<p>The <strong>median</strong> 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 values.</p>

<ul>
	<li>For examples, if <code>arr = [2,<u>3</u>,4]</code>, the median is <code>3</code>.</li>
	<li>For examples, if <code>arr = [1,<u>2,3</u>,4]</code>, the median is <code>(2 + 3) / 2 = 2.5</code>.</li>
</ul>

<p>You are given an integer array <code>nums</code> and an integer <code>k</code>. There is a sliding window of size <code>k</code> which is moving from the very left of the array to the very right. You can only see the <code>k</code> numbers in the window. Each time the sliding window moves right by one position.</p>

<p>Return <em>the median array for each window in the original array</em>. Answers within <code>10<sup>-5</sup></code> of the actual value will be accepted.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,3,-1,-3,5,3,6,7], k = 3
<strong>Output:</strong> [1.00000,-1.00000,-1.00000,3.00000,5.00000,6.00000]
<strong>Explanation:</strong> 
Window position                Median
---------------                -----
[<strong>1  3  -1</strong>] -3  5  3  6  7        1
 1 [<strong>3  -1  -3</strong>] 5  3  6  7       -1
 1  3 [<strong>-1  -3  5</strong>] 3  6  7       -1
 1  3  -1 [<strong>-3  5  3</strong>] 6  7        3
 1  3  -1  -3 [<strong>5  3  6</strong>] 7        5
 1  3  -1  -3  5 [<strong>3  6  7</strong>]       6
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,3,4,2,3,1,4,2], k = 3
<strong>Output:</strong> [2.00000,3.00000,3.00000,3.00000,2.00000,3.00000,2.00000]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= k &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>-2<sup>31</sup> &lt;= nums[i] &lt;= 2<sup>31</sup> - 1</code></li>
</ul>

class Solution {
public:
    vector<double> medianSlidingWindow(vector<int>& nums, int k) {
        // 2 multiset - lower and upper
        vector<double> medians(nums.size()-k+1);
        if (k==1) {
            for (int i=0; i<nums.size(); i++) medians[i] = nums[i];
            return medians;
        }
        int m = k/2; 
        int n = k-m;
        multiset<int> lower;
        multiset<int> upper;
        vector<int> v(nums.begin(), nums.begin()+k);
        sort(v.begin(), v.end());
        for (int i=0; i<k; i++) {
            if (i<m) {
                lower.insert(v[i]);
            } else {
                upper.insert(v[i]);
            }
        }
        for (int i=0; i+k<=nums.size(); i++) {
            // cout << "i:" << i << ", lower:" << *prev(lower.end()) << ",upper:" << *upper.begin() << endl;
            double median = lower.size()==upper.size()? ((double)(*upper.begin()) + *prev(lower.end()))/2 : *upper.begin();
            medians[i] = median;
            if (i+k == nums.size()) break;
            // remove
            int to_remove = nums[i];
            int to_insert = nums[i+k];
            if (to_remove == to_insert) continue;
            if (to_insert >= *upper.begin()) {
                upper.insert(to_insert);
            } else {
                lower.insert(to_insert);
            }
            if (to_remove >= *upper.begin()) {
                auto it = upper.find(to_remove);
                upper.erase(it);
            } else {
                auto it = lower.find(to_remove);
                lower.erase(it);
            }
            // readjust
            while (lower.size() > upper.size()) {
                int to_move = *prev(lower.end());
                lower.erase(prev(lower.end()));
                upper.insert(to_move);
            }
            while (upper.size() > lower.size() + 1) {
                int to_move = *upper.begin();
                upper.erase(upper.begin());
                lower.insert(to_move);
            }
            // cout << "lower:";
            // for (auto num : lower) {
            //     cout << num << ",";
            // }
            // cout << endl;
            // cout << "upper:";
            // for (auto num : upper) {
            //     cout << num << ",";
            // }
            // cout << endl;
        }
        return medians;
    }
};
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