<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> leftsmall(vector<int> h) {
        stack<int> s;
        s.push(-1);
        vector<int> ans;
        for (int i = 0; i < h.size(); i++) {
            while (s.top() != -1 && h[i] <= h[s.top()]) {
                s.pop();
            }
            ans.push_back(s.top());
            s.push(i);
        }
        return ans;
    }
    vector<int> rightsmall(vector<int> h) {
        stack<int> s;
        s.push(-1);
        vector<int> ans(h.size());
        for (int i = h.size() - 1; i >= 0; i--) {
            while (s.top() != -1 && h[i] <= h[s.top()]) {
                s.pop();
            }
            if(s.top()==-1)
            {
                ans[i]=h.size();
            }
            else
            {
                ans[i] = (s.top());
            }
            
            s.push(i);
        }
        return ans;
    }
    int largestRectangleArea(vector<int>& heights) {
        vector<int> left;
        vector<int> right;
        left = leftsmall(heights);
        right = rightsmall(heights);
    
        int ans;
        int ansmax = INT_MIN;
        for (int i = 0; i < heights.size(); i++) {
             
                ans=(right[i]-left[i]-1)*heights[i];
                ansmax = max(ans, ansmax);
        
        }
        return ansmax;
    }
};
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