<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>& heights) {
    //     vector<int>& a = heights;
    //     int n = heights.size();
    //     int NSN[n], PSN[n];
    //     fill(NSN, NSN + n, n);
    //     fill(PSN, PSN + n, -1);
    //     // vector<int> NSN(n,n);
    //     // vector<int> PSN(n,-1);
    //     stack<int> s;

    //     for (int i = 0; i < n; i++)
    //     {
    //         while (!s.empty() && a[i] < a[s.top()])
    //         {
    //             NSN[s.top()] = i;
    //             s.pop();
    //         }
    //         if (!s.empty())
    //             PSN[i] = s.top();
    //         s.push(i);
    //     }

    //     int max_area = 0;
    //     for (int i = 0; i < n; i++)
    //     {
    //         int area = (NSN[i] - PSN[i] - 1) * a[i];
    //         max_area = max(max_area, area);
    //     }

    //     return max_area;

    // }


        vector<int>& a = heights;
        int n = heights.size();
        int PSE[n], NSE[n];
        fill(PSE, PSE+n, -1);
        fill(NSE, NSE+n, n);
        stack<int> s;

        for (int i = 0; i < n; i++){
            while(!s.empty() && a[i] < a[s.top()])
            {
                NSE[s.top()] = i;
                s.pop();
            }
            if (!s.empty())
            {
                PSE[i] = s.top();
            }
            s.push(i);
        }

        int max_area = 0;
        for (int i = 0; i < n; i++)
        {
            int area = (NSE[i] - PSE[i] - 1) * a[i];
            max_area = max(max_area, area);
        }

        return max_area;
    }
};
80516