<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> fbefore(vector<int> heights) {
        int n = heights.size();
        stack<pair<int, int>> s;
        s.push(make_pair(heights[0],0));
        vector<int> v(n);
        v[0] = -1;
        for (int i = 1; i < n; i++) {
            if (s.top().first < heights[i]) {
                int topElVal = s.top().first;
                int topElPos = s.top().second;
                s.push(make_pair(heights[i], i));
                v[i] = topElPos;
            } 
            else {
                while (!(s.empty()) && (s.top().first >= heights[i])) {
                    s.pop();
                }
                if (s.empty()) {
                    v[i] = -1;
                } else {
                    int topElVal = s.top().first;
                    int topElPos = s.top().second;
                    v[i] = topElPos;
                }
                s.push(make_pair(heights[i], i));
            }
        }
        return v;
    }

    vector<int> fafter(vector<int> heights) {
        int n = heights.size();
        stack<pair<int, int>> s;
        s.push(make_pair(heights[n-1],n-1));
        vector<int> v(n);
        v[n-1] = n;
        for (int i = n-2; i >=0; i--) {
            if (s.top().first <= heights[i]) {
                int topElVal = s.top().first;
                int topElPos = s.top().second;
                s.push(make_pair(heights[i], i));
                v[i] = topElPos;
            } 
            else {
                while (!(s.empty()) && (s.top().first > heights[i])) {
                    s.pop();
                }
                if (s.empty()) {
                    v[i] = n;
                } else {
                    int topElVal = s.top().first;
                    int topElPos = s.top().second;
                    v[i] = topElPos;
                }
                s.push(make_pair(heights[i], i));
            }
        }
        return v;
    }

    int largestRectangleArea(vector<int>& heights) {
        int n = heights.size();
        vector<int> vbefore = fbefore(heights);
        vector<int> vafter = fafter(heights);
        // for (int i = 0; i < n; i++) {
        //     cout << i-vbefore[i] << " ";
        // }
        // cout<<endl;
        // for (int i = 0; i < n; i++) {
        //     cout << vafter[i]-i << " ";
        // }
        int out = 0;
        for(int i=0;i<n;i++)
        {   
            int left=(i-vbefore[i]);
            int right=(vafter[i]-i);
            int total_length=left+right-1;
            out=max(out,(total_length*heights[i]));
        }
        return out;
    }
};
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