<p>Given an array of integers <code>nums</code> and an integer <code>limit</code>, return the size of the longest <strong>non-empty</strong> subarray such that the absolute difference between any two elements of this subarray is less than or equal to <code>limit</code><em>.</em></p>

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

<pre>
<strong>Input:</strong> nums = [8,2,4,7], limit = 4
<strong>Output:</strong> 2 
<strong>Explanation:</strong> All subarrays are: 
[8] with maximum absolute diff |8-8| = 0 &lt;= 4.
[8,2] with maximum absolute diff |8-2| = 6 &gt; 4. 
[8,2,4] with maximum absolute diff |8-2| = 6 &gt; 4.
[8,2,4,7] with maximum absolute diff |8-2| = 6 &gt; 4.
[2] with maximum absolute diff |2-2| = 0 &lt;= 4.
[2,4] with maximum absolute diff |2-4| = 2 &lt;= 4.
[2,4,7] with maximum absolute diff |2-7| = 5 &gt; 4.
[4] with maximum absolute diff |4-4| = 0 &lt;= 4.
[4,7] with maximum absolute diff |4-7| = 3 &lt;= 4.
[7] with maximum absolute diff |7-7| = 0 &lt;= 4. 
Therefore, the size of the longest subarray is 2.
</pre>

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

<pre>
<strong>Input:</strong> nums = [10,1,2,4,7,2], limit = 5
<strong>Output:</strong> 4 
<strong>Explanation:</strong> The subarray [2,4,7,2] is the longest since the maximum absolute diff is |2-7| = 5 &lt;= 5.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [4,2,2,2,4,4,2,2], limit = 0
<strong>Output:</strong> 3
</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>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>
	<li><code>0 &lt;= limit &lt;= 10<sup>9</sup></code></li>
</ul>

class Solution {
public:
    struct monotone_deque {
        deque<int> dq;
        bool _mini;

        monotone_deque(bool mini) : _mini(mini) {}

        void insert(int x) {
            if (_mini) {
                while (!dq.empty() && dq.back() > x) {
                    dq.pop_back();
                }
                dq.push_back(x);
            } else {
                while (!dq.empty() && dq.back() < x) {
                    dq.pop_back();
                }
                dq.push_back(x);
            }
        }

        void erase(int x) {
            if (!dq.empty() && dq.front() == x) {
                dq.pop_front();
            }
        }

        int get() const {
            return dq.front();
        }
    };

    int longestSubarray(vector<int>& nums, int limit) {
        int n = nums.size();
        int maxLength = 0;
        int left = 0;
        int right = 0;

        monotone_deque minim(true);   // Monotone deque for minimum
        monotone_deque maxim(false);  // Monotone deque for maximum

        while (right < n) {
            // Expand the window by including nums[right]
            minim.insert(nums[right]);
            maxim.insert(nums[right]);

            // Check if the window is valid
            while (maxim.get() - minim.get() > limit) {
                // If the window is invalid, move the left pointer
                minim.erase(nums[left]);
                maxim.erase(nums[left]);
                ++left;
            }

            // Update the maximum length of the valid subarray
            maxLength = max(maxLength, right - left + 1);

            // Move the right pointer to expand the window
            ++right;
        }

        return maxLength;
    }
};

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