<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) {
        heights.insert(heights.begin(),-1);
        heights.push_back(-1);
        int n = heights.size();

        vector<int> next(n),prev(n);

        prev[0] = 0;
        for(int i = 1;i<heights.size();i++){
            int p = i-1;
            while(p>0 && heights[p] >= heights[i]) p = prev[p];
            prev[i] = p;
        }

        next[n-1] = n-1;
        for(int i = n-2;i>0;i--){
            int p = i+1;
            while(p<n-1 && heights[p]>=heights[i]) p = next[p];

            next[i] = p;
        }

        int ans = 0;
        for(int i = 1;i<heights.size()-1;i++){
            ans = max(ans,(next[i] - prev[i]-1)*heights[i]);
        }
        return ans;
    }
};

/*
0,5,4,3,2,1

0,1,2,3,3,4,5



5,8,9,8,5
Next smaller element position -> 6

(next smaller - i)*height[i]

previous smaller element -> using stacks

-1,2,1,5,6,2,3,-1

Next smaller element -> -1,2,5

-1
*/
83183