<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>& arr) {
        int n = arr.size();
        stack<int>st;
        int nsi[n];
        nsi[n-1] = n;
        st.push(n-1);
        for(int i = n-2 ; i>=0 ; i-- ){
            while(st.size()>0 && arr[st.top()]>=arr[i]){
                st.pop();
            }
            if(st.size()==0){
                nsi[i] = n;
            }
            else{
                nsi[i] = st.top();
            }
            st.push(i);
        }

        stack<int>gt;
        int psi[n];
        psi[0] = -1;
        gt.push(0);
        for(int i = 1 ;i<n ; i++){
            while(gt.size()>0 && arr[gt.top()]>=arr[i]){
           gt.pop();
            }
           if(gt.size()==0)
            psi[i] = -1;
            else{
                psi[i] = gt.top();

            }
         gt.push(i);
           }


           int maxarea = 0;
           for(int i = 0 ; i<n ; i++){
            int height = arr[i];
            int breadth = nsi[i] - psi[i] -1;
            int area = height*breadth;
            maxarea = max(maxarea,area);
           }
           return maxarea;
        
    }
};
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