<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> index;
        vector<int> right(heights.size(), 0);
        vector<int> left (heights.size(), 0);
        int maxarea = 0;
        for(int i = 0; i < heights.size(); i++){
            while(!index.empty() && heights[index.top()] > heights[i]){
                int current = i - index.top();         
                right[index.top()] = current;
                index.pop();
            }
            index.push(i);
        }
        while(!index.empty()){
            right[index.top()] = heights.size() - index.top();
            index.pop();
        }

        stack<int> leftindex;
        for(int i = 0; i < heights.size(); i++){
            while(!leftindex.empty() && heights[leftindex.top()] >= heights[i]){
                leftindex.pop();
                if(leftindex.empty()){
                    left[i] = i;
                }
                else{
                    left[i] = i - leftindex.top() - 1;
                }
            }
            leftindex.push(i);
        }

        for(int i = 0; i < heights.size(); i++){
            maxarea = max(maxarea, (right[i] + left[i]) * heights[i]);
        }
        return maxarea;
    }
};
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