<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:
    vector<int> findPSE(vector<int> heights){
        vector<int> ans;
        stack<int> st;
        for(int i=0;i<heights.size();i++){
            while(!st.empty() && heights[st.top()]>=heights[i]){
                st.pop();
            }
            if(st.empty())
            {
                ans.push_back(-1);
            }
            else{
                ans.push_back(st.top());
            }
            st.push(i);


        }
        return ans;
    }
    vector<int> findNSE(vector<int> heights){
        vector<int> ans(heights.size(),0);
        stack<int> st;
        for(int i=heights.size()-1;i>=0;i--){
            while(!st.empty() && heights[st.top()]>=heights[i]){
                st.pop();
            }
            if(st.empty())
            {
                ans[i]=(heights.size());
            }
            else{
                ans[i]=(st.top());
            }
            st.push(i);


        }
        return ans;
    }
    int largestRectangleArea(vector<int>& heights) {
        vector<int> pse=findPSE(heights);
        vector<int> nse=findNSE(heights);
        int width=0,area=0,maxA=0;
        for(int i=0;i<heights.size();i++){
             width = nse[i] - pse[i] - 1 ;
             area=width*heights[i];
             maxA=max(maxA,area);
        }
        return maxA;
    }
};
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