<p>Given an <code>m x n</code> binary <code>matrix</code> filled with <code>0</code>&#39;s and <code>1</code>&#39;s, <em>find the largest square containing only</em> <code>1</code>&#39;s <em>and return its area</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/26/max1grid.jpg" style="width: 400px; height: 319px;" />
<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> 4
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/26/max2grid.jpg" style="width: 165px; height: 165px;" />
<pre>
<strong>Input:</strong> matrix = [[&quot;0&quot;,&quot;1&quot;],[&quot;1&quot;,&quot;0&quot;]]
<strong>Output:</strong> 1
</pre>

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

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

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

<ul>
	<li><code>m == matrix.length</code></li>
	<li><code>n == matrix[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 300</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 largestSquare(vector<int>& heights) {
        stack<int> st;
        int maxArea = 0;

        heights.push_back(0); // Add a zero height to flush out remaining elements in the stack.

        for (int i = 0; i < heights.size(); ++i) {
            while (!st.empty() && heights[i] < heights[st.top()]) {
                int height = heights[st.top()];
                st.pop();
                int width = st.empty() ? i : i - st.top() - 1;
                int side = min(height, width);
                maxArea = max(maxArea, side * side);
            }
            st.push(i);
        }

        return maxArea;
    }

    int maximalSquare(vector<vector<char>>& matrix) {
        if (matrix.empty())
            return 0;

        int maxArea = 0;
        int n = matrix.size();
        int m = matrix[0].size();

        vector<int> height(m, 0);

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                // Update the height of the histogram.
                if (matrix[i][j] == '1')
                    height[j]++;
                else
                    height[j] = 0;
            }
            // Calculate the largest square area for the current histogram.
            int area = largestSquare(height);
            maxArea = max(maxArea, area);
        }

        return maxArea;
    }
};

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