<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 maxAreaInHistogram(vector<int> &heights)\
    {
        int n = heights.size();
        stack<int> st;
        int maxArea = 0;
        for(int i=0;i<n;i++){
            while(!st.empty() && heights[i]<heights[st.top()]){
                int index = st.top();st.pop();
                if(!st.empty()){
                    maxArea = max(maxArea,heights[index]*(i-st.top()-1));
                }
                else
                {
                    maxArea = max(maxArea,heights[index]*(i));
                }
            }
            st.push(i);
        }
        while(!st.empty()) {
               int index = st.top();st.pop();
                if(!st.empty()){
                    maxArea = max(maxArea,heights[index]*(n-st.top()-1));
                }
                else
                {
                    maxArea = max(maxArea,heights[index]*(n));
                }
        }
        return maxArea;

    }
    int maximalRectangle(vector<vector<char>>& matrix) {
       int n = matrix.size();
       int m = matrix[0].size();
       vector<int> h(m,0);
       int maxArea = 0;
       for(int i=0;i<n;i++){
        for(int j=0;j<m;j++){
            if(matrix[i][j]!='0')
               h[j]+=1;
            else 
               h[j]=0;
        }
        maxArea = max(maxArea,maxAreaInHistogram(h));
       }
       return maxArea;
    }
};

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