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].

主要思路：维护一个大小为k的集合，并且在插入和删除的时候都调整mid的位置，使之最后仍能指向k/2的位置。

1 class Solution { 2 public: 3     vector
     
       medianSlidingWindow(vector
      
       & nums, int k) { 4         multiset
       
        window(nums.begin(),nums.begin()+k); 5         auto mid=next(window.begin(),k/2); 6         vector
        
         ans; 7         for(int i=k;;i++){ 8             ans.push_back((double(*mid)+*next(mid,k%2-1))/2); 9             if(i==nums.size())return ans; 10             window.insert(nums[i]);11             if(nums[i]<*mid)mid--;//add12             13             if(nums[i-k]<=*mid)mid++;//before delete14             window.erase(window.lower_bound(nums[i-k]));15         }16     }17 };