<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) {
        int n = heights.size();
        vector<int> psm(n); // Previous smaller element index
        vector<int> nsm(n); // Next smaller element index
        
        // Compute psm (Previous Smaller Element)
        for (int i = 0; i < n; i++) {
            int val = i - 1;
            while (val != -1 && heights[val] >= heights[i]) {
                val = psm[val];
            }
            psm[i] = val;
        }

        // Compute nsm (Next Smaller Element)
        for (int i = n - 1; i >= 0; i--) {
            int val = i + 1;
            while (val != n && heights[val] >= heights[i]) {
                val = nsm[val];
            }
            nsm[i] = val;
        }

        // Calculate the maximum area
        long long area = 0;
        for (int i = 0; i < n; i++) {
            long long height = heights[i];
            long long width = nsm[i] - psm[i] - 1;
            area = max(area, height * width);
        }

        return area;
    }
};

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