<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 largestRectangleArea(vector<int>& heights) {
        int n=heights.size();
        if(n==1) return heights[0];
        vector<int> ps(n),ns(n);
        stack<int> s,s1;
        for(int i=0;i<heights.size();i++){
            while(!s.empty() && heights[s.top()]>=heights[i]){
                s.pop();
            }
            if(s.empty()){
                s.push(i);
                ps[i]=-1;
                continue;
            }
            ps[i]=s.top();
            s.push(i);
        }
        for(int i=heights.size()-1;i>=0;i--){
            while(!s1.empty() && heights[s1.top()]>=heights[i]){
                s1.pop();
            }
            if(s1.empty()){
                s1.push(i);
                ns[i]=n;
                continue;
            }
            ns[i]=s1.top();
            s1.push(i);
        }
        int maxi=INT_MIN;
        for(int i=0;i<n;i++){
            maxi=max((ns[i]-ps[i]-1)*heights[i],maxi);
        }
        return maxi;
    }

    int maximalRectangle(vector<vector<char>>& matrix) {
        vector<int> v(matrix[0].size()); int maxi=INT_MIN;
        for(int i=0;i<matrix.size();i++){
            for(int j=0;j<matrix[i].size();j++){
                if(matrix[i][j]=='1')
                v[j]+=int(matrix[i][j])-48;
                else v[j]=0;
            }
            maxi=max(largestRectangleArea(v),maxi);
        }
        return maxi;
    }
};
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