<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> nextelement(vector<int>& heights, int n )
{
    stack<int>st;
    st.push(-1);
    vector<int>ans(n);
    for(int i =n-1;i>=0;i--)
    {
        int curr= heights[i];
        while(st.top()!=-1 && heights[st.top()]>=curr)
        {
            st.pop();
        }
    ans[i]=st.top();
    st.push(i);
    }
    return ans;
}

vector<int> prevelement(vector<int>& heights, int n )
{
    stack<int>st;
    st.push(-1);
    vector<int>ans(n);
    for(int i =0;i<n;i++)
    {
        int curr= heights[i];
        while(st.top()!=-1 && heights[st.top()]>=curr)
        {
            st.pop();
        }
    ans[i]=st.top();
    st.push(i);
    }
    return ans;
}
public:
    int largestRectangleArea(vector<int>& heights) {
       int n =heights.size();
       int area= INT_MIN;

       vector<int>next(n);
       vector<int>prev(n);

       next=nextelement(heights,n); 
       prev=prevelement(heights,n); 

       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;
    }
};
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