<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 helper(vector<int>& height){
        stack<pair<int,int>> s;
        auto max_area = height[0] ? 1 : 0, start = 0;
        for (auto i = 0; i < height.size()-1; i++){
            if (height[i] <= height[i+1]) {
                s.push({height[i], start});
                start = i+1;
            }
            else {
                auto minim = min(i-start+1, height[i]);
                max_area = max(minim*minim, max_area);
                while (not s.empty() and s.top().first > height[i+1]){
                    auto [heights, front] = s.top();
                    s.pop();
                    minim = min(i-front+1, heights);
                    max_area = max(max_area, minim*minim);
                    start = front;
                }
            }
        }
        auto minim = min((int)height.size()-start, height[height.size()-1]);
        max_area = max(minim*minim, max_area);
        while (not s.empty()){
            auto [heights, front] = s.top();
            s.pop();
            minim = min((int)height.size()-front, heights);
            max_area = max(max_area, minim*minim);
        }
        return max_area;
    }
    int maximalSquare(vector<vector<char>>& matrix) {
        auto max_area = 0;
        vector<int> hist(matrix[0].size());
        for (auto i = 0; i < matrix.size(); i++){
            for (auto j = 0; j < matrix[0].size(); j++){
                if (matrix[i][j] == '1') hist[j]++;
                else hist[j] = 0;
            }
            max_area = max(max_area, helper(hist));
        }
        return max_area;
    }
};
28000