sliding window, keep the big value in the double sided queue to avoid rescan 

from collections import deque
class Solution(object):
    def maxSlidingWindow(self, nums, k):
        """
        :type nums: List[int]
        :type k: int
        :rtype: List[int]
        """
        dq=deque()
        max_numbers=[]
        
        for i in xrange(len(nums)):
            #delete all the values in the dequeue smaller than the new value 
            #therefore, the values in the dequeue is always in descending order 
            while dq and nums[i]>nums[dq[-1]]:
                dq.pop()
            #append the index of the new value
            dq.append(i)
            #if the dequeue include elements outside the window, delete it
            if i>=k and dq[0]<=i-k:
                dq.popleft()
            #when we have scanned at least k elements 
            #append the left most value in the dequeue
            if i>=k-1:
                max_numbers.append(nums[dq[0]])

    return max_numbers