Sliding_Window_Maximum.cpp

class Solution {
public:
   vector<int> maxSlidingWindow(vector<int>& nums, int k) {
       deque<int> queue;
       vector<int> ans;
       for (int left = 0; left < nums.size(); ++left) {
           // As the window move on, element nums[left-k] will be outdated.
           if (queue.front() == left - k) queue.pop_front();
           // Now we are ready to push our new element nums[left]'s index into the queue.
           // But before that, we should clear elements which is smaller then nums[left].
           // Why? Because if nums[left] is bigger then nums[i], 
           // there will be no way for nums[i] be selected as the max number in range (left-k, left]
           while (!queue.empty() && nums[queue.back()] < nums[left]) queue.pop_back();
           // Now push the index into our queue.
           queue.push_back(left);
           // Okay, now nums[queue.front()] mush be the max number in range (left-k, left] 
           if (left - k + 1 >= 0) ans.push_back(nums[queue.front()]);
       }
       return ans;
   }
};