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

一刷
題解：
構造一個maxHeap, minHeap,
maxHeap與minHeap的size相同或者大1
maxHeap里面的值都小于minHeap

class MedianFinder {
    
    private Queue<Integer> maxHeap;
    private Queue<Integer> minHeap;

    /** initialize your data structure here. */
    public MedianFinder() {
        maxHeap = new PriorityQueue<Integer>(10, Collections.reverseOrder());
        minHeap = new PriorityQueue<Integer>(); 
        //maxHeap size == minHeap size (+1)
    }
    
    public void addNum(int num) {
        if(maxHeap.size() == minHeap.size()){
            if(!minHeap.isEmpty() && minHeap.peek()<num){
                maxHeap.offer(minHeap.poll());
                minHeap.offer(num);
            }else{
                maxHeap.offer(num);
            }
        }else{
           if(num<maxHeap.peek()){
               minHeap.offer(maxHeap.poll());
               maxHeap.offer(num);
           }else{
               minHeap.offer(num);
           }
        }
    }
    
    public double findMedian() {
        if(minHeap.size() == maxHeap.size()) {
            double a = maxHeap.peek();
            double b = minHeap.peek();
            return (a + b)/2;
        }
        else return maxHeap.peek();
    }
}

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