480. Sliding Window Median

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
Given an array nums, there is a sliding window of size k which is moving from the very left of the array to the very right. You can only see the k numbers in the window. Each time the sliding window moves right by one position. Your job is to output the median array for each window in the original array.
For example,
Given nums = [1,3,-1,-3,5,3,6,7], and k = 3.
Window position                Median
---------------               -----
[1  3  -1] -3  5  3  6  7       1
 1 [3  -1  -3] 5  3  6  7       -1
 1  3 [-1  -3  5] 3  6  7       -1
 1  3  -1 [-3  5  3] 6  7       3
 1  3  -1  -3 [5  3  6] 7       5
 1  3  -1  -3  5 [3  6  7]      6
Therefore, return the median sliding window as [1,-1,-1,3,5,6].
Note: 
You may assume k is always valid, ie: k is always smaller than input array's size for non-empty array.


https://leetcode.com/problems/sliding-window-median/discuss/96348/Java-solution-using-two-PriorityQueues

Almost the same idea of Find Median from Data Stream https://leetcode.com/problems/find-median-from-data-stream/

1. Use two Heaps to store numbers. maxHeap for numbers smaller than current median, minHeap for numbers bigger than and equal to current median. A small trick I used is always make size of minHeap equal (when there are even numbers) or 1 element more (when there are odd numbers) than the size of maxHeap. Then it will become very easy to calculate current median.
2. Keep adding number from the right side of the sliding window and remove number from left side of the sliding window. And keep adding current median to the result.