<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 {
private:
    vector<int> nextSmallerElement(vector<int> arr, int n) {
        stack<int> s;
        s.push(-1);
        vector<int> ans(n);

        for(int i=n-1; i>=0 ; i--) {
            int curr = arr[i];
            while(s.top() != -1 && arr[s.top()] >= curr)
            {
                s.pop();
            }
            ans[i] = s.top();
            s.push(i);
        }
        return ans;
    }
    
    vector<int> prevSmallerElement(vector<int> arr, int n) {
        stack<int> s;
        s.push(-1);
        vector<int> ans(n);

        for(int i=0; i<n; i++) {
            int curr = arr[i];
            while(s.top() != -1 && arr[s.top()] >= curr)
            {
                s.pop();
            }
            ans[i] = s.top();
            s.push(i);
        }
        return ans; 
    }
    
public:
    int largestRectangleArea(vector<int>& heights) {
        int n= heights.size();
        
        vector<int> next(n);
        next = nextSmallerElement(heights, n);
            
        vector<int> prev(n);
        prev = prevSmallerElement(heights, n);
        
        int area = INT_MIN;
        for(int i=0; i<n; i++) {
            int l = heights[i];
            
            if(next[i] == -1) {
                next[i] = n;
            }
             int b = next[i] - prev[i] - 1;
            int newArea = l*b;
            area = max(area, newArea);
        }
        return area;
    }
};
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