<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) {
        stack<int> left;
        stack<int> right;

        int sizes[heights.size()];

        int maxArea = 0;

        for (int i = 0; i < heights.size(); ++i) {
            while (!left.empty() && heights[left.top()] > heights[i]) {
                int j = left.top(); left.pop();
                int area = (i - j) * heights[j];

                sizes[j] = area;

                if (area > maxArea) 
                    maxArea = area; 
            }

            left.push(i);
        }

        while (!left.empty()) {
            int j = left.top(); left.pop();
            int area = (heights.size() - j) * heights[j];

            sizes[j] = area;

            if (area > maxArea) 
                maxArea = area; 
        }

        for (int i = heights.size() - 1; i > -1; --i) {
            while (!right.empty() && heights[right.top()] > heights[i]) {
                int j = right.top(); right.pop();
                int area = (j - i) * heights[j];

                area = sizes[j] + area - heights[j];

                if (area > maxArea) 
                    maxArea = area; 
            }

            right.push(i);
        }

        while (!right.empty()) {
            int j = right.top(); right.pop();
            int area = j * heights[j];

            area = sizes[j] + area;

            if (area > maxArea) 
                maxArea = area; 
        }

        return maxArea;
    }
};
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