<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 ans = 0;
        int r[100005],l[100005];
        priority_queue<pair<int,int>> pq;
        for(int i = 0; i < heights.size(); i++){
            if(pq.empty()){
                pq.push(make_pair(heights[i],i));
            }
            else{
                while(!pq.empty() && pq.top().first > heights[i] ){
                    r[pq.top().second] = i - 1;
                    pq.pop(); 
                }
                pq.push(make_pair(heights[i],i));
            }
        }
         while(!pq.empty()){
            r[pq.top().second] = heights.size()-1;
            pq.pop(); 
        }

        for(int i = heights.size()-1; i >= 0; i--){
            if(pq.empty()){
                pq.push(make_pair(heights[i],i));
            }
            else{
                while(!pq.empty() && pq.top().first > heights[i] ){
                    l[pq.top().second] = i + 1;
                    pq.pop(); 
                }
                pq.push(make_pair(heights[i],i));
            }
        }
         while(!pq.empty()){
            l[pq.top().second] = 0;
            pq.pop(); 
        }
        // for(int i = 0; i < heights.size(); i++){
        //     printf("%i %i %i ",heights[i],l[i], r[i]);
        // }
        for(int i = 0; i < heights.size(); i++){
            if(heights[i]*(r[i]-l[i] + 1) > ans){
                printf("%i %i %i\n",i,l[i],r[i]);
                ans = heights[i]*(r[i] - l[i] + 1);
            }
        }
        return ans;
    }
};
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