<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) {

        int n = heights.size();

        vector<int> width(n, 1);

        stack<pair<int,int>> q;
         
        int i;
        for(i = 0; i<n; i++){
            while(!q.empty() && q.top().first > heights[i]) {
                pair<int,int> front_ele = q.top();
                width[front_ele.second] += (i - 1 - front_ele.second);
                q.pop();
            }
            q.push({heights[i], i});
        }
        while(!q.empty()){
            pair<int,int> front_ele = q.top();
            width[front_ele.second] += (i - 1 - front_ele.second);
            q.pop();
        }

        for(i = n-1; i>=0; i--){
            while(!q.empty() && q.top().first > heights[i]) {
                pair<int,int> front_ele = q.top();
                width[front_ele.second] += (front_ele.second -1 -i);
                q.pop();
            }
            q.push({heights[i], i});
        }
        while(!q.empty()){
            pair<int,int> front_ele = q.top();
            width[front_ele.second] += (front_ele.second -1 -i);
            q.pop();
        }

        int area = 0;
        for(int i = 0; i<n; i++){
            area = max(area, heights[i]*width[i]);
       }
        return area;      
    }
};
89003