<p>Given a <code>rows x cols</code>&nbsp;binary <code>matrix</code> filled with <code>0</code>&#39;s and <code>1</code>&#39;s, find the largest rectangle containing only <code>1</code>&#39;s and return <em>its area</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/09/14/maximal.jpg" style="width: 402px; height: 322px;" />
<pre>
<strong>Input:</strong> matrix = [[&quot;1&quot;,&quot;0&quot;,&quot;1&quot;,&quot;0&quot;,&quot;0&quot;],[&quot;1&quot;,&quot;0&quot;,&quot;1&quot;,&quot;1&quot;,&quot;1&quot;],[&quot;1&quot;,&quot;1&quot;,&quot;1&quot;,&quot;1&quot;,&quot;1&quot;],[&quot;1&quot;,&quot;0&quot;,&quot;0&quot;,&quot;1&quot;,&quot;0&quot;]]
<strong>Output:</strong> 6
<strong>Explanation:</strong> The maximal rectangle is shown in the above picture.
</pre>

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

<pre>
<strong>Input:</strong> matrix = [[&quot;0&quot;]]
<strong>Output:</strong> 0
</pre>

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

<pre>
<strong>Input:</strong> matrix = [[&quot;1&quot;]]
<strong>Output:</strong> 1
</pre>

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

<ul>
	<li><code>rows == matrix.length</code></li>
	<li><code>cols == matrix[i].length</code></li>
	<li><code>1 &lt;= row, cols &lt;= 200</code></li>
	<li><code>matrix[i][j]</code> is <code>&#39;0&#39;</code> or <code>&#39;1&#39;</code>.</li>
</ul>

class Solution {
public:
    int maximalRectangle(vector<vector<char>>& matrix) {
        int rows = matrix.size();
        int cols = matrix[0].size();
        int max = 0;
        vector<int> height(cols);
        vector<int> left(cols);
        vector<int> right(cols);
        int pos = 0;
        for (int i = 0; i < cols; ++i)
            if (matrix[0][i] == '1')
            {
                height[i] = 1;
                ++pos;
                if (max < pos)
                    max = pos;
            }
            else
            {
                height[i] = 0;
                pos = 0;
            }
        for (int i = 1; i < rows; ++i)
        {
            for (int j = 0; j < cols; ++j)
            {
                if (matrix[i][j] == '1')
                    height[j] = height[j] + 1;
                else
                    height[j] = 0;
                for (pos = j - 1; pos >= 0 && height[pos] >= height[j]; pos = left[pos]);
                left[j] = pos;
            }
            for (int j = cols - 1; j >= 0; --j)
            {
                for (pos = j + 1; pos < cols && height[pos] >= height[j]; pos = right[pos]);
                right[j] = pos;
            }
            for (int j = 0; j < cols; ++j)
                if (max < height[j] * (right[j] - left[j] - 1))
                    max = height[j] * (right[j] - left[j] - 1);
        }
        return max;
    }
};
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