<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 {
    private:

    vector<int>NSL(vector<int>&heights,int &n){
    stack<pair<int,int>>s;
     vector<int>li;
    for(int i=0;i<n;i++){
        int pi=-1;
       
        if(s.size()==0) li.push_back(pi);
        else if(s.size()>0 && s.top().first<heights[i]) li.push_back(s.top().second);
        else if(s.size()>0 && s.top().first>=heights[i]){
            while(s.size()>0 && s.top().first>=heights[i]){
                s.pop();
            }
            if(s.size()==0) li.push_back(pi);
            else li.push_back(s.top().second);
        }
        s.push({heights[i],i});
    }
    return li;
   }
   
   vector<int>NSR(vector<int>&heights,int &n){
    stack<pair<int,int>>s;
    vector<int>Ri;
    for(int i=heights.size()-1;i>=0;i--){
        int pi=n;
        
        if(s.size()==0) Ri.push_back(pi);
        else if(s.size()>0 && s.top().first<heights[i]) Ri.push_back(s.top().second);
        else if(s.size()>0 && s.top().first>=heights[i]){
            while(s.size()>0 && s.top().first>=heights[i]){
                s.pop();
            }
            if(s.size()==0) Ri.push_back(pi);
            else Ri.push_back(s.top().second);
        }
        s.push({heights[i],i});
    }
    reverse(Ri.begin(),Ri.end());
    return Ri;
   }

public:
   
    int largestRectangleArea(vector<int>& heights) {
        vector<int>li;
        vector<int>Ri;
      int n=heights.size();
      li=NSL(heights,n);
      Ri=NSR(heights,n);
      int width[n],area[n];
      for(int i=0;i<n;i++){
        width[i]=Ri[i]-li[i]-1;
        area[i]=width[i]*heights[i];
      }
     int MAH= *max_element(area,area+n);
     return MAH;
    }
};
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