<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:
    // Function to calculate the largest rectangle area in a histogram
int largestRectangleArea(vector<int>& heights) {
    stack<int> st;
    int max_area = 0;
    int i = 0;

    while (i < heights.size()) {
        // Push current index to the stack if the stack is empty or the current height is greater than the height at the stack's top index
        if (st.empty() || heights[i] >= heights[st.top()]) {
            st.push(i++);
        } else {
            // Calculate area with the height of the bar at the top of the stack
            int h = heights[st.top()];
            st.pop();
            int width = st.empty() ? i : i - st.top() - 1;
            max_area = max(max_area, h * width);
        }
    }

    // Calculate area for remaining bars in the stack
    while (!st.empty()) {
        int h = heights[st.top()];
        st.pop();
        int width = st.empty() ? i : i - st.top() - 1;
        max_area = max(max_area, h * width);
    }

    return max_area;
}
    int maximalRectangle(vector<vector<char>>& matrix) {
        if (matrix.empty() || matrix[0].empty()) return 0;

    int rows = matrix.size();
    int cols = matrix[0].size();
    vector<int> height(cols, 0);  // Height array for histogram
    int max_area = 0;

    for (int i = 0; i < rows; ++i) {
        for (int j = 0; j < cols; ++j) {
            // Update the height of the histogram for each column
            height[j] = matrix[i][j] == '1' ? height[j] + 1 : 0;
        }

        // Calculate the maximum rectangle area for the histogram derived from the current row
        max_area = max(max_area, largestRectangleArea(height));
    }

    return max_area;
    }
};
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