<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:
    void nextSmallerElement(vector<int>arr,vector<int>& nse,stack<int>st){
        int n = arr.size();
        for(int i=n-1;i>=0;i--){
            while(!st.empty() && arr[i]<=arr[st.top()])
                st.pop();
            if(!st.empty())
                nse[i]=st.top();
            st.push(i);
        }
    }
    void prevSmallerElement(vector<int>arr, vector<int>& pse,int n,stack<int>st){
        for(int i=0;i<n;i++){
            while(!st.empty() && arr[i]<=arr[st.top()])
                st.pop();
            if(!st.empty())
                pse[i] = st.top();
            st.push(i);
        }
    }

    int largestRectangleArea(vector<int>& heights) {
        int n = heights.size();
        vector<int>nse(n,n);
        vector<int>pse(n,-1);
        stack<int>st;
        nextSmallerElement(heights,nse,st);
        prevSmallerElement(heights,pse,n,st);
        int maxi =0;
        for(int i=0;i<n;i++){
            // cout<<nse[i]<<endl;
            // cout<<"pse"<<pse[i]<<endl;
            maxi = max(maxi,heights[i]*(nse[i]-pse[i]-1));
        }

        return maxi;

    }
};
90943