<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> nextSmallerElement(vector<int> arr,int n){

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

        for(int i=n-1;i>=0;i--){
            int curr=arr[i];

            while(s.top() != -1 && arr[s.top()] >= curr){
                s.pop();
            }

            ans[i]=s.top();
            s.push(i);
        }
        return ans;
    }

    vector<int> prevSmallerElement(vector<int> arr,int n){

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

        for(int i=0;i<n;i++){
            int curr=arr[i];

            while(s.top() != -1 && arr[s.top()] >= curr){
                s.pop();
            }

            ans[i]=s.top();
            s.push(i);
        }

        return ans;
    }

    int largestRectangleArea(vector<int>& heights) {

        int n=heights.size();

        vector<int> next(n);
        next=nextSmallerElement(heights,n);

        vector<int> prev(n);
        prev=prevSmallerElement(heights,n);

        int area = INT_MIN;

        for(int i=0;i<n;i++){
            int l=heights[i];

            if(next[i]==-1)
                next[i]=n;

            int b=next[i]-prev[i]-1;
            int newArea=l*b;
            area=max(area,newArea);
        }
       
       return area;
    }

    int maximalRectangle(vector<vector<char>>& matrix) 
    {
        int maxi = INT_MIN;

        vector<int> histogram(matrix[0].size(),0);

        for(int i=0;i<matrix.size();i++){
            //to create histogram array'
            for(int j=0;j<histogram.size();j++){

                if(matrix[i][j] == '1')
                    histogram[j]++;
                else
                    histogram[j] = 0;
            }

            maxi = max(maxi,largestRectangleArea(histogram));
        }

        return maxi;
    }
};
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