<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:
vector<int> getNSR(vector<int>& height){
    int n=height.size();
    vector<int> NSR(n);
    stack<int>st;
    for(int i=n-1; i>=0; i--){
        if(st.empty()) NSR[i]=n;

        else{
            while(!st.empty() && height[st.top()]>=height[i]){
                st.pop();
            }
            if(st.empty()) NSR[i]=n;
            else{
                NSR[i]=st.top();
            }
        }
        st.push(i);
    }
    return NSR;
}
vector<int> getNSL(vector<int>& height){
    int n=height.size();
    stack<int>st;
    vector<int>NSL(n);
    for(int i=0; i<n; i++){
        if(st.empty()) NSL[i]=-1;

        else{
            while(!st.empty() && height[st.top()]>=height[i]){
                st.pop();
            }
            if(st.empty()) NSL[i]=-1;
            else{
                NSL[i]=st.top();
            }
        }
        st.push(i);
    }
    return NSL;
}
int findmaxarea(vector<int> height){
    vector<int>NSR=getNSR(height);
    vector<int>NSL=getNSL(height);

    int n=height.size();
    vector<int>width(n);
    for(int i=0; i<n; i++){
        width[i]=NSR[i]-NSL[i]-1;
    }
    int Maxarea=0;
    for(int i=0; i<n; i++){
        int a=width[i]*height[i];
        Maxarea=max(Maxarea,a);
    }
    return Maxarea;
}
    int maximalRectangle(vector<vector<char>>& matrix) {
        int m=matrix.size();
        int n=matrix[0].size();

        vector<int>height(n);

        for(int i=0; i<n; i++){
            height[i]=(matrix[0][i]=='1') ? 1 : 0;
        }

        int Maxarea=findmaxarea(height);

        for(int row=1; row<m; row++){
            for(int col=0; col<n; col++){
                if(matrix[row][col]=='0'){
                    height[col]=0;
                }
                else{
                    height[col]+=1;
                }
            }
            Maxarea=max(Maxarea,findmaxarea(height));
        }
        return Maxarea; 
    }
};
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