<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> findNSE(vector<int>&arr){
        int n = arr.size();
        stack<int> stk;
        vector<int> ans(n);
        for(int i=n-1; i>=0; i--){
            while(!stk.empty() && arr[stk.top()] >= arr[i]) stk.pop();
            if(stk.empty()) ans[i] = n;
            else ans[i] = stk.top();
            stk.push(i);
        }
        return ans;
    }
    vector<int> findPSE(vector<int>&arr){
        int n = arr.size();
        stack<int> stk;
        vector<int> ans(n);
        for(int i=0; i<n; i++){
            while(!stk.empty() && arr[stk.top()] >= arr[i]) stk.pop();
            if(stk.empty()) ans[i] = -1;
            else ans[i] = stk.top();
            stk.push(i);
        }
        return ans;
    }
    int largestRectangleArea(vector<int>& arr) {
        int n = arr.size();
        stack<int> stk;
        vector<int> nse = findNSE(arr);
        vector<int> pse = findPSE(arr);
        int ans = 0;
        for(int i=0; i<n; i++){
            int area = arr[i]*(nse[i]-1-pse[i]);
            ans = max(ans, area);
        }
        return ans;
    }
};
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