maxHeap.size() - minHeap.size() <= -2){
            maxHeap.offer(minHeap.poll());
        }
    }
}

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