<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 calculateMaxArea(vector<int> arr, int n) {
        int area = 0;
        vector<int> minleft(n), minright(n);
        stack<int> st;
        for (int i = 0; i < n; i++) {
            while (!st.empty() && arr[st.top()] >= arr[i]) {
                st.pop();
            }
            if (st.empty()) {
                minleft[i] = -1;
            } else {
                minleft[i] = st.top();
            }
            st.push(i);
        }
        st = stack<int>();
        for (int i = n - 1; i >= 0; i--) {
            while (!st.empty() && arr[st.top()] >= arr[i]) {
                st.pop();
            }
            if (st.empty()) {
                minright[i] = n;
            } else {
                minright[i] = st.top();
            }
            st.push(i);
        }
        for (int i = 0; i < n; i++) {
            int width = minright[i] - minleft[i] - 1;
            area = max(area, width * arr[i]);
        }
        return area;
    }

    int maximalRectangle(vector<vector<char>>& matrix) {
        int rows = matrix.size(), cols = matrix[0].size();
        if (rows == 0)
            return 0;
        vector<int> prefixArr;
        int area = 0;
        prefixArr.resize(cols, 0);
        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                prefixArr[j] = (matrix[i][j] == '0') ? 0 : prefixArr[j] + 1;
            }
            area = max(area, calculateMaxArea(prefixArr, cols));
        }
        return area;
    }
};
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