<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> nextsmall(vector<int> v, int n){

    stack<int> s;
    s.push(-1);
    vector<int>ans(n);

    for(int j=n-1;j>=0;j--){
        //int num=v[j];
        while(s.top() != -1 && v[s.top()] >= v[j]){
            s.pop();
        }

        ans[j]=s.top();
        s.push(j); // puting index...
    }

    return ans;

}

vector<int> prevsmall(vector<int> v, int n){

    stack<int> s;
    s.push(-1);
    vector<int>ans(n);

    for(int j=0;j<n ;j++){
        int num=v[j];
        while(s.top() != -1 && v[s.top()] > v[j]){
            s.pop();
        }

        ans[j]=s.top();
        s.push(j); // puting index...
    }

    return ans;

}

// finding largest area in given vector... largest area in histogram
int largestarea(vector<int>v , int n){

    vector<int> next(n) ;
      next= nextsmall(v,n); // function call...
    vector<int> prev(n) ;
      prev= prevsmall(v,n); // function call...

    int length;
    int bredth;
    int area;
    int maxx=INT_MIN;

    for(int i=0;i<n;i++){
        length=v[i];

        if(next[i] == -1){
            next[i] = n;
        }
        int bredth=next[i] - prev[i] - 1;

        area=length*bredth;
        maxx=max(area,maxx);
    }
    return maxx; // returning max area from perticula row...
}


    int maximalRectangle(vector<vector<char>>& matrix) {


         int col=matrix[0].size();
         int row=matrix.size();

        vector<int> v(col,0); // initializing vector of column size...
        int maxx=INT_MIN;
        int area;

        for(int i=0;i<row;i++){
            // for each row... changing the vector v...
            for(int j=0;j<col;j++){
                if(matrix[i][j] == '0'){
                    v[j]=0;
                }
                else{
                    //v[j]=v[j]+matrix[i][j];
                    v[j]++;
                }
            }

            area=largestarea(v,col); // function call
            maxx=max(area,maxx);
        }

       return maxx;

    }
};
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