monotone queue intuition code example

Example: monotonic deque

deque<int> dq;
vector<int> ans;
for (int i=0; i<nums.size(); i++) {
if (!dq.empty() && dq.front() == i-k) dq.pop_front();
while (!dq.empty() && nums[dq.back()] < nums[i])
dq.pop_back();
dq.push_back(i);
if (i>=k-1) ans.push_back(nums[dq.front()]);
}