<p>You are given an array of integers&nbsp;<code>nums</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 max sliding window</em>.</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> [3,3,5,5,6,7]
<strong>Explanation:</strong> 
Window position                Max
---------------               -----
[1  3  -1] -3  5  3  6  7       <strong>3</strong>
 1 [3  -1  -3] 5  3  6  7       <strong>3</strong>
 1  3 [-1  -3  5] 3  6  7      <strong> 5</strong>
 1  3  -1 [-3  5  3] 6  7       <strong>5</strong>
 1  3  -1  -3 [5  3  6] 7       <strong>6</strong>
 1  3  -1  -3  5 [3  6  7]      <strong>7</strong>
</pre>

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

<pre>
<strong>Input:</strong> nums = [1], k = 1
<strong>Output:</strong> [1]
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>-10<sup>4</sup> &lt;= nums[i] &lt;= 10<sup>4</sup></code></li>
	<li><code>1 &lt;= k &lt;= nums.length</code></li>
</ul>

class MaxHeap:
    def __init__(self) -> None:
        self.heap = []

    def size(self) -> int:
        return len(self.heap)

    def push(self, x: int) -> None:
        heapq.heappush(self.heap, -x)

    def pop(self) -> int:
        return -heapq.heappop(self.heap)

    def top(self) -> int:
        return -self.heap[0]


class Solution:
    def maxSlidingWindow(self, nums: List[int], k: int) -> List[int]:
        if k == 1:
            return nums
        ans = []
        tmp = nums[0]
        max_heap = MaxHeap()
        mydict = defaultdict(int)
        for i in range(k):
            tmp = max(tmp, nums[i])
            max_heap.push(nums[i])
            mydict[nums[i]] += 1
        ans.append(tmp)

        for i in range(1, len(nums) - k + 1):
            prev_max = ans[-1]
            mydict[nums[i-1]] -= 1

            if nums[i-1] == prev_max:
                while mydict[prev_max] == 0 and max_heap.size() > 1:
                    max_heap.pop()
                    prev_max = max_heap.top()
            if nums[i+k-1] > prev_max:
                ans.append(nums[i+k-1])
            else:
                ans.append(prev_max)
                
            max_heap.push(nums[i+k-1])
            mydict[nums[i+k-1]] += 1
        return ans


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