<p>Given an array of integers <code>heights</code> representing the histogram&#39;s bar height where the width of each bar is <code>1</code>, return <em>the area of the largest rectangle in the histogram</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/01/04/histogram.jpg" style="width: 522px; height: 242px;" />
<pre>
<strong>Input:</strong> heights = [2,1,5,6,2,3]
<strong>Output:</strong> 10
<strong>Explanation:</strong> The above is a histogram where width of each bar is 1.
The largest rectangle is shown in the red area, which has an area = 10 units.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/01/04/histogram-1.jpg" style="width: 202px; height: 362px;" />
<pre>
<strong>Input:</strong> heights = [2,4]
<strong>Output:</strong> 4
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= heights.length &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= heights[i] &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution {
public:


    int largestRectangleArea(vector<int>& heights) {
         vector<int>v1(heights.size() , heights.size());
         stack<pair<int , int> > s ; 
       for (int i = heights.size()-1 ; i >= 0 ; i--)
       {  
          while( !s.empty() && heights[i] <= s.top().first)
          {
            s.pop();
          }
          if(  !s.empty() && s.top().first < heights[i])
          {

            v1[i] = s.top().second;

          }
       
          s.push({heights[i] , i });
       }

       stack<pair<int , int> > s1 ; 
       vector<int>v2( heights.size() , -1) ;
       for ( int i = 0 ; i < heights.size() ; i++)
       { 
          while( !s1.empty() && heights[i] <= s1.top().first)
          {
            s1.pop();
          }
          if( !s1.empty() && s1.top().first < heights[i])
          {
             v2[i] = s1.top().second; 
        
          } 
          
            s1.push({heights[i] , i });
       }

        vector<int> v ; 
        for( int i = 0 ; i < heights.size() ; i++)
        {   int NSL = v2[i]; 

             int NSR = v1[i]; 
             int area = (NSR-NSL-1)* heights[i];
             v.push_back(area);
             
        }

    return *max_element(v.begin() , v.end());

    
    }
};
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