<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:
    void findnextsmall(vector<int> &heights, vector<int>&nextsmall, stack<int>&s2)
    {
            nextsmall[heights.size()-1]=heights.size();
            s2.push(heights.size()-1);

            for(int i=heights.size()-2; i>=0; i--)
            {
                 if(heights[s2.top()]<heights[i])
                 {
                    nextsmall[i]=s2.top();
                    s2.push(i);
                 }
                 else {
                     while(!s2.empty() && heights[s2.top()] >= heights[i])
                     s2.pop();

                     if(s2.empty())
                     nextsmall[i]=heights.size();
                     else
                     nextsmall[i]=s2.top();

                     s2.push(i);
                 } 
            }
    }
    void findprevsmall(vector<int> &heights, vector<int>&prevsmall, stack<int>&s1)
    {
            prevsmall.push_back(-1);
            s1.push(0);

            for(int i=1; i<heights.size(); i++)
            {
                 if(heights[s1.top()]<heights[i])
                 {
                    prevsmall.push_back(s1.top());
                    s1.push(i);
                 }
                 else {
                     while(!s1.empty() && heights[s1.top()] >= heights[i])
                     s1.pop();

                     if(s1.empty())
                     prevsmall.push_back(-1);
                     else
                     prevsmall.push_back(s1.top());

                     s1.push(i);
                 } 
            }
    }
    int largestRectangleArea(vector<int>& heights)
    {
        vector<int> nextsmall(heights.size()), prevsmall;

        if(heights.size()==0)
        return 0;

        if(heights.size()==1)
        return heights[0];

        stack<int> s1,s2;

        findprevsmall(heights,prevsmall,s1);
        findnextsmall(heights,nextsmall,s2);

        int maximum=0;
        for(int i=0; i<nextsmall.size(); i++)
        {
          //  cout<<nextsmall[i]<<" ";
            int area = heights[i] * (nextsmall[i]-prevsmall[i]-1);
            maximum = max(maximum,area);
        }

        return maximum;

    }
};
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