<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 {
private:
    int getMaxRectangle(vector<int> &heights) {
        stack<int> st;
        int size = heights.size();
        int maxRectangle = 0;
        
        for (int i=0; i<=size; i++) {
            // cout<<heights[i]<<" ";
            while (st.size() && (i == size || heights[i] < heights[st.top()])) {
                int index = st.top();
                st.pop();
                if (st.empty()) {
                    maxRectangle = max(maxRectangle, min(heights[index]*heights[index], i*i));
                }
                else {
                    maxRectangle = max(maxRectangle, min(heights[index]*heights[index], 
                                                         (i-st.top()-1)*(i-st.top()-1)));
                }
            }
            st.push(i);
        }
        return maxRectangle;
    }

    int maximalRectangle(vector<vector<char>>& matrix) {
        int m = matrix.size();
        int n = matrix[0].size();
        
        vector<int> heights(n, 0);
        int maxRectangle = 0;
        for (int i=0; i<m; i++) {
            for (int j=0; j<n; j++) {
                if (matrix[i][j] == '0') {
                    heights[j] = 0;
                }
                else {
                    heights[j]++;
                }
            }
            maxRectangle = max(maxRectangle, getMaxRectangle(heights));
        }
        
        return maxRectangle;
    }

public:
    int maximalSquare(vector<vector<char>>& matrix) {
        return maximalRectangle(matrix);
    }
};
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